research paper on maths topics

251+ Math Research Topics [2024 Updated]

$Math research topics$

Mathematics, often dubbed as the language of the universe, holds immense significance in shaping our understanding of the world around us. It’s not just about crunching numbers or solving equations; it’s about unraveling mysteries, making predictions, and creating innovative solutions to complex problems. In this blog, we embark on a journey into the realm of math research topics, exploring various branches of mathematics and their real-world applications.

How Do You Write A Math Research Topic?

Writing a math research topic involves several steps to ensure clarity, relevance, and feasibility. Here’s a guide to help you craft a compelling math research topic:

Identify Your Interests: Start by exploring areas of mathematics that interest you. Whether it’s pure mathematics, applied mathematics, or interdisciplinary topics, choose a field that aligns with your passion and expertise.
Narrow Down Your Focus: Mathematics is a broad field, so it’s essential to narrow down your focus to a specific area or problem. Consider the scope of your research and choose a topic that is manageable within your resources and time frame.
Review Existing Literature: Conduct a thorough literature review to understand the current state of research in your chosen area. Identify gaps, controversies, or unanswered questions that could form the basis of your research topic.
Formulate a Research Question: Based on your exploration and literature review, formulate a clear and concise research question. Your research question should be specific, measurable, achievable, relevant, and time-bound (SMART).
Consider Feasibility: Assess the feasibility of your research topic in terms of available resources, data availability, and research methodologies. Ensure that your topic is realistic and achievable within the constraints of your project.
Consult with Experts: Seek feedback from mentors, advisors, or experts in the field to validate your research topic and refine your ideas. Their insights can help you identify potential challenges and opportunities for improvement.
Refine and Iterate: Refine your research topic based on feedback and further reflection. Iterate on your ideas to ensure clarity, coherence, and relevance to the broader context of mathematics research.
Craft a Title: Once you have finalized your research topic, craft a compelling title that succinctly summarizes the essence of your research. Your title should be descriptive, engaging, and reflective of the key themes of your study.
Write a Research Proposal: Develop a comprehensive research proposal outlining the background, objectives, methodology, and expected outcomes of your research. Your research proposal should provide a clear roadmap for your study and justify the significance of your research topic.

By following these steps, you can effectively write a math research topic that is well-defined, relevant, and poised to make a meaningful contribution to the field of mathematics.

251+ Math Research Topics: Beginners To Advanced

Prime Number Distribution in Arithmetic Progressions
Diophantine Equations and their Solutions
Applications of Modular Arithmetic in Cryptography
The Riemann Hypothesis and its Implications
Graph Theory: Exploring Connectivity and Coloring Problems
Knot Theory: Unraveling the Mathematics of Knots and Links
Fractal Geometry: Understanding Self-Similarity and Dimensionality
Differential Equations: Modeling Physical Phenomena and Dynamical Systems
Chaos Theory: Investigating Deterministic Chaos and Strange Attractors
Combinatorial Optimization: Algorithms for Solving Optimization Problems
Computational Complexity: Analyzing the Complexity of Algorithms
Game Theory: Mathematical Models of Strategic Interactions
Number Theory: Exploring Properties of Integers and Primes
Algebraic Topology: Studying Topological Invariants and Homotopy Theory
Analytic Number Theory: Investigating Properties of Prime Numbers
Algebraic Geometry: Geometry Arising from Algebraic Equations
Galois Theory: Understanding Field Extensions and Solvability of Equations
Representation Theory: Studying Symmetry in Linear Spaces
Harmonic Analysis: Analyzing Functions on Groups and Manifolds
Mathematical Logic: Foundations of Mathematics and Formal Systems
Set Theory: Exploring Infinite Sets and Cardinal Numbers
Real Analysis: Rigorous Study of Real Numbers and Functions
Complex Analysis: Analytic Functions and Complex Integration
Measure Theory: Foundations of Lebesgue Integration and Probability
Topological Groups: Investigating Topological Structures on Groups
Lie Groups and Lie Algebras: Geometry of Continuous Symmetry
Differential Geometry: Curvature and Topology of Smooth Manifolds
Algebraic Combinatorics: Enumerative and Algebraic Aspects of Combinatorics
Ramsey Theory: Investigating Structure in Large Discrete Structures
Analytic Geometry: Studying Geometry Using Analytic Methods
Hyperbolic Geometry: Non-Euclidean Geometry of Curved Spaces
Nonlinear Dynamics: Chaos, Bifurcations, and Strange Attractors
Homological Algebra: Studying Homology and Cohomology of Algebraic Structures
Topological Vector Spaces: Vector Spaces with Topological Structure
Representation Theory of Finite Groups: Decomposition of Group Representations
Category Theory: Abstract Structures and Universal Properties
Operator Theory: Spectral Theory and Functional Analysis of Operators
Algebraic Number Theory: Study of Algebraic Structures in Number Fields
Cryptanalysis: Breaking Cryptographic Systems Using Mathematical Methods
Discrete Mathematics: Combinatorics, Graph Theory, and Number Theory
Mathematical Biology: Modeling Biological Systems Using Mathematical Tools
Population Dynamics: Mathematical Models of Population Growth and Interaction
Epidemiology: Mathematical Modeling of Disease Spread and Control
Mathematical Ecology: Dynamics of Ecological Systems and Food Webs
Evolutionary Game Theory: Evolutionary Dynamics and Strategic Behavior
Mathematical Neuroscience: Modeling Brain Dynamics and Neural Networks
Mathematical Physics: Mathematical Models in Physical Sciences
Quantum Mechanics: Foundations and Applications of Quantum Theory
Statistical Mechanics: Statistical Methods in Physics and Thermodynamics
Fluid Dynamics: Modeling Flow of Fluids Using Partial Differential Equations
Mathematical Finance: Stochastic Models in Finance and Risk Management
Option Pricing Models: Black-Scholes Model and Beyond
Portfolio Optimization: Maximizing Returns and Minimizing Risk
Stochastic Calculus: Calculus of Stochastic Processes and Itô Calculus
Financial Time Series Analysis: Modeling and Forecasting Financial Data
Operations Research: Optimization of Decision-Making Processes
Linear Programming: Optimization Problems with Linear Constraints
Integer Programming: Optimization Problems with Integer Solutions
Network Flow Optimization: Modeling and Solving Flow Network Problems
Combinatorial Game Theory: Analysis of Games with Perfect Information
Algorithmic Game Theory: Computational Aspects of Game-Theoretic Problems
Fair Division: Methods for Fairly Allocating Resources Among Parties
Auction Theory: Modeling Auction Mechanisms and Bidding Strategies
Voting Theory: Mathematical Models of Voting Systems and Social Choice
Social Network Analysis: Mathematical Analysis of Social Networks
Algorithm Analysis: Complexity Analysis of Algorithms and Data Structures
Machine Learning: Statistical Learning Algorithms and Data Mining
Deep Learning: Neural Network Models with Multiple Layers
Reinforcement Learning: Learning by Interaction and Feedback
Natural Language Processing: Statistical and Computational Analysis of Language
Computer Vision: Mathematical Models for Image Analysis and Recognition
Computational Geometry: Algorithms for Geometric Problems
Symbolic Computation: Manipulation of Mathematical Expressions
Numerical Analysis: Algorithms for Solving Numerical Problems
Finite Element Method: Numerical Solution of Partial Differential Equations
Monte Carlo Methods: Statistical Simulation Techniques
High-Performance Computing: Parallel and Distributed Computing Techniques
Quantum Computing: Quantum Algorithms and Quantum Information Theory
Quantum Information Theory: Study of Quantum Communication and Computation
Quantum Error Correction: Methods for Protecting Quantum Information from Errors
Topological Quantum Computing: Using Topological Properties for Quantum Computation
Quantum Algorithms: Efficient Algorithms for Quantum Computers
Quantum Cryptography: Secure Communication Using Quantum Key Distribution
Topological Data Analysis: Analyzing Shape and Structure of Data Sets
Persistent Homology: Topological Invariants for Data Analysis
Mapper Algorithm: Method for Visualization and Analysis of High-Dimensional Data
Algebraic Statistics: Statistical Methods Based on Algebraic Geometry
Tropical Geometry: Geometric Methods for Studying Polynomial Equations
Model Theory: Study of Mathematical Structures and Their Interpretations
Descriptive Set Theory: Study of Borel and Analytic Sets
Ergodic Theory: Study of Measure-Preserving Transformations
Combinatorial Number Theory: Intersection of Combinatorics and Number Theory
Additive Combinatorics: Study of Additive Properties of Sets
Arithmetic Geometry: Interplay Between Number Theory and Algebraic Geometry
Proof Theory: Study of Formal Proofs and Logical Inference
Reverse Mathematics: Study of Logical Strength of Mathematical Theorems
Nonstandard Analysis: Alternative Approach to Analysis Using Infinitesimals
Computable Analysis: Study of Computable Functions and Real Numbers
Graph Theory: Study of Graphs and Networks
Random Graphs: Probabilistic Models of Graphs and Connectivity
Spectral Graph Theory: Analysis of Graphs Using Eigenvalues and Eigenvectors
Algebraic Graph Theory: Study of Algebraic Structures in Graphs
Metric Geometry: Study of Geometric Structures Using Metrics
Geometric Measure Theory: Study of Measures on Geometric Spaces
Discrete Differential Geometry: Study of Differential Geometry on Discrete Spaces
Algebraic Coding Theory: Study of Error-Correcting Codes
Information Theory: Study of Information and Communication
Coding Theory: Study of Error-Correcting Codes
Cryptography: Study of Secure Communication and Encryption
Finite Fields: Study of Fields with Finite Number of Elements
Elliptic Curves: Study of Curves Defined by Cubic Equations
Hyperelliptic Curves: Study of Curves Defined by Higher-Degree Equations
Modular Forms: Analytic Functions with Certain Transformation Properties
L-functions: Analytic Functions Associated with Number Theory
Zeta Functions: Analytic Functions with Special Properties
Analytic Number Theory: Study of Number Theoretic Functions Using Analysis
Dirichlet Series: Analytic Functions Represented by Infinite Series
Euler Products: Product Representations of Analytic Functions
Arithmetic Dynamics: Study of Iterative Processes on Algebraic Structures
Dynamics of Rational Maps: Study of Dynamical Systems Defined by Rational Functions
Julia Sets: Fractal Sets Associated with Dynamical Systems
Mandelbrot Set: Fractal Set Associated with Iterations of Complex Quadratic Polynomials
Arithmetic Geometry: Study of Algebraic Geometry Over Number Fields
Diophantine Geometry: Study of Solutions of Diophantine Equations Using Geometry
Arithmetic of Elliptic Curves: Study of Elliptic Curves Over Number Fields
Rational Points on Curves: Study of Rational Solutions of Algebraic Equations
Galois Representations: Study of Representations of Galois Groups
Automorphic Forms: Analytic Functions with Certain Transformation Properties
L-functions: Analytic Functions Associated with Automorphic Forms
Selberg Trace Formula: Tool for Studying Spectral Theory and Automorphic Forms
Langlands Program: Program to Unify Number Theory and Representation Theory
Hodge Theory: Study of Harmonic Forms on Complex Manifolds
Riemann Surfaces: One-dimensional Complex Manifolds
Shimura Varieties: Algebraic Varieties Associated with Automorphic Forms
Modular Curves: Algebraic Curves Associated with Modular Forms
Hyperbolic Manifolds: Manifolds with Constant Negative Curvature
Teichmüller Theory: Study of Moduli Spaces of Riemann Surfaces
Mirror Symmetry: Duality Between Calabi-Yau Manifolds
Kähler Geometry: Study of Hermitian Manifolds with Special Symmetries
Algebraic Groups: Linear Algebraic Groups and Their Representations
Lie Algebras: Study of Algebraic Structures Arising from Lie Groups
Representation Theory of Lie Algebras: Study of Representations of Lie Algebras
Quantum Groups: Deformation of Lie Groups and Lie Algebras
Algebraic Topology: Study of Topological Spaces Using Algebraic Methods
Homotopy Theory: Study of Continuous Deformations of Spaces
Homology Theory: Study of Algebraic Invariants of Topological Spaces
Cohomology Theory: Study of Dual Concepts to Homology Theory
Singular Homology: Homology Theory Defined Using Simplicial Complexes
Sheaf Theory: Study of Sheaves and Their Cohomology
Differential Forms: Study of Multilinear Differential Forms
De Rham Cohomology: Cohomology Theory Defined Using Differential Forms
Morse Theory: Study of Critical Points of Smooth Functions
Symplectic Geometry: Study of Symplectic Manifolds and Their Geometry
Floer Homology: Study of Symplectic Manifolds Using Pseudoholomorphic Curves
Gromov-Witten Invariants: Invariants of Symplectic Manifolds Associated with Pseudoholomorphic Curves
Mirror Symmetry: Duality Between Symplectic and Complex Geometry
Calabi-Yau Manifolds: Ricci-Flat Complex Manifolds
Moduli Spaces: Spaces Parameterizing Geometric Objects
Donaldson-Thomas Invariants: Invariants Counting Sheaves on Calabi-Yau Manifolds
Algebraic K-Theory: Study of Algebraic Invariants of Rings and Modules
Homological Algebra: Study of Homology and Cohomology of Algebraic Structures
Derived Categories: Categories Arising from Homological Algebra
Stable Homotopy Theory: Homotopy Theory with Stable Homotopy Groups
Model Categories: Categories with Certain Homotopical Properties
Higher Category Theory: Study of Higher Categories and Homotopy Theory
Higher Topos Theory: Study of Higher Categorical Structures
Higher Algebra: Study of Higher Categorical Structures in Algebra
Higher Algebraic Geometry: Study of Higher Categorical Structures in Algebraic Geometry
Higher Representation Theory: Study of Higher Categorical Structures in Representation Theory
Higher Category Theory: Study of Higher Categorical Structures
Homotopical Algebra: Study of Algebraic Structures in Homotopy Theory
Homotopical Groups: Study of Groups with Homotopical Structure
Homotopical Categories: Study of Categories with Homotopical Structure
Homotopy Groups: Algebraic Invariants of Topological Spaces
Homotopy Type Theory: Study of Foundations of Mathematics Using Homotopy Theory

In conclusion, the world of mathematics is vast and multifaceted, offering endless opportunities for exploration and discovery. Whether delving into the abstract realms of pure mathematics or applying mathematical principles to solve real-world problems, mathematicians play a vital role in advancing human knowledge and shaping the future of our world.

By embracing diverse math research topics and interdisciplinary collaborations, we can unlock new possibilities and harness the power of mathematics to address the challenges of today and tomorrow. So, let’s embark on this journey together as we unravel the mysteries of numbers and explore the boundless horizons of mathematical inquiry.

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181 Mathematics Research Topics From PhD Experts

$math research topics$

If you are reading this blog post, it means you are looking for some exceptional math research topics. You want them to be original, unique even. If you manage to find topics like this, you can be sure your professor will give you a top grade (if you write a decent paper, that is). The good news is that you have arrived at just the right place – at the right time. We have just finished updating our list of topics, so you will find plenty of original ideas right on this page. All our topics are 100 percent free to use as you see fit. You can reword them and you don’t need to give us any credit.

And remember: if you need assistance from a professional, don’t hesitate to reach out to us. We are not just the best place for math research topics for high school students; we are also the number one choice for students looking for top-notch research paper writing services.

Our Newest Research Topics in Math

We know you probably want the best and most recent research topics in math. You want your paper to stand out from all the rest. After all, this is the best way to get some bonus points from your professor. On top of this, finding some great topics for your next paper makes it easier for you to write the essay. As long as you know at least something about the topic, you’ll find that writing a great paper or buy phd thesis isn’t as difficult as you previously thought.

So, without further ado, here are the 181 brand new topics for your next math research paper:

Cool Math Topics to Research

Are you looking for some cool math topics to research? We have a list of original topics for your right here. Pick the one you like and start writing now:

Roll two dice and calculate a probability
Discuss ancient Greek mathematics
Is math really important in school?
Discuss the binomial theorem
The math behind encryption
Game theory and its real-life applications
Analyze the Bernoulli scheme
What are holomorphic functions and how do they work?
Describe big numbers
Solving the Tower of Hanoi problem

Undergraduate Math Research Topics

If you are an undergraduate looking for some research topics for your next math paper, you will surely appreciate our list of interesting undergraduate math research topics:

Methods to count discrete objects
The origins of Greek symbols in mathematics
Methods to solve simultaneous equations
Real-world applications of the theorem of Pythagoras
Discuss the limits of diffusion
Use math to analyze the abortion data in the UK over the last 100 years
Discuss the Knot theory
Analyze predictive models (take meteorology as an example)
In-depth analysis of the Monte Carlo methods for inverse problems
Squares vs. rectangles (compare and contrast)

Number Theory Topics to Research

Interested in writing about number theory? It is not an easy subject to discuss, we know. However, we are sure you will appreciate these number theory topics:

Discuss the greatest common divisor
Explain the extended Euclidean algorithm
What are RSA numbers?
Discuss Bézout’s lemma
In-depth analysis of the square-free polynomial
Discuss the Stern-Brocot tree
Analyze Fermat’s little theorem
What is a discrete logarithm?
Gauss’s lemma in number theory
Analyze the Pentagonal number theorem

Math Research Topics for High School

High school students shouldn’t be too worried about their math papers because we have some unique, and quite interesting, math research topics for high school right here:

Discuss Brun’s constant
An in-depth look at the Brahmagupta–Fibonacci identity
What is derivative algebra?
Describe the Symmetric Boolean function
Discuss orders of approximation in limits
Solving Regiomontanus’ angle maximization problem
What is a Quadratic integral?
Define and describe complementary angles
Analyze the incircle and excircles of a triangle
Analyze the Bolyai–Gerwien theorem in geometry
Math in our everyday life

Complex Math Topics

If you want to give some complex math topics a try, we have the best examples below. Remember, these topics should only be attempted by students who are proficient in mathematics:

Mathematics and its appliance in Artificial Intelligence
Try to solve an unsolved problem in math
Discuss Kolmogorov’s zero-one law
What is a discrete random variable?
Analyze the Hewitt–Savage zero-one law
What is a transferable belief model?
Discuss 3 major mathematical theorems
Describe and analyze the Dempster-Shafer theory
An in-depth analysis of a continuous stochastic process
Identify and analyze Gauss-Markov processes

Easy Math Research Paper Topics

Perhaps you don’t want to spend too much time working on your next research paper. Who can blame you? Check out these easy math research paper topics:

Define the hyperbola
Do we need to use a calculator during math class?
The binomial theorem and its real-world applications
What is a parabola in geometry?
How do you calculate the slope of a curve?
Define the Jacobian matrix
Solving matrix problems effectively
Why do we need differential equations?
Should math be mandatory in all schools?
What is a Hessian matrix?

Logic Topics to Research

We have some interesting logical topics for research papers. These are perfect for students interested in writing about math logic. Pick one right now:

Discuss the reductio ad absurdum approach
Discuss Boolean algebra
What is consistency proof?
Analyze Trakhtenbrot’s theorem (the finite model theory)
Discuss the Gödel completeness theorem
An in-depth analysis of Morley’s categoricity theorem
How does the Back-and-forth method work?
Discuss the Ehrenfeucht–Fraïssé game technique
Discuss Aleph numbers (Aleph-null and Aleph-one)
Solving the Suslin problem

Algebra Topics for a Research Paper

Would you like to write about an algebra topic? No problem, our seasoned writers have compiled a list of the best algebra topics for a research paper:

Discuss the differential equation
Analyze the Jacobson density theorem
The 4 properties of a binary operation in algebra
Analyze the unary operator in depth
Analyze the Abel–Ruffini theorem
Epimorphisms vs. monomorphisms: compare and contrast
Discuss the Morita duality in algebraic structures
Idempotent vs. nilpotent in Ring theory
Discuss the Artin-Wedderburn theorem
What is a commutative ring in algebra?
Analyze and describe the Noetherian ring

Math Education Research Topics

There is nothing wrong with writing about math education, especially if your professor did not give you writing prompts. Here are some very nice math education research topics:

What are the goals a mathematics professor should have?
What is math anxiety in the classroom?
Teaching math in UK schools: the difficulties
Computer programming or math in high school?
Is math education in Europe at a high enough level?
Common Core Standards and their effects on math education
Culture and math education in Africa
What is dyscalculia and how does it manifest itself?
When was algebra first thought in schools?
Math education in the United States versus the United Kingdom

Computability Theory Topics to Research

Writing about computability theory can be a very interesting adventure. Give it a try! Here are some of our most interesting computability theory topics to research:

What is a multiplication table?
Analyze the Scholz conjecture
Explain exponentiating by squaring
Analyze the Myhill-Nerode theorem
What is a tree automaton?
Compare and contrast the Pushdown automaton and the Büchi automaton
Discuss the Markov algorithm
What is a Turing machine?
Analyze the post correspondence problem
Discuss the linear speedup theorem
Discuss the Boolean satisfiability problem

Interesting Math Research Topics

We know you want topics that are interesting and relatively easy to write about. This is why we have a separate list of our most interesting math research topics:

What is two-element Boolean algebra?
The life of Gauss
The life of Isaac Newton
What is an orthodiagonal quadrilateral?
Tessellation in Euclidean plane geometry
Describe a hyperboloid in 3D geometry
What is a sphericon?
Discuss the peculiarities of Borel’s paradox
Analyze the De Finetti theorem in statistics
What are Martingales?
The basics of stochastic calculus

Applied Math Research Topics

Interested in writing about applied mathematics? Our team managed to create a list of awesome applied math research topics from scratch for you:

Discuss Newton’s laws of motion
Analyze the perpendicular axes rule
How is a Galilean transformation done?
The conservation of energy and its applications
Discuss Liouville’s theorem in Hamiltonian mechanics
Analyze the quantum field theory
Discuss the main components of the Lorentz symmetry
An in-depth look at the uncertainty principle

Geometry Topics for a Research Paper

Geometry can be a very captivating subject, especially when you know plenty about it. Check out our list of geometry topics for a research paper and pick the best one today:

Most useful trigonometry functions in math
The life of Archimedes and his achievements
Trigonometry in computer graphics
Using Vincenty’s formulae in geodesy
Define and describe the Heronian tetrahedron
The math behind the parabolic microphone
Discuss the Japanese theorem for concyclic polygons
Analyze Euler’s theorem in geometry

Math Research Topics for Middle School

Yes, even middle school children can write about mathematics. We have some original math research topics for middle school right here:

Finding critical points in a graph
The basics of calculus
What makes a graph ultrahomogeneous?
How do you calculate the area of different shapes?
What contributions did Euclid have to the field of mathematics?
What is Diophantine geometry?
What makes a graph regular?
Analyze a full binary tree

Math Research Topics for College Students

As you’ve probably already figured out, college students should pick topics that are a bit more complex. We have some of the best math research topics for college students right here:

What are extremal problems and how do you solve them?
Discuss an unsolvable math problem
How can supercomputers solve complex mathematical problems?
An in-depth analysis of fractals
Discuss the Boruvka’s algorithm (related to the minimum spanning tree)
Discuss the Lorentz–FitzGerald contraction hypothesis in relativity
An in-depth look at Einstein’s field equation
The math behind computer vision and object recognition

Calculus Topics for a Research Paper

Let’s face it: calculus is not a very difficult field. So, why don’t you pick one of our excellent calculus topics for a research paper and start writing your essay right away:

When do we need to apply the L’Hôpital rule?
Discuss the Leibniz integral rule
Calculus in ancient Egypt
Discuss and analyze linear approximations
The applications of calculus in real life
The many uses of Stokes’ theorem
Discuss the Borel regular measure
An in-depth analysis of Lebesgue’s monotone convergence theorem

Simple Math Research Paper Topics for High School

This is the place where you can find some pretty simple topics if you are a high school student. Check out our simple math research paper topics for high school:

The life and work of the famous Pierre de Fermat
What are limits and why are they useful in calculus?
Explain the concept of congruency
The life and work of the famous Jakob Bernoulli
Analyze the rhombicosidodecahedron and its applications
Calculus and the Egyptian pyramids
The life and work of the famous Jean d’Alembert
Discuss the hyperplane arrangement in combinatorial computational geometry
The smallest enclosing sphere method in combinatorics

Business Math Topics

If you want to surprise your professor, why don’t you write about business math? We have some exceptional topics that nobody has thought about right here:

Is paying a loan with another loan a good approach?
Discuss the major causes of a stock market crash
Best debt amortization methods in the US
How do bank loans work in the UK?
Calculating interest rates the easy way
Discuss the pros and cons of annuities
Basic business math skills everyone should possess
Business math in United States schools
Analyze the discount factor

Probability and Statistics Topics for Research

Probability and statistics are not easy fields. However, you can impress your professor with one of our unique probability and statistics topics for research:

What is the autoregressive conditional duration?
Applying the ANOVA method to ranks
Discuss the practical applications of the Bates distribution
Explain the principle of maximum entropy
Discuss Skorokhod’s representation theorem in random variables
What is the Factorial moment in the Theory of Probability?
Compare and contrast Cochran’s C test and his Q test
Analyze the De Moivre-Laplace theorem
What is a negative probability?

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Trends in mathematics education and insights from a meta-review and bibliometric analysis of review studies

Original Paper
Open access
Published: 15 May 2024

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Mustafa Cevikbas ORCID: orcid.org/0000-0002-7844-4707 1 ,
Gabriele Kaiser 2 , 3 &
Stanislaw Schukajlow 4

1 Altmetric

Review studies are vital for advancing knowledge in many scientific fields, including mathematics education, amid burgeoning publications. Based on an extensive consideration of existing review typologies, we conducted a meta-review and bibliometric analysis to provide a comprehensive overview of and deeper insights into review studies within mathematics education. After searching Web of Science, we identified 259 review studies, revealing a significant increase in such studies over the last five years. Systematic reviews were the most prevalent type, followed by meta-analyses, generic literature reviews, and scoping reviews. On average, the review studies had a sample size of 99, with the Preferred Reporting Items for Systematic Reviews and Meta-Analysis (PRISMA) guidelines commonly employed. Despite certain studies offering nuanced distinctions among review types, ambiguity persisted. Only about a quarter of the studies explicitly reported employing specific theoretical frameworks (particularly, technology, knowledge, and competence models). Co-authored publications were most common within American institutions and the leading countries are the United States, Germany, China, Australia, and England in publishing most review studies. Educational review journals, educational psychology journals, special education journals, educational technology journals, and mathematics education journals provided platforms for review studies, and prominent research topics included digital technologies, teacher education, mathematics achievement, and learning disabilities. In this study, we synthesised a range of reviews to facilitate readers’ comprehension of conceptual congruities and disparities across various review types, as well as to track current research trends. The results suggest that there is a need for discipline-specific standards and guidelines for different types of mathematics education reviews, which may lead to more high-quality review studies to enhance progress in mathematics education.

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1 Introduction

Comprehensive literature reviews serve as foundational pillars for advancing scholarly discourse, offering critical insights into existing research and shaping future inquiries across disciplines. In the realm of academic writing, spanning from journal articles to dissertations, literature reviews are highly regarded for their capacity to synthesize knowledge, identify gaps, and provide a cohesive framework for understanding complex topics (Boote & Beile, 2005 ). Moreover, reviews play a significant role in academia by setting new research agendas and informing decision-making processes in practice, policy, and society (Kunisch et al., 2023 ).

As empirical and theoretical research burgeons in diverse fields, the need for literature review studies has become even more pronounced, facilitating a deeper understanding of specific research areas or themes (Hart, 2018 ; Nane et al., 2023 ). Additional factors contributing to the popularity of review studies in recent years include the rise of specialized review journals (Kunisch et al., 2023 ), challenges associated with conducting various types of empirical studies during the prolonged COVID-19 crisis (Cevikbas & Kaiser, 2023 ), and a competitive research climate wherein factors such as impact factors and citations hold significant weight (Ketcham & Crawford, 2007 ). Review studies are particularly attractive as they often garner a substantial number of citations, thereby enhancing researchers’ visibility and scholarly impact (Grant & Booth, 2009 ; Taherdoost, 2023 ).

The importance of review studies has been duly acknowledged in mathematics education, as evidenced by the inclusion of review papers in thematically oriented special issues of journals such as ZDM– Mathematics Education (Kaiser & Schukajlow, 2024 ), which has been originally founded as review journal. Several upcoming or already published special issues of ZDM– Mathematics Education , which emphasise ‘reviews on important themes in mathematics education’, highlight the importance of review studies as valuable contributions to the field.

The proliferation of literature reviews has increased interest in developing typologies to categorise them and understand different literature review approaches (Grant & Booth, 2009 ; Paré et al., 2015 ; Schryen & Sperling, 2023 ). Despite its significance, there remains a notable lack of research aimed at comprehensively understanding review studies within the field of mathematics education from a meta-perspective. In response to this gap, we conducted a systematic meta-review with the aim of providing an overview of different types of review studies in mathematics education over the past few decades and consolidating insights from multiple high-level review studies (Becker & Oxman, 2008 ; Schryen & Sperling, 2023 ). Meta-reviews offer concise yet comprehensive synopses and curated lists of pertinent reviews, adeptly addressing the perennial challenge of balancing thorough coverage with focused specificity (Grant & Booth, 2009 ).

In addition, we applied bibliometric analysis as a valuable tool for identifying research trends, progress, reliable sources, and future directions within the field. The bibliometric analysis aids in identifying hot research topics and trends (Song et al., 2019 ), assessing progress, identifying reliable sources, recognising major contributors, and predicting future research success (Geng et al., 2017 ). Furthermore, it helps researchers to pinpoint potential topics, suitable institutions for cooperation, and potential scholars for scientific collaboration (Martínez et al., 2015 ). By combining a meta-review and bibliometric analysis, we aim to offer a comprehensive overview of and deeper insights into state-of-the-art review studies within mathematics education.

Specifically, we seek to understand how the distribution and development of literature review studies in mathematics education have evolved over the years, examining factors such as publication years, publishers, review types, sample sizes, and the use of theoretical or conceptual frameworks. Additionally, we aim to assess adherence to review study guidelines and protocols, providing insights into the rigor and quality of research methodologies employed, particularly in light of the lack of clear guidance on producing rigorous and impactful literature reviews (Kunisch et al., 2023 ).

Furthermore, we endeavour to identify authors who have made contribution to the field of mathematics education through review studies, as well as those whose work is most frequently cited. We also identify co-authorship network analysis as understanding research networks allows researchers to identify potential collaborators and build partnerships with other scholars in various countries. Collaborative research endeavours can lead to enhanced research outcomes, broader dissemination of findings, and increased opportunities for funding and professional development. It can also highlight interdisciplinary connections and collaborations within and across fields, leading to innovative approaches and solutions to complex research questions (RQs) that transcend disciplinary boundaries.

Moreover, we analysed the distribution of common keywords across review studies, identifying focal subjects and thematic areas prevalent in mathematics education research. This analysis can provide valuable insights into key topics and trends shaping the field, guiding future research directions and priorities.

Lastly, we identified the most cited review papers in mathematics education and the journals in which they have been published, recognizing seminal works and influential publications that have contributed to the advancement of the field.

Overall, in light of the preceding discourse, we addressed the following RQs to uncover the characteristics of review studies, identify research trends, and delineate future research directions in mathematics education:

How can the distribution and development of review studies in mathematics education over time be characterised according to the number of manuscripts, publishers, review types, sample sizes, the use of theoretical or conceptual frameworks, and adherence to review study guidelines and protocols?

Which authors have contributed the largest number of review studies in mathematics education, and which authors’ review papers are most frequently cited in the literature?

From which countries are the authors of the review studies in mathematics education?

Which author keywords can be identified in the review studies in mathematics education, how are these keywords distributed across the analysed review studies, and which focal topics do these keywords indicate?

What are the most cited review papers in mathematics education, and in which journals have they been published?

2 Literature review studies and review typologies– background information

In this chapter, we provide a thorough analysis of different typologies for review studies, as we seek to elucidate the primary characteristics of various review studies conducted within mathematics education (Sect. 2.1 ). This effort led to the identification of 28 review types presented in Table 1 , which were used in the current study’s literature search processes to access existing review studies and the analysis of identified studies in the field of mathematics education. Furthermore, we discuss the advancement of guidelines and protocols, highlighting their role in shaping the conduct of review studies (Sect. 2.2). Finally, we conclude the chapter by underscoring the importance and potential impact of meta-reviews and bibliometric analyses in the context of mathematics education (Sect. 2.3).

2.1 Literature review typologies

Researchers have defined and emphasized different review types with distinct features, objectives, and methodologies. To address the challenge of ambiguous review categorisations, we conducted an extensive search and analysis of the literature on Web of Science (WoS) using the search strings ‘typology of reviews’ and ‘taxonomy of reviews’ to search the titles of studies. We focused particularly on influential theoretical, conceptual, and review papers discussing the taxonomy and typology of review studies and recent advances driven by scholars across diverse fields.

2.1.1 Seminal work by Grant and Booth ( 2009 ) on the discourse of literature review typologies

The categorisation of literature reviews has been profoundly influenced by the seminal work of Grant and Booth ( 2009 ), on which typologies of literature reviews are often based. Their paper garnered significant attention, with over 10,304 citations as of 20 April 2024 according to Google Scholar. Originally in the field of health information theory and practice, these authors founded their work on earlier approaches, notably Cochrane’s ( 1979 ) approach. Grant and Booth ( 2009 ) claimed that the developed typology could standardise the diverse terminology used. They distinguished 14 review types, which we summarise below, highlighting the main scope and search methodologies (Grant & Booth, 2009 , pp. 94–95):

A critical review ‘goes beyond mere description of identified articles and includes a degree of analysis and conceptual innovation’; no formalised or systematic approach is required because the aim of such a review is ‘to identify conceptual contributions to embody existing or derive new theory’.

A generic literature review incorporates ‘published materials that provide examination of recent of current literature’; comprehensive searching may or may not be necessary.

A mapping review/systematic mapping is used to ‘categorize existing literature’ and identify gaps in the research literature. The completeness of a search is important, but no formal quality assessment is needed.

A meta-analysis is a ‘technique that statistically combines the results of quantitative studies to provide a more precise effect of the results’; a comprehensive search is conducted based on the inclusion and exclusion criteria.

A mixed-studies review/mixed-methods review incorporates ‘a combination of review approaches, for example combining quantitative with qualitative research… and requires a very sensitive search’.

An overview is a generic term describing a ‘summary of the… literature that attempts to survey the literature and describe its characteristics’; it may or may not include comprehensive searching and quality assessment.

A qualitative systematic review/qualitative evidence synthesis is a ‘method for integrating or comparing the findings from qualitative studies’, and it may involve selective sampling.

A rapid review comprises an ‘assessment of what is already known about a policy or practice issue, by using systematic review methods to search and critically appraise existing research’; a characteristic of such a review is that the ‘completeness of searching is determined by time constraints’.

A scoping review is a ‘preliminary assessment of the potential size and scope of available research literature’, with the ‘completeness of searching determined by time/scope constraints’.

A state-of-the-art review ‘tend[s] to address more current matters in contrast to other combined retrospective and current approaches’ and ‘aims for comprehensive searching of current literature’.

A systematic review ‘seeks to systematically search for, appraise and synthesise research evidence’ and should be comprehensive and based on inclusion/exclusion criteria.

A systematic search and review ‘combines [the] strengths of critical review with a comprehensive search process’, typically addressing broad questions to produce ‘best evidence synthesis’ based on ‘exhaustive, comprehensive searching’.

A systematised review ‘include[s] elements of systematic review process while stopping short of systematic review’, ‘typically conducted as postgraduate student assignment’; it ‘may or may not include comprehensive searching’.

An umbrella review ‘specifically refers to review compiling evidence from multiple reviews into one accessible and usable document’ via ‘identification of component reviews, but no search for primary studies’. ‘Primary studies’ refer to original research studies or individual studies conducted by researchers to gather data first-hand.

Booth with colleagues later expanded the typology by introducing the concept of a review family construct and amalgamating various types of reviews for further refinement, such as traditional reviews, systematic reviews, review of reviews, rapid reviews, mixed-methods reviews, and purpose-specific reviews (for details, see Sutton et al., 2019 ).

2.1.2 Further development of the review typologies

Many classifications for review studies have been developed, and in the following section, we present more recent approaches. Paré et al. ( 2015 ), in another highly cited study (2,059 Google Scholar citations as of 20 April 2024) considered seven recurrent dimensions: the goal of the review, the scope of the review questions, the search strategy, the nature of the primary sources, the explicitness of the study selection, quality appraisal, and the methods used to analyse/synthesise the findings. Based on these dimensions, they formulated nine different literature review types: narrative reviews, descriptive reviews, scoping/mapping reviews, meta-analyses, qualitative systematic reviews, umbrella reviews, critical reviews, theoretical reviews, and realist reviews.

In Paré et al.’s ( 2015 ) classification, the review categories that differ from Grant and Booth’s ( 2009 ) classification are theoretical reviews, realist reviews, narrative reviews, and descriptive reviews, which we therefore describe them briefly. A theoretical review draws on conceptual and empirical studies to develop a conceptual framework or model using structured approaches, such as taxonomies, to discover patterns or commonalities. The aim of a realist review (also called a meta-narrative review) is to formulate explanations; such reviews ‘are theory-driven interpretative reviews which were developed to inform, enhance, extend, or alternatively supplement conventional systematic reviews by making sense of heterogeneous evidence about complex interventions applied in diverse contexts in a way that informs policy decision making’ (Paré et al., 2015 , p. 188). The purpose of a narrative review is to survey the existing literature on a particular subject or topic without necessarily seeking generalisations or cumulative insights from the material reviewed (Davies, 2000 ). Typically, such reviews do not detail the underpinning review processes or involve systematic and exhaustive searches of all pertinent literature. This category resembles Grant and Booth’s ( 2009 ) description of ‘literature reviews’ and overlaps with Samnani et al.’s ( 2017 ) narrative reviews, literature reviews, and overviews, resulting in a somewhat ambiguous typology. The aim of a descriptive review is to identify patterns and trends across a set of empirical studies within a specific research field, encompassing pre-existing propositions, theories, methodological approaches, or findings. To accomplish this objective, descriptive reviews collect, structure, and analyse numerical data that reflect the frequency distribution of research elements.

MacEntee ( 2019 ), Samnani et al. ( 2017 ), Schryen et al. ( 2020 ), and Taherdoost ( 2023 ) corroborated Grant and Booth’s ( 2009 ) and Paré et al.’s ( 2015 ) classifications, identifying various common review categories (see Table 1 ). In Samnani et al.’s ( 2017 ) classification, a distinct review type based on the previously mentioned categories is meta-synthesis , the aim of which is to provide explanations for phenomena, in contrast to meta-analysis, which focuses on quantitative outcomes.

Later, Schryen and Sperling ( 2023 ) introduced a slightly revised typology of literature review studies, which they applied to a meta-review of operations research. Their study distinguished nine types of literature reviews, newly introduced categories included tutorial reviews, selective reviews, algorithmic reviews, computational reviews, and meta-reviews. The objective of a tutorial review is to offer a research-oriented summary of principles, mathematical fundamentals, and concepts, aiming to inspire and direct future research endeavours. The authors’ emphasis on foundational aspects has often provided a launching pad for research advances. A selective review typically has a limited scope because it is not based on a thorough search of all relevant literature. This type of review concentrates on specific segments of the literature, such as journals, time periods, methodologies, or issues, to delve deeper into specific questions and phenomena. An algorithmic review focuses on advances in algorithms and frameworks in the literature that address a spectrum of problems. It employs either selective or comprehensive search strategies, predominantly examining algorithm-related sources. A computational review investigates algorithms and/or parameterisations proposed in the literature, largely considering implementations and computational studies, measurement efficiency, effectiveness, and different forms of robustness. Finally, Schryen and Sperling ( 2023 ) defined a meta-review as an overview of systematic reviews or a systematic review of reviews and pointed out that a meta-review can also be called an umbrella review (which is the case by Grant and Booth), again confirming the fuzzy nature of the currently available typologies. According to Schryen and Sperling ( 2023 ), meta-reviews primarily aim to furnish descriptive overviews of literature reviews, serving as tertiary studies that integrate evidence from multiple (qualitative or quantitative) reviews into unified and user-friendly documents (Becker & Oxman, 2008 ; Paré et al., 2015 ). In contrast to the previously mentioned perspectives, Schryen and Sperling ( 2023 ) argued that meta-reviews are not limited to addressing specific research questions but can also address a wide range of enquiries.

Chigbu et al. ( 2023 , pp. 5–6) emphasised that there ‘is a continuum of literature types’ (p. 4) and distinguished twelve different types of literature reviews, six of which were not covered by the classifications provided by previously mentioned studies: integrated reviews, interpretative reviews, iterative reviews, semi-systematic reviews, and bibliometric reviews. According to their approach, an integrative review builds ‘new knowledge based on the existing body of literature following a rationalist perspective’, an interpretative review ‘interprets what other scholars have written to put into specific perspectives’, and an iterative review is an ‘algorithm-based approach performed to collate all studies in a specific field of research’. Moreover, a meta-synthesis review examines and analyses qualitative study findings and is often employed to clarify specific concepts. Additionally, a semi-systematic review analyses the data and findings of other studies to address specific research inquiries, using a partial systematic review methodology. Lastly, a bibliometric review systematically examines the literature on a specific subject or research discipline by quantitatively measuring indicators such as authors, citations, journals, countries, and years of publications.

As previously noted in this paper, this detailed description of review types is instrumental in facilitating our investigation of various review studies in the realm of mathematics education.

2.2 Advancements in guidelines and protocols for review studies

Various researchers have developed guidelines, protocols, and statements to assist authors in conducting, evaluating, and reporting their review studies. This academic endeavour has predominantly focused on enhancing the rigour and transparency of systematic reviews, meta-analyses, and, more recently, scoping reviews. For instance, the population, intervention, comparison, and outcomes (PICO) model, originally conceived to support evidence-based healthcare, serves as a cornerstone for establishing review criteria, crafting research questions and search strategies, and delineating the characteristics of included studies or meta-analyses (Richardson et al., 1995 ). In response to the observed deficiencies in reporting standards within meta-analyses, an international consortium introduced the Quality of Reporting of Meta-Analyses (QUOROM) statement in 1996, primarily to enhance the reporting quality of meta-analyses involving randomised controlled trials (Moher et al., 1999 ). Subsequently, Moher et al. ( 2009 ) updated these guidelines, which are now known as the PRISMA guidelines, and incorporated various conceptual and methodological advances in systematic reviews and meta-analyses. Additionally, Shea et al. ( 2007 ) introduced the Assessment of Multiple Systematic Reviews (AMSTAR) checklist to evaluate methodological quality and guide the conduct of systematic reviews, while Grant and Booth ( 2009 ) developed the search, appraisal, synthesis, and analysis (SALSA) framework to analyse and characterise review types. Most recently, Page et al. ( 2021 ) updated the PRISMA guidelines, providing updated reporting standards that reflect advances in methods for identifying, selecting, appraising, and synthesising studies, with the aim of promoting more transparent, complete, and accurate reporting of systematic reviews and meta-analyses. An extension of PRISMA guidelines for scoping reviews, known as PRISMA-ScR, aids readers in understanding relevant terminology, core concepts, and key items for reporting scoping reviews (Tricco et al., 2018 ). Despite the value of these efforts, further studies are warranted, particularly comprehensive guidelines for each type of review studies.

2.3 Literature reviews in mathematics education

The preceding section delineates various types of review studies, underscoring their key methodological attributes. Within the realm of mathematics education, akin to other disciplines, literature review studies, particularly systematic reviews, and meta-analyses, received considerable attention (Cevikbas et al., 2022 ; Cevikbas & Kaiser, 2023 ; Kaiser & Schukajlow, 2024 ). However, the understanding of the prevailing characteristics of review studies in mathematics education, including prevalent review types, trends, gaps, and avenues for future improvement, remains limited.

Meta-reviews can offer a promising avenue for pinpointing research gaps, evaluating evidence quality, and informing policy and intervention strategies and guiding evidence-based decision-making processes by synthesizing findings from multiple review studies (Schryen & Sperling, 2023 ). In addition to meta-reviews, the bibliometric analyses serve to ascertain the scope of prior research, discern contemporary review trends, identify literature gaps, and propose future research agendas (Chigbu et al., 2023 ). While meta-reviews provide a comprehensive assessment of the literature, bibliometric analyses aid in systematically screening literature on a specific subject, topic, or research discipline by quantitatively measuring various indicators such as authors, citations, journals, countries, and years of publication. These methodological approaches hold promise for instituting a systematic, transparent, and reproducible review process, thereby augmenting the overall quality of reviews in mathematics education. Bibliometric techniques serve as valuable tools in literature reviews, guiding researchers by pinpointing influential works and impartially mapping the research landscape prior to in-depth exploration (Zupic & Cater, 2015 ).

Despite their significance, meta-reviews and bibliometric analyses remain seldom within the domain of mathematics education, signifying a substantial gap in the literature. Our comprehensive literature review underscores an urgent need for meta-review studies encompassing literature review studies in the realm of mathematics education. Additionally, while no bibliometric analysis study specifically focusing on review studies in mathematics education was identified, several bibliometric studies in mathematics education on various topics were noted, such as mathematics anxiety (Radevic & Milovanovic, 2023 ), problem-solving (Suseelan et al., 2022 ), and teacher noticing (Wei et al., 2023 ).

Overall, there exists a compelling need for meta-reviews enriched by bibliometric analyses to explore the current state of literature review research in mathematics education, and the current study aims to address this gap in a timely manner.

3 Methodology

3.1 literature search and manuscript selection process.

In this study, following the latest PRISMA guidelines (Page et al., 2021 ), we aimed to conduct a systematic review of previous review studies in mathematics education. Specifically, we employed the meta-review (umbrella review) method supplemented by bibliometric analyses. We processed the manuscript selection under three stages: identification, screening, and included.

3.1.1 Identification

On 10 January 2024 (last access), we conducted an extensive literature search using the WoS electronic database, which includes publications in high-ranking peer-reviewed journals and is widely acknowledged as a primary source of review and bibliometric data that meet high quality standards (Korom, 2019 ). WoS facilitates effective literature searches, supports various information purposes, and aids research topic mapping, trend monitoring as well as scholarly activity analysis (Birkle et al., 2020 ).

To comprehensively identify potentially relevant review studies in mathematics education, we developed an inclusive search query targeting specific terms in the titles, abstracts, and keywords of papers. The query comprised terms that we extracted from the typologies of literature reviews described in Chap. 2, particularly the more general, commonly used types of reviews:

( TOPIC ) ((literature review*OR literature survey* OR systematic review* OR rapid review* OR scoping review* OR critical review* OR meta-analysis OR narrative review* OR umbrella review* OR meta review* OR meta-review OR bibliometric review OR bibliometric analysis OR mapping review OR mixed-methods review OR integrative review OR interpretative review OR iterative review OR meta-synthesis OR descriptive review OR theoretical review OR realist review OR selective review OR algorithmic review OR computational review)) AND ( TOPIC ) ((math* OR geometry OR algebra OR calculus OR probability OR statistics OR arithmetic).

Based on these search strings, we conducted an online search that initially yielded 63,462 records.

3.1.2 Screening

In this stage, we applied data cleaning filters based on the manuscript inclusion and exclusion criteria (see Table 2 ). First, we electronically filtered the identified records based on language, resulting in the retention of 61,787 papers published in English. Subsequently, we narrowed down the selection to 10,098 papers using the following five categories of research areas within the WoS: ‘education/educational research, psychology, social sciences other topics, mathematics, or science technology other topics’. Following this categorisation, we further refined the dataset by excluding non-review papers and accessing 3,344 records within the ‘review article’ and ‘early access’ categories of the WoS database. We categorised records lacking a final publication date that had undergone peer review and acceptance as ‘early access’. Notably, to comprehensively capture publication trends, we imposed no restrictions on the publication years of the studies. In the subsequent phase, a meticulous manual screening of the titles, abstracts, and keywords of 3,344 papers led to the identification of 357 studies in mathematics education.

3.1.3 Included

Ultimately, after an extensive review of the full-text versions of initially identified 357 papers, 259 eligible review articles remained for analysis as these papers fulfilled our criteria comprehensively (see the Appendix for the list of included studies; see Fig. 1 for the flow diagram of the entire manuscript selection process). Subsequently, as detailed below, the data analysis process commenced with the inclusion of these eligible review papers in mathematics education.

Flow diagram of the manuscript selection process

3.2 Data analysis

After incorporating 259 studies into this meta-review and bibliometric analysis, we compiled the identified records into a marked list on WoS. Subsequently, we exported the records into Excel, EndNote, and plain text file formats for analysis. The analysis consisted of content analysis and bibliometric analysis (see Fig. 2 , adapted from Wei et al., 2023 ).

For the content analysis, we meticulously organised the records using EndNote reference management software and Excel worksheets. We scrutinised the full-text versions of all included articles, coding them based on (1) publication year, (2) publisher, (3) review type, (4) number of included studies (sample size), (5) guidelines and protocols for the article selection process, and (6) the theoretical and conceptual framework of the studies.

Our coding manual, informed by prior studies (Cevikbas et al., 2022 , 2024 ), guided this process (see appendix for a sample of the coding manual). After completing the content analysis coding procedure, 20% of the papers ( n = 52) were double-coded based on the initial coding protocol. The intercoder reliability, gauged at 0.92, signifies the presence of a coding system that exhibits satisfactory reliability (Creswell, 2013 ). Any discrepancies were addressed through discussions among the coders until consensus was reached.

For the bibliometric analysis, we employed VOSviewer software (version 1.6.20), which is widely recognised and extensively used in various fields, including the educational sciences (van Eck & Waltman, 2010 ). Chigbu et al. ( 2023 ) pointed out that the WoS database plays a pivotal role in facilitating bibliometric analyses across various disciplines. These analyses help establish trends in the development and application of knowledge within specific subjects and disciplines.

In our study, the bibliometric network presented in the results chapter consists of nodes and edges, with nodes representing entities such as publications, journals, researchers, or keywords. Edges denote relationships between pairs of nodes, indicating not only the presence or absence of connections but also conveying the intensity or strength of relationships (van Eck & Waltman, 2010 ). For distance-based approaches, the positioning of nodes in a bibliometric network reflects their approximate relatedness based on proximity.

Utilising VOSviewer software, we conducted (1) co-authorship analysis (authors and countries) to elucidate collaboration patterns and contributions, (2) co-occurrence analysis (focusing Author Keywords) to scrutinise knowledge structures and the distribution and development of key research topics in mathematics education, and (3) citation analysis to delve deeper into research influences and citation networks, drawing insights from the documents and sources.

This multifaceted approach allowed us to gain a comprehensive understanding of the bibliometric landscape and unravel collaborative structures, thematic foci, and the influence of key works on mathematics education.

Analytical process for this study

In this chapter, we present the key results of the meta-review and bibliometric analyses divided into two main categories: an overview of the review studies in mathematics education based on the content analysis, addressing RQ1, and the results of the bibliometric analysis, addressing RQ2 – RQ5.

4.1 Overview of review studies in mathematics education (RQ1)

To discern the research trends and essential attributes of review studies in mathematics education, we conducted a content analysis within our meta-review to examine the 259 included review studies. Our analysis encompassed publication years, publishers, review types, guidelines, protocols used, sample sizes, and the theoretical and conceptual frameworks employed in these review studies. A general overview of the included studies is presented in Table 3 .

Our literature search with no restriction on the publication years yielded review studies published between 1996 and 2023, with a notable increase within the last five years (2019–2023, see Fig. 3 ).

Distribution of publications from 1996 to 2023

The analysis showed that the Springer Group is the primary publisher of review articles in mathematics education, followed by Taylor & Francis, Elsevier, Sage, Frontiers, Wiley, MDPI, and the American Psychological Association (APA) (see Table 4 ). Other publishers published the remaining review articles ( n = 43). This result may be attributed to the predominance of mathematics education journals published by Springer within the WoS database.

To explore the prevailing types of review studies in mathematics education, we scrutinised the review methodologies of the included studies, considering the review types presented earlier in Table 1 . The findings revealed that researchers conducted (according to their own classification) 10 different types of reviews in mathematics education as outlined in Fig. 4 .

Types of review studies Note: *systematic reviews and meta-analyses ( n = 6), systematic reviews and bibliometric analyses ( n = 3), meta-analyses and narrative reviews ( n = 2), and meta-analysis and critical review ( n = 1)

Our analysis did not yield further review types in mathematics education. Time-related analysis showed that recent studies were systematic reviews, meta-analyses, literature reviews, and scoping reviews, whereas early examples of review studies in mathematics education were primarily narrative or critical reviews or were not explicitly classified according to review type by their authors. Figure 4 shows that some researchers ( n = 18) described their studies as literature reviews using Grant and Booth’s ( 2009 ) generic term, without providing further details about the type of review.

To comprehend the methodologies employed by researchers to conduct reviews and select eligible studies, we conducted an analysis of the guidelines and protocols the researchers used. The findings revealed that the PRISMA guidelines were the most frequently employed ( n = 121), aligning with the distribution of review types—PRISMA guidelines are basically recommended for systematic reviews and meta-analyses (Page et al., 2021 ). For scoping reviews, the guidelines developed by Arksey and O’Malley ( 2005 ) were the most prevalent and were used in seven studies. In six instances, researchers applied various guidelines (e.g. PICO or SALSA guidelines) sourced from the literature. Almost half of the studies ( n = 125) did not specify the use of guidelines for conducting literature searches and selecting eligible studies. Additionally, three studies aimed to provide protocols for conducting review studies. Furthermore, seven studies were preregistered as review studies, following the Open Science Framework (OSF) and/or the International Prospective Register of Systematic Reviews (PROSPERO) protocol.

A prevalent discourse among researchers in review studies revolved around determining the most suitable number of studies to include in reviews. Our results revealed that the sample sizes of the included studies (i.e. the number of primary studies) in the field of mathematics education ranged from 8 to 3,485. Unfortunately, this information was not reported in 19 review articles. In the remaining 240 review articles, the average was 99 included studies, with an overall total of 23,761. Most of the studies ( n = 202) had sample sizes of less than 100, with an average of 34 (see Table 5 ). Although we harboured concerns that the review studies identified in this investigation might not have been aptly named and conceptualised by their authors, we deliberately refrained from addressing this issue because it fell outside the scope of our study. While including a substantial number of studies is common and potentially suitable for bibliometric analyses and meta-analyses, conducting a systematic review, scoping review, or narrative review that critically analyses exceptionally high volumes of studies may pose challenges. In this meta-review, for example, we observed that five articles included more than 1,000 studies in the review process. Two studies, enriched by bibliometric analysis, took this approach, while another study was identified by the authors as a scoping review with a sample size of 2,433. Additionally, two studies were labelled as systematic reviews with sample sizes of 1,968, and 3,485, respectively.

Finally, we conducted a content analysis to scrutinise the theoretical and conceptual frameworks underpinning the included review studies in mathematics education. The findings revealed that out of 259 review studies, only 61 incorporated any theoretical or conceptual framework. Notably, a subset of studies ( n = 14) was based on technology-related conceptual frameworks, such as Technological Pedagogical Content Knowledge (TPACK), frameworks pertaining to augmented and virtual reality, embodied design, artificial intelligence, big data, and the European Framework for the Digital Competence for Educators (DigCompEdu). Another prevalent category ( n = 10) relied on frameworks related to the knowledge and competence of individuals (e.g. teachers and/or students), encompassing models such as the competence as continuum framework, TPACK, the didactic-mathematical knowledge and competencies model, mathematical content knowledge, pedagogical content knowledge, mathematical knowledge for teaching, teacher noticing competence, and an integrative model for the study of developmental competencies in minority children. Bronfenbrenner’s ecological theories (e.g. ecological theory of human development, bioecological model of human development, ecological systems theory, and ecological dynamics—a blend of dynamic-systems theory and ecological psychology) were employed by researchers in five review studies in mathematics education. In a limited subset of the studies, social and cultural theories (e.g. sociocultural theory, social learning theory, and cultural activity theory ( n = 3)), cognitive theories (e.g. cognitive developmental theory ( n = 2)), affective theories (e.g. self-determination theory and expectancy-value theory ( n = 2)), linguistic theories ( n = 2), and constructivist theories ( n = 2) were used as frameworks. Additionally, researchers used conceptual frameworks concerning computational thinking ( n = 2) and engagement ( n = 3) alongside a few less frequently reported frameworks.

4.2 Results of the bibliometric analysis (RQ2–RQ5)

To identify productive and most cited authors, important journals, and countries of origin of the authors, along with the underlying research collaborations between researchers and countries, as well as research trends and key topics of review studies in mathematics education, we conducted a bibliometric analysis based on co-authorship, co-occurrence, and citations.

4.2.1 Co-authorship analysis

We conducted a co-authorship analysis according to authors and countries within the units of analysis.

Co-authorship and author analysis

The bibliometric analysis, using VOSviewer, revealed that 761 authors contributed to mathematics education, each of whom conducted at least one review study. The review papers were predominantly authored through collaboration, with most being written by two authors (30,2%), followed by three authors (20,2%), four authors (19,4%), a single author (10,1%), five authors (8,9%), six authors (6,2%), seven authors (3,5%), eight authors (1,6%), and nine authors (0,4%). These results showed that researchers primarily collaborate with their colleagues in conducting review studies—a practice vital for reducing workload and enhancing the quality of analyses—with the advantage of incorporating the various perspectives of different authors.

Table 6 highlights the top 17 authors who published a minimum of three review papers each. Notably, Lieven Verschaffel is the only scholar present in both lists of prolific and highly cited authors. The researchers listed in Table 7 , except Lieven Verschaffel, contributed to the field with a single review study. Consequently, while these researchers rank among most cited authors, the low total link strength (TLS) values indicate their limited collaboration with other scholars. The TLS was automatically calculated by VOSviewer and represents the overall intensity of co-authorship connections between a particular researcher and others. According to the co-authorship analysis, it is also noteworthy that many of the highly cited authors’ review studies typically date back over ten years, which is expected as citations tend to accumulate gradually over time. The results from the detailed citation analyses provided in Sect. 4.2.3.

Upon examining the research domains of prolific and highly cited authors, we found a diverse range of topics spanning mathematics education, psychology, educational psychology, special education, and neuroscience. This diversity highlights the interdisciplinary nature of research in mathematics education, with contributions to the literature review studies from psychologists and special education and neuroscience scholars alongside mathematics educators.

Figure 5 shows a co-authorship network map for the authors of the included review studies based on the TLS. We set the minimum number of documents for an author as one, which encompassed 761 authors who contributed to review papers in mathematics education. This bibliometric co-authorship analysis yielded 51 clusters, each containing a minimum of five items (researchers). The prominent co-authorship clusters included a green cluster (led by Lieven Verschaffel), a blue cluster (led by Gabriele Kaiser and Mustafa Cevikbas), a red cluster (led by Nelson Gena), and a yellow cluster (led by Diane P. Bryant). Nelson Gena had the highest number of collaboration links, with a TLS of 26, followed by Lieven Verschaffel (TLS = 22), Gabriele Kaiser (TLS = 16), Soyoung Park (TLS = 16), Tassia Bradford (TLS = 13), Diane P. Bryant (TLS = 12), Johannes König (TLS = 12), Mikyung Shin (TLS = 12), Min Wook Ok (TLS = 12), Bert de Smedt (TLS = 10), Fred Spooner (TLS = 10), Jihyun Lee (TLS = 10), Mustafa Cevikbas (TLS = 10), Rosella Santagata (TLS = 10), Sarah R. Powell (TLS = 10), and Thorsten Scheiner (TLS = 10).

Co-authorship and author networks

Co-authorship and country analysis

We conducted a co-authorship–country analysis, setting the minimum number of documents for a country as one, and identified 50 countries. This selection resulted in five clusters, each containing a minimum of five items (countries).

The most prominent cluster was the green cluster, encompassing eight countries from various global regions: the United States (US; TLS = 30), Germany (TLS = 23), Australia (TLS = 21), China (TLS = 11), South Korea (TLS = 6), Sweden (TLS = 4), New Zealand (TLS = 2), and Jordan (TLS = 1). The US dominated research collaborations both within this cluster and overall.

The red cluster included nine countries, predominantly Nordic and European countries: Norway (TLS = 13), Finland (TLS = 7), Belgium (TLS = 6), the Netherlands (TLS = 6), Lithuania (TLS = 1), Portugal (TLS = 1), Luxembourg (TLS = 1), Scotland (TLS = 1), and Israel (TLS = 1).

The yellow cluster contained seven countries: Canada (TLS = 7), Malaysia (TLS = 7), Denmark (TLS = 3), Libya (TLS = 2), Singapore (TLS = 2), Indonesia (TLS = 1), and the United Arab Emirates (TLS = 1).

The blue cluster primarily highlighted European collaborations and included seven countries: England (TLS = 22), Switzerland (TLS = 4), Italy (TLS = 3), France (TLS = 3), Greece (TLS = 1), Chile (TLS = 1), and Saudi Arabia (TLS = 1).

Lastly, the purple cluster represented a network of predominantly South and North American countries featuring, among others, Brazil (TLS = 6), Ireland (TLS = 5), Mexico (TLS = 4), Ecuador (TLS = 2), and Cuba (TLS = 2)(See Fig. 6 ).

Co-authorship and country networks

4.2.2 Co-occurrence analysis

To explore the research hotspots within mathematics education, we ran a keyword co-occurrence analysis using Author Keywords.

Co-occurrence analysis based on author keywords

The author keyword co-occurrence analysis indicated that our repository contained 691 keywords (see Fig. 7 , left side), of which 23 met the minimum occurrence threshold of five occurrences ( n = 5) (see Fig. 7 , right side). In the figure, the size of a node corresponds to the frequency of a keyword co-selected in review studies in mathematics education. The distance between any two keywords reflects their relative strength and topic similarity. Nodes within the same colour cluster indicate similar topics among these publications.

The red cluster comprises 11 closely related items, including ‘mathematics, meta-analysis, mathematics achievement, intervention, scoping review, bibliometric analysis, review, technology, learning disabilities, children, and math anxiety’. The green cluster emerges as the second prominent cluster, featuring 8 interrelated items such as ‘mathematics education, systematic review, systematic literature review, literature review, teacher education, education, teaching, and flipped classroom’. Lastly, the blue cluster consists of 4 items, namely ‘math, science, early childhood, and identity’.

Co-occurrence analysis of author keywords

Notably, the most frequently cited author keyword was ‘mathematics education’ ( n = 55), followed by ‘systematic review’ ( n = 44), ‘mathematics’ ( n = 41), ‘meta-analysis’ ( n = 34), ‘systematic literature review’ ( n = 14), ‘literature review’ ( n = 11), ‘teacher education’ ( n = 9), ‘mathematics achievement’ ( n = 8), ‘intervention’ ( n = 6), ‘education’ ( n = 6), ‘teaching’ ( n = 6), ‘science’ ( n = 6), ‘scoping review’ ( n = 5), ‘bibliometric analysis’ ( n = 5), ‘review’ ( n = 5), ‘math’ ( n = 5), ‘technology’ ( n = 5), ‘flipped classroom’ ( n = 5), ‘early childhood’ ( n = 5), ‘children’ ( n = 5), ‘identity’ ( n = 5), ‘learning disabilities’ ( n = 5), and ‘math anxiety’ ( n = 6).

The keywords chosen by the authors highlighted the focus areas of reviews in mathematics education, emphasising themes such as mathematics achievement, teacher education, interventions, technology, and technology-enhanced approaches (e.g. flipped classrooms), special education, and early childhood education. Furthermore, the author keywords reflected the prevalent review types in mathematics education, specifically systematic reviews and meta-analyses. Additionally, they highlighted the interdisciplinary nature of reviews in mathematics education, encompassing both mathematics education and science education.

Furthermore, we conducted distinct author keyword co-occurrence analyses for review studies published within the periods of 2019 to 2023 and those preceding 2019, aiming to discern temporal trends in author keywords, particularly in recent years. The analysis yielded 606 keywords for the 2019–2023 period and 144 keywords for the period before 2019 (see Table 8 for the most popular 15 author keywords). A noteworthy disparity in prevalent keywords was observed between the two temporal segments. While predominant keyword regarding the review types prior to 2019 was meta-analysis, followed by literature review and systematic review, over the past five years, additional keywords such as scoping review and bibliometric analysis emerged, signalling an augmentation in the diversity of review types and methodologies. The findings indicated a notable increase in the popularity of systematic reviews over the past five years.

4.2.3 Citation analysis

To explore the most cited publications and journals in mathematics education, we conducted a citation analysis based on the units of analysis in documents and sources.

Citation and document analysis

The analysis of the 259 review papers in mathematics education included in this study indicated that they received a total of 7,050 citations between 1996 and 2023, averaging 251.79 citations per year and 27.22 citations per paper. Notably, 67% of these citations were received in the last five years (2019–2023).

The threshold for the minimum number of citations of documents was set at one, which 221 review studies out of 259 met. Figure 8 visualises the network between these review papers with the largest citation links and Table 9 shows the most cited documents. Not all the studies listed in Table 9 are among the top 10 studies with the highest TLS. Among them, only Gersten et al. ( 2009 ), Cheung and Slavin ( 2008 ), and Slavin and Lake ( 2008 ) are within the top 10 review studies in mathematics education with the highest TLS. While highly cited documents are influential in terms of direct references, the TLS metric provides additional insights into the collaborative relationships and connections between researchers and their work, which may not always correlate perfectly with citation counts as seen in our findings.

Our results showed that the largest number of citation links were for meta-analyses and systematic review studies. The most prominent review type among the most cited studies listed in Table 9 is meta-analysis ( n = 6), followed by literature review ( n = 2), systematic review ( n = 1), and narrative review ( n = 1). This result indicates the potential of meta-analysis studies in terms of citation performance. Most of these review studies were primarily published in high-ranking educational review journals ( n = 6). Other review papers published in teacher education ( n = 2), psychology ( n = 1), and behavioural science and neuroscience journals ( n = 1). These ten most cited review articles were all published in SSCI journals over a decade ago. Regarding research topics in the most cited papers, the dominant topics were mathematics achievement, content knowledge, working memory, learning disabilities, and educational technologies.

Specifically, we analysed the citation trends of the most cited 10 review papers over time and separately for the first five years after publication and the past five years (2019–2023). The results indicate a significant increase in the citations review studies have received in the last five years. We found that eight out of the ten most cited papers received more citations in the past five years (2019–2023) than in the first five years after their publication. The analysis revealed that the average annual citations for each paper ranged from 7 to 30. While the majority of these review studies ( n = 8) received the least citations in the year of their publication, they received the most citations on average approximately 12 years after publication. This indicates that the peak citation period for review articles in mathematics education extends beyond the first decade following their publication.

Additionally, we investigated the ‘Enriched Cited References’ feature, which provides insight into why an author cited a particular reference; this beta enhancement is only available in selected journals (Clarivate, 2024 ). These references are presented to aid readers in quickly assessing sections of a review paper, allowing them to identify the most closely related or impactful references and infer their purpose. Articles containing enriched cited references are marked with the following labels (Clarivate, 2024 ):

Previously published research that contextualizes the current study within an academic domain.

References that supply the datasets, methodologies, concepts, and ideas directly utilized by the author or upon which the author’s work relies.

References introduced because the current study engages in a more thorough discussion.

References cited by the current study as yielding similar results. This may encompass methodological similarities or, in certain instances, replication of findings.

References noted by the current study as presenting contrasting results. This may also involve disparities in methodology or sample differences, influencing the outcomes.

The results, displayed in Table 10 , pertain to the classification of references based on the Enriched Cited References analysis conducted automatically by WoS. These results suggest that the most cited review studies in mathematics education were predominantly utilized by researchers to establish the background for their own research. Furthermore, these reviews also frequently employed to shape the discussion within the papers. In addition, some researchers utilize the mentioned most cited review studies to establish a conceptual, theoretical, or methodological basis. While the limited number of the studies cited these reviews to support their findings, they were not used to present opposing evidence. This suggests a reliance on existing literature review studies to inform, validate, or potentially challenge new research within the field.

Citation and source analysis

We conducted a citation source analysis and present the citation network map for the journals in Fig. 9 , listing the top 15 journals in Table 11 based on the citation and TLS metrics to represent the frequency of citations between articles in any two journals. The threshold for the minimum number of documents citing a source was one, and 103 records met the minimum number of citations of a source, also set at one. The network map shown in Fig. 9 indicates prominent clusters. The red cluster included 23 items (mostly special education, educational psychology, and educational review journals). The blue cluster included 16 items (predominantly educational psychology, educational technology, and educational review journals). The green cluster comprised 17 items (including mathematics and mathematics education journals, educational technology journals, and educational psychology journals).

The number of articles and the distribution of journals across various research fields were as follows: 25 educational sciences journals (43 papers), 20 psychology and educational psychology journals (41 papers), 15 special education journals (32 papers), 12 mathematics education journals (52 papers), 10 educational review journals (41 papers), 9 educational technology journals (28 papers), 3 mathematics journals (14 papers), and 9 other journals (8 articles).

Our findings indicate that ZDM– Mathematics Education ( n = 16) has, so far, published the most review studies focusing on mathematics education, which is not unexpected due to the origin of the journal as a review journal publishing only special issues, for which a review article is compulsory in each issue. This was followed by Frontiers in Psychology ( n = 14), Educational Research Review ( n = 13), and Mathematics ( n = 10) (see Table 11 for the top 15 journals).

The results highlighted that the most frequently cited papers were often published in specific educational review journals (e.g. Review of Educational Research , Educational Research Review , and Educational Psychology Review ), psychology and educational psychology journals (e.g. Frontiers in Psychology , Educational Psychology Review , European Journal of Cognitive Psychology , and Psychological Bulletin ), special education journals (e.g. Exceptional Children , Learning Disabilities Research & Practice , Learning Disability Quarterly , and Remedial and Special Educati on), educational technology journals (e.g. Computers & Education , Journal of Computer Assisted Learning , and Education and Information Technologies ), and mathematics and mathematics education journals (e.g. ZDM– Mathematics Education , Educational Studies in Mathematics , and Mathematics ).

Although the most visible mathematics education journals in citation network map were ZDM– Mathematics Education and Educational Studies in Mathematics (see Fig. 9 ), as mentioned earlier, twelve mathematics education journals provided platforms for review studies. These were ZDM– Mathematics Education ( n = 16), Educational Studies in Mathematics ( n = 5), International Journal of Science and Mathematics Education ( n = 5), International Journal of Mathematical Education in Science and Technology ( n = 5), International Electronic Journal of Mathematics Education ( n = 3), Mathematics Education Research Journal ( n = 3), International Journal for Technology in Mathematics Education ( n = 3), International Journal of Education in Mathematics, Science and Technology ( n = 3), Journal for Research in Mathematics Education ( n = 2), Canadian Journal of Science, Mathematics and Technology Education ( n = 1), Journal für Mathematik-Didaktik ( n = 1), and Research in Mathematics Education ( n = 1).

5 Discussion, conclusions, and limitations

In this study, we conducted a meta-review of literature review studies in mathematics education, enriched by a comprehensive bibliometric analysis. This paper significantly contributes to scholarly discourse by unravelling nuanced research trends, the most common review methodologies, and prevalent theoretical approaches in review studies in mathematics education. Based on content and bibliometric analysis, it delves into the research foci, providing an understanding of the relevant academic landscape. Additionally, it illuminates intricate connections among researchers, countries, and journals, elucidating collaborative networks in mathematics education research.

5.1 Insights from the meta-review and implications

The findings revealed a significant increase in the number of literature reviews in mathematics education, particularly in the past five years; 79% of the reviews we examined were published during this period. Multiple factors may have contributed to this surge, including researchers’ increased publication output during the pandemic (Cevikbas & Kaiser, 2023 ; Nane et al., 2023 ), challenges in collecting empirical data during the pandemic crisis (Uleanya & Yu, 2023 ), the relatively high citation rates associated with literature review studies, the growing prestige of educational review journals based on their increased impact factors (Miranda & Garcia-Carpintero, 2018 ), and the publication of review-oriented special issues in mathematics education journals.

Our findings revealed a prevalence of systematic reviews and meta-analyses; however, researchers also conducted diverse types of reviews, including scoping reviews, critical reviews, narrative reviews, theoretical reviews, and tutorial reviews. This methodological diversity is important as the advantages of one method can potentially overcome the disadvantages of another and combining different approaches can mitigate disadvantages (Taherdoost, 2023 ). Furthermore, our study revealed that rapid reviews, meta-reviews, umbrella reviews, mapping reviews, mixed-methods reviews, integrative reviews, interpretative reviews, iterative reviews, meta-syntheses, descriptive reviews, realist reviews, selective reviews, algorithmic reviews, and computational reviews indexed in WoS were not represented in mathematics education. The well-established PRISMA guidelines offer a defined framework for systematic reviews and meta-analyses to assist researchers in conducting reviews while adhering to quality and transparency criteria (Moher et al., 2009 ; Page et al., 2021 ). This adherence may have encouraged researchers to undertake such reviews, and future advancements in the development of specific guidelines and methodologies for each review type may further motivate researchers to conduct other types of reviews in mathematics education more frequently.

There were nuanced overlaps between the review types, leading to ambiguous distinctions. For instance, the structural similarity between systematic reviews and scoping reviews has led to misunderstandings. Munn et al. ( 2018 ) confirm inconsistency and confusion regarding the differentiation between scoping reviews and systematic reviews and offered guidelines for this decision-making process: a systematic review is preferable when addressing specific questions regarding the feasibility, appropriateness, significance, or efficacy of a specific treatment or practice. However, if the authors intend to demarcate the research field and explore its potential size and scope, a scoping review is more appropriate. Grant and Booth ( 2009 ) and Munn et al. ( 2018 ) clarified that a scoping review is preparation for a systematic literature review, not a deep study for a systematic literature review. The diverse taxonomies proposed by researchers have contributed to this complexity, with some employing various terms for similar review characteristics, and others applying the same terms to studies with distinct review attributes. Consequently, a consensus regarding the categorisation of review studies, both in a broad context and specifically in mathematics education, remains elusive. We also observed instances of researchers labelling their reviews inaccurately. However, we refrained from judging the appropriateness of these terminologies as they fall outside the scope of our study and may be difficult to justify due to the ambiguity of the current typologies. Borges Migliavaca et al. ( 2020 ) expressed a similar concern, highlighting substantial disparities in review studies concerning their conceptualisation, conduct, reporting, risk of bias assessment, and data synthesis. They called for the evidence synthesis community to promptly develop guidance and reporting standards for review studies. Future researchers could potentially examine inconsistencies in the conducting of review studies and their categorisation in mathematics education. In this study, we distilled the various existing types of review studies to provide clear explanations of the main review types and to help researchers and readers understand the key characteristics of various review studies (see Chap. 2).

An additional noteworthy consideration pertains to the sample sizes of review studies. A prevalent discourse considers the appropriate number of studies to be included in a review, but establishing such a minimum or maximum number may be challenging and not appropriate because this depends on various contextual factors, such as the research area, topic, inclusion/exclusion criteria, and applied protocols. For example, in technical terms, a systematic review can be conducted with as few as two studies or as many as a thousand. A review study with a small sample (e.g. two or three studies) may be due to the literature search methods used or insufficient number of existing studies in a particular field, suggesting a limited demand for such a review. As previously noted, the primary function of review studies is to inform readers in the relevant field about published studies to address the challenge posed by an increasing number of studies and to identify trends and research gaps (Fusar-Poli & Radua, 2018 ). Conversely, although it is technically feasible to include a substantial number of studies in a review (e.g. 1,000 or 2,000), conducting a comprehensive analysis (e.g. content analysis) of such a large dataset can present major time, cost, storage, memory, bias, and security challenges (Cohen et al., 2015 ). Nevertheless, the findings of our study provide insight into this issue. Notably, the sample size of the studies we analysed varied from 8 to 3,485, with an average of 99. Notably, most of these studies (78%) had sample sizes of less than 100, with an average of 34. Although this observation does not serve as a prescriptive recommendation, it offers valuable insights into the typical sample sizes with which mathematics education researchers have tended to work in the past.

Furthermore, as evidenced by our findings, literature reviews may serve various purposes, such as assessing the use of theoretical models or conceptual and methodological approaches, or advancing new theories, concepts, or research models through critical appraisal of previous research within a specific subject area (Cooper, 1988 ). However, our findings also indicate that it is not common in practice to use or develop a theoretical or conceptual framework in mathematics education review studies. Only 24% of the reviewed studies explicitly reported employing a specific framework, and very few sought to formulate a framework based on the literature under scrutiny. The results highlighted the researchers’ interest in frameworks related to technology, knowledge, and competence models. A few studies incorporated grand theories, such as constructivism, sociocultural theory, and cognitive development theory.

It is remarkable that despite focusing on mathematics education, there is a notable scarcity of review studies employing content-specific frameworks in mathematics education, such as those centred on problem-solving, reasoning, and mathematical thinking. Only a minority of the studies used frameworks related to mathematical modelling and mathematical content knowledge. This observation may reflect a gap in the literature, suggesting a need for greater integration of domain-specific frameworks into review studies in mathematics education to enhance the depth and specificity of the studies. Moreover, this trend prompts a critical examination of potential underlying factors. One plausible explanation lies in the interdisciplinary nature of review studies in mathematics education, which draws contributions from diverse fields including psychology, educational technology, special education, and neuroscience. The diverse disciplinary backgrounds of the researchers may influence their preferences for frameworks that are not necessarily specific to mathematics education but rather draw from broader fields.

5.2 Insights from the bibliometric analyses and implications

The bibliometric analysis revealed contributions to mathematics education, with 761 authors from 50 countries conducting review studies. In future studies, researchers may consider conducting detailed analyses of how these initiatives have influenced the landscape of mathematics education, examining their specific impacts on various subfields, and assessing their overall influence.

Our findings reveal a notable participation in literature review studies within mathematics education by scholars from diverse backgrounds, including educational psychologists, mathematics educators, and specialists in special education and neuroscience. This multidisciplinary engagement underscores the broader interest of researchers beyond the field of mathematics education. Notably, co-authorship connections within US institutions were the most extensive. The leading countries that published review studies included the US, Germany, China, Australia, and England. A robust network emerged among researchers in North America, Europe, Asia, and Australia, emphasising collaboration opportunities that warrant exploration by African and South American researchers.

Systematic reviews and meta-analyses stood out as the predominant review types in mathematics education, both in terms of the number of publications and citation counts. Systematic reviews offer rigorous and comprehensive syntheses of existing literature on specific research questions, providing valuable insights, identifying gaps in knowledge, and informing evidence-based decision-making in various fields. Moreover, meta-analyses enhance statistical power, resolve conflicting findings, and offer more precise estimates of effect sizes by combining data from various sources. However, there is a discernible need to diversify the types of reviews conducted in mathematics education.

The findings underscore a significant surge in both the quantity of review studies and their citation counts within mathematics education especially over the recent five-year period (2019–2023). This trend suggests a prevalent practice among authors to draw upon previously published reviews to contextualize their own studies, frequently engaging in discussions and citing references to corroborate or challenge existing findings. Such reliance on established literature highlights the discipline’s emphasis on leveraging prior knowledge to inform and substantiate new research endeavours.

The most cited review papers were associated with specific educational review journals, educational psychology journals, special education journals, educational technology journals, and mathematics education journals, further highlighting the interdisciplinary nature of impactful research in the field. The results revealed that ZDM– Mathematics Education , Educational Studies in Mathematics , International Journal of Science and Mathematics Education , and International Journal of Mathematical Education in Science and Technology were the key mathematics education journals committed to publishing review studies. The performance of these journals, particularly in recent years, reflects the escalating significance of review studies in mathematics education. Nevertheless, the limited visibility of some mathematics education journals in publishing review studies could be attributed, among other factors, to their restricted representation in the WoS database or to the overall small number of studies published yearly in particular mathematics education journals.

Prominent research topics in mathematics education review studies are digital technologies, technology-enhanced approaches (e.g. flipped classrooms), teacher education, mathematics achievement, early childhood education, and learning disabilities. Recent technological advances, including artificial intelligence and augmented/virtual reality, may soon attract mathematics education researchers’ attention to emerging technologies (Cevikbas, Bulut et al., 2023 ; Cevikbas, Greefrath et al., 2023 ). In addition to technology-enhanced mathematics education and special education, researchers have also explored the cognitive and affective aspects of learning and teaching mathematics.

In short, the absence of high-quality research syntheses may impede theoretical and conceptual advances within mathematics education (Webster & Watson, 2002 ). Therefore, future researchers may endeavour to develop discipline-specific standards and guidelines for conducting various types of review studies in mathematics education. Moreover, they could focus on expanding the content of mathematics education journals to accommodate a greater number of review studies. The scientific influence of review journals may also provide an opportunity to establish a dedicated review journal with a pronounced focus on mathematics education.

5.3 Limitations and conclusion

Finally, we want to point out that in this comprehensive meta-review, enriched by bibliometric analysis, we meticulously compiled and scrutinised the largest dataset of reviews in mathematics education available within the WoS database. Although this was a substantial sample ( n = 259) that was reasonably representative of published review studies in mathematics education, it is important to acknowledge certain limitations. Our search was confined to WoS, and we specifically focused on review articles published in English. It is worth noting that the characteristics of review studies published in journals, international handbooks, or conference proceedings not indexed in WoS or published in a language other than English could potentially differ from those we examined. In addition, despite studies indexed in WoS theoretically being of high quality, we identified inconsistencies and variability in the review studies we examined, and it is possible that a more extensive search would have yielded different results.

In conclusion, we advocate producing high-quality review papers that adeptly synthesise available knowledge to improve professional practice (Templier & Paré, 2015 ). Such efforts may further advance mathematics education and contribute to the continuous improvement of teaching and learning activities, despite the demanding nature of comprehensive review studies.

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Gabriele Kaiser

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Cevikbas, M., Kaiser, G. & Schukajlow, S. Trends in mathematics education and insights from a meta-review and bibliometric analysis of review studies. ZDM Mathematics Education (2024). https://doi.org/10.1007/s11858-024-01587-7

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Department members engage in cutting-edge research on a wide variety of topics in mathematics and its applications. Topics continually evolve to reflect emerging interests and developments, but can roughly grouped into the following areas.

Algebra, Combinatorics, and Geometry

Algebra, combinatorics, and geometry are areas of very active research at the University of Pittsburgh.

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The biological world stands as the next great frontier for mathematical modeling and analysis. This group studies complex systems and dynamics arising in various biological phenomena.

Mathematical Finance

A rapidly growing area of mathematical finance is Quantitative Behavioral Finance. The high-tech boom and bust of the late 1990s followed by the housing and financial upheavals of 2008 have made a convincing case for the necessity of adopting broader assumptions in finance.

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The diversity of this group is reflected in its research interests: numerical analysis of partial differential equations , adaptive methods for scientific computing, computational methods of fluid dynamics and turbulence, numerical solution of nonlinear problems arising from porous media flow and transport, optimal control, and simulation of stochastic reaction diffusion systems.

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Mathematics Research Paper Topics

See our list of mathematics research paper topics . Mathematics is the science that deals with the measurement, properties, and relationships of quantities, as expressed in either numbers or symbols. For example, a farmer might decide to fence in a field and plant oats there. He would have to use mathematics to measure the size of the field, to calculate the amount of fencing needed for the field, to determine how much seed he would have to buy, and to compute the cost of that seed. Mathematics is an essential part of every aspect of life—from determining the correct tip to leave for a waiter to calculating the speed of a space probe as it leaves Earth’s atmosphere.

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Boolean algebra
Chaos theory
Complex numbers
Correlation
Fraction, common
Game theory
Graphs and graphing
Imaginary number
Multiplication
Natural numbers
Number theory
Numeration systems
Probability theory
Proof (mathematics)
Pythagorean theorem
Trigonometry

Mathematics undoubtedly began as an entirely practical activity— measuring fields, determining the volume of liquids, counting out coins, and the like. During the golden era of Greek science, between about the sixth and third centuries B.C., however, mathematicians introduced a new concept to their study of numbers. They began to realize that numbers could be considered as abstract concepts. The number 2, for example, did not necessarily have to mean 2 cows, 2 coins, 2 women, or 2 ships. It could also represent the idea of “two-ness.” Modern mathematics, then, deals both with problems involving specific, concrete, and practical number concepts (25,000 trucks, for example) and with properties of numbers themselves, separate from any practical meaning they may have (the square root of 2 is 1.4142135, for example).

Fields of Mathematics

Mathematics can be subdivided into a number of special categories, each of which can be further subdivided. Probably the oldest branch of mathematics is arithmetic, the study of numbers themselves. Some of the most fascinating questions in modern mathematics involve number theory. For example, how many prime numbers are there? (A prime number is a number that can be divided only by 1 and itself.) That question has fascinated mathematicians for hundreds of years. It doesn’t have any particular practical significance, but it’s an intriguing brainteaser in number theory.

Geometry, a second branch of mathematics, deals with shapes and spatial relationships. It also was established very early in human history because of its obvious connection with practical problems. Anyone who wants to know the distance around a circle, square, or triangle, or the space contained within a cube or a sphere has to use the techniques of geometry.

Algebra was established as mathematicians recognized the fact that real numbers (such as 4 and 5.35) can be represented by letters. It became a way of generalizing specific numerical problems to more general situations.

Analytic geometry was founded in the early 1600s as mathematicians learned to combine algebra and geometry. Analytic geometry uses algebraic equations to represent geometric figures and is, therefore, a way of using one field of mathematics to analyze problems in a second field of mathematics.

Over time, the methods used in analytic geometry were generalized to other fields of mathematics. That general approach is now referred to as analysis, a large and growing subdivision of mathematics. One of the most powerful forms of analysis—calculus—was created almost simultaneously in the early 1700s by English physicist and mathematician Isaac Newton (1642–1727) and German mathematician Gottfried Wilhelm Leibniz (1646–1716). Calculus is a method for analyzing changing systems, such as the changes that take place as a planet, star, or space probe moves across the sky.

Statistics is a field of mathematics that grew in significance throughout the twentieth century. During that time, scientists gradually came to realize that most of the physical phenomena they study can be expressed not in terms of certainty (“A always causes B”), but in terms of probability (“A is likely to cause B with a probability of XX%”). In order to analyze these phenomena, then, they needed to use statistics, the field of mathematics that analyzes the probability with which certain events will occur.

Each field of mathematics can be further subdivided into more specific specialties. For example, topology is the study of figures that are twisted into all kinds of bizarre shapes. It examines the properties of those figures that are retained after they have been deformed.

Back to Science Research Paper Topics .

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260 Interesting Math Topics for Essays & Research Papers

Mathematics is the science of numbers and shapes. Writing about it can give you a fresh perspective and help to clarify difficult concepts. You can even use mathematical writing as a tool in problem-solving.

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In this article, you will find plenty of interesting math topics. Besides, you will learn about branches of mathematics that you can choose from. And if the thought of letters and numbers makes your head swim, try our custom writing service . Our professionals will craft a paper for you in no time!

And now, let’s proceed to math essay topics and tips.

🔝 Top 10 Interesting Math Topics

✅ branches of mathematics, ✨ fun math topics.

🏫 Math Topics for High School
🎓 College Math Topics
🤔 Advanced Math
📚 Math Research
✏️ Math Education
💵 Business Math

🔍 References

Number theory in everyday life.
Logicist definitions of mathematics.
Multivariable vs. vector calculus.
4 conditions of functional analysis.
Random variable in probability theory.
How is math used in cryptography?
The purpose of homological algebra.
Concave vs. convex in geometry.
The philosophical problem of foundations.
Is numerical analysis useful for machine learning?

What exactly is mathematics ? First and foremost, it is very old. Ancient Greeks and Persians were already utilizing mathematical tools. Nowadays, we consider it an interdisciplinary language.

Biologists, linguists, and sociologists alike use math in their work. And not only that, we all deal with it in our daily lives. For instance, it manifests in the measurement of time. We often need it to calculate how much our groceries cost and how much paint we need to buy to cover a wall.

Simply put, mathematics is a universal instrument for problem-solving. We can divide pure math into three branches: geometry, arithmetic, and algebra. Let’s take a closer look:

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Geometry By studying geometry, we try to comprehend our physical surroundings. Geometric shapes can be simple, like a triangle. Or, they can form complicated figures, like a rhombicosidodecahedron.
Arithmetic Arithmetic deals with numbers and simple operations: subtraction, addition, division, and multiplication.
Algebra Algebra is used when the exact numbers are unclear. Instead, they are replaced with letters. Businesses often need algebra to predict their sales.

It’s true that most high school students don’t like math. However, that doesn’t mean it can’t be a fun and compelling subject. In the following section, you will find plenty of enthralling mathematical topics for your paper.

If you’re struggling to start working on your essay, we have some fun and cool math topics to offer. They will definitely engage you and make the writing process enjoyable. Besides, fun math topics can show everyone that even math can be entertaining or even a bit silly.

The link between mathematics and art – analyzing the Golden Ratio in Renaissance-era paintings.
An evaluation of Georg Cantor’s set theory.
The best approaches to learning math facts and developing number sense.
Different approaches to probability as explored through analyzing card tricks.
Chess and checkers – the use of mathematics in recreational activities.
The five types of math used in computer science.
Real-life applications of the Pythagorean Theorem .
A study of the different theories of mathematical logic.
The use of game theory in social science.
Mathematical definitions of infinity and how to measure it.
What is the logic behind unsolvable math problems?
An explanation of mean, mode, and median using classroom math grades.
The properties and geometry of a Möbius strip.
Using truth tables to present the logical validity of a propositional expression.
The relationship between Pascal’s Triangle and The Binomial Theorem.
The use of different number types: the history.
The application of differential geometry in modern architecture.
A mathematical approach to the solution of a Rubik’s Cube.
Comparison of predictive and prescriptive statistical analyses.
Explaining the iterations of the Koch snowflake.
The importance of limits in calculus.
Hexagons as the most balanced shape in the universe.
The emergence of patterns in chaos theory.
What were Euclid’s contributions to the field of mathematics?
The difference between universal algebra and abstract algebra.

🏫 Math Essay Topics for High School

When writing a math paper, you want to demonstrate that you understand a concept. It can be helpful if you need to prepare for an exam. Choose a topic from this section and decide what you want to discuss.

Explain what we need Pythagoras’ theorem for.
What is a hyperbola?
Describe the difference between algebra and arithmetic.
When is it unnecessary to use a calculator ?
Find a connection between math and the arts.
How do you solve a linear equation?
Discuss how to determine the probability of rolling two dice.
Is there a link between philosophy and math?
What types of math do you use in your everyday life?
What is the numerical data?
Explain how to use the binomial theorem.
What is the distributive property of multiplication?
Discuss the major concepts in ancient Egyptian mathematics .
Why do so many students dislike math?
Should math be required in school?
How do you do an equivalent transformation?
Why do we need imaginary numbers?
How can you calculate the slope of a curve?
What is the difference between sine, cosine, and tangent?
How do you define the cross product of two vectors?
What do we use differential equations for?
Investigate how to calculate the mean value.
Define linear growth.
Give examples of different number types.
How can you solve a matrix?

🎓 College Math Topics for a Paper

Sometimes you need more than just formulas to explain a complex idea. That’s why knowing how to express yourself is crucial. It is especially true for college-level mathematics. Consider the following ideas for your next research project:

What do we need n-dimensional spaces for?
Explain how card counting works.
Discuss the difference between a discrete and a continuous probability distribution .
How does encryption work?
Describe extremal problems in discrete geometry.
What can make a math problem unsolvable?
Examine the topology of a Möbius strip.

What is K-theory?
Discuss the core problems of computational geometry.
Explain the use of set theory .
What do we need Boolean functions for?
Describe the main topological concepts in modern mathematics.
Investigate the properties of a rotation matrix.
Analyze the practical applications of game theory.
How can you solve a Rubik’s cube mathematically?
Explain the math behind the Koch snowflake.
Describe the paradox of Gabriel’s Horn.
How do fractals form?
Find a way to solve Sudoku using math.
Why is the Riemann hypothesis still unsolved?
Discuss the Millennium Prize Problems.
How can you divide complex numbers?
Analyze the degrees in polynomial functions.
What are the most important concepts in number theory?
Compare the different types of statistical methods.

🤔 Advanced Topics in Math to Write a Paper on

Once you have passed the trials of basic math, you can move on to the advanced section. This area includes topology, combinatorics, logic, and computational mathematics. Check out the list below for enticing topics to write about:

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What is an abelian group?
Explain the orbit-stabilizer theorem.
Discuss what makes the Burnside problem influential.
What fundamental properties do holomorphic functions have?
How does Cauchy’s integral theorem lead to Cauchy’s integral formula?
How do the two Picard theorems relate to each other?
When is a trigonometric series called a Fourier series?
Give an example of an algorithm used for machine learning.
Compare the different types of knapsack problems.
What is the minimum overlap problem?
Describe the Bernoulli scheme.
Give a formal definition of the Chinese restaurant process.
Discuss the logistic map in relation to chaos.
What do we need the Feigenbaum constants for?
Define a difference equation.
Explain the uses of the Fibonacci sequence.
What is an oblivious transfer?
Compare the Riemann and the Ruelle zeta functions.
How can you use elementary embeddings in model theory?
Analyze the problem with the wholeness axiom and Kunen’s inconsistency theorem.
How is Lie algebra used in physics ?
Define various cases of algebraic cycles.
Why do we need étale cohomology groups to calculate algebraic curves?
What does non-Euclidean geometry consist of?
How can two lines be ultraparallel?

📚 Math Research Topics for a Paper

Choosing the right topic is crucial for a successful research paper in math. It should be hard enough to be compelling, but not exceeding your level of competence. If possible, stick to your area of knowledge. This way your task will become more manageable. Here are some ideas:

Write about the history of calculus.
Why are unsolved math problems significant?
Find reasons for the gender gap in math students.
What are the toughest mathematical questions asked today?
Examine the notion of operator spaces.
How can we design a train schedule for a whole country?
What makes a number big?

Mathematical writing should be well-structured, precise, and easy readable

How can infinities have various sizes?
What is the best mathematical strategy to win a game of Go?
Analyze natural occurrences of random walks in biology.
Explain what kind of mathematics was used in ancient Persia.
Discuss how the Iwasawa theory relates to modular forms.
What role do prime numbers play in encryption?
How did the study of mathematics evolve?
Investigate the different Tower of Hanoi solutions.
Research Napier’s bones. How can you use them?
What is the best mathematical way to find someone who is lost in a maze?
Examine the Traveling Salesman Problem. Can you find a new strategy?
Describe how barcodes function.
Study some real-life examples of chaos theory. How do you define them mathematically?
Compare the impact of various ground-breaking mathematical equations .
Research the Seven Bridges of Königsberg. Relate the problem to the city of your choice.
Discuss Fisher’s fundamental theorem of natural selection.
How does quantum computing work?
Pick an unsolved math problem and say what makes it so difficult.

✏️ Math Education Research Topics

For many teachers, the hardest part is to keep the students interested. When it comes to math, it can be especially challenging. It’s crucial to make complicated concepts easy to understand. That’s why we need research on math education.

Compare traditional methods of teaching math with unconventional ones.
How can you improve mathematical education in the U.S.?
Describe ways of encouraging girls to pursue careers in STEM fields.
Should computer programming be taught in high school?
Define the goals of mathematics education .
Research how to make math more accessible to students with learning disabilities .
At what age should children begin to practice simple equations?
Investigate the effectiveness of gamification in algebra classes.
What do students gain from taking part in mathematics competitions?
What are the benefits of moving away from standardized testing ?
Describe the causes of “ math anxiety .” How can you overcome it?
Explain the social and political relevance of mathematics education.
Define the most significant issues in public school math teaching.
What is the best way to get children interested in geometry?
How can students hone their mathematical thinking outside the classroom?
Discuss the benefits of using technology in math class.
In what way does culture influence your mathematical education?
Explore the history of teaching algebra.
Compare math education in various countries.

How does dyscalculia affect a student’s daily life?
Into which school subjects can math be integrated?
Has a mathematics degree increased in value over the last few years?
What are the disadvantages of the Common Core Standards?
What are the advantages of following an integrated curriculum in math?
Discuss the benefits of Mathcamp.

🧮 Algebra Topics for a Paper

The elegance of algebra stems from its simplicity. It gives us the ability to express complex problems in short equations. The world was changed forever when Einstein wrote down the simple formula E=mc². Now, if your algebra seminar requires you to write a paper, look no further! Here are some brilliant prompts:

Give an example of an induction proof.
What are F-algebras used for?
What are number problems?
Show the importance of abstract algebraic thinking .
Investigate the peculiarities of Fermat’s last theorem.
What are the essentials of Boolean algebra?
Explore the relationship between algebra and geometry.
Compare the differences between commutative and noncommutative algebra.
Why is Brun’s constant relevant?
How do you factor quadratics?
Explain Descartes’ Rule of Signs.
What is the quadratic formula?
Compare the four types of sequences and define them.
Explain how partial fractions work.
What are logarithms used for?
Describe the Gaussian elimination.
What does Cramer’s rule state?
Explore the difference between eigenvectors and eigenvalues.
Analyze the Gram-Schmidt process in two dimensions.
Explain what is meant by “range” and “domain” in algebra.
What can you do with determinants?
Learn about the origin of the distance formula.
Find the best way to solve math word problems.
Compare the relationships between different systems of equations.
Explore how the Rubik’s cube relates to group theory.

📏 Geometry Topics for a Research Paper

Shapes and space are the two staples of geometry. Since its appearance in ancient times, it has evolved into a major field of study. Geometry’s most recent addition, topology, explores what happens to an object if you stretch, shrink, and fold it. Things can get pretty crazy from here! The following list contains 25 interesting geometry topics:

What are the Archimedean solids?
Find real-life uses for a rhombicosidodecahedron.
What is studied in projective geometry?
Compare the most common types of transformations.
Explain how acute square triangulation works.
Discuss the Borromean ring configuration.
Investigate the solutions to Buffon’s needle problem.
What is unique about right triangles?

The role of study of non-Euclidean geometry

Describe the notion of Dirac manifolds.
Compare the various relationships between lines.
What is the Klein bottle?
How does geometry translate into other disciplines, such as chemistry and physics?
Explore Riemannian manifolds in Euclidean space.
How can you prove the angle bisector theorem?
Do a research on M.C. Escher’s use of geometry.
Find applications for the golden ratio .
Describe the importance of circles.
Investigate what the ancient Greeks knew about geometry.
What does congruency mean?
Study the uses of Euler’s formula.
How do CT scans relate to geometry?
Why do we need n-dimensional vectors?
How can you solve Heesch’s problem?
What are hypercubes?
Analyze the use of geometry in Picasso’s paintings.

➗ Calculus Topics to Write a Paper on

You can describe calculus as a more complicated algebra. It’s a study of change over time that provides useful insights into everyday problems. Applied calculus is required in a variety of fields such as sociology, engineering, or business. Consult this list of compelling topics on a calculus paper:

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What are the differences between trigonometry, algebra, and calculus?
Explain the concept of limits.
Describe the standard formulas needed for derivatives.
How can you find critical points in a graph?
Evaluate the application of L’Hôpital’s rule.
How do you define the area between curves?
What is the foundation of calculus?

Calculus was developed by Isaac Newton and Gottfried Leibnitz.

How does multivariate calculus work?
Discuss the use of Stokes’ theorem.
What does Leibniz’s integral rule state?
What is the Itô stochastic integral?
Explore the influence of nonstandard analysis on probability theory.
Research the origins of calculus.
Who was Maria Gaetana Agnesi?
Define a continuous function.
What is the fundamental theorem of calculus?
How do you calculate the Taylor series of a function?
Discuss the ways to resolve Runge’s phenomenon.
Explain the extreme value theorem.
What do we need predicate calculus for?
What are linear approximations?
When does an integral become improper?
Describe the Ratio and Root Tests.
How does the method of rings work?
Where do we apply calculus in real-life situations?

💵 Business Math Topics to Write About

You don’t have to own a company to appreciate business math. Its topics range from credits and loans to insurance, taxes, and investment. Even if you’re not a mathematician, you can use it to handle your finances. Sounds interesting? Then have a look at the following list:

What are the essential skills needed for business math?
How do you calculate interest rates?
Compare business and consumer math.
What is a discount factor?
How do you know that an investment is reasonable?
When does it make sense to pay a loan with another loan?
Find useful financing techniques that everyone can use.
How does critical path analysis work?
Explain how loans work.
Which areas of work utilize operations research?
How do businesses use statistics?
What is the economic lot scheduling problem?
Compare the uses of different chart types.
What causes a stock market crash?
How can you calculate the net present value?
Explore the history of revenue management.
When do you use multi-period models?
Explain the consequences of depreciation.
Are annuities a good investment?
Would the U.S. financially benefit from discontinuing the penny?
What caused the United States housing crash in 2008?
How do you calculate sales tax?
Describe the notions of markups and markdowns.
Investigate the math behind debt amortization.
What is the difference between a loan and a mortgage?

With all these ideas, you are perfectly equipped for your next math paper. Good luck!

What Is Calculus?: Southern State Community College
What Is Mathematics?: Tennessee Tech University
What Is Geometry?: University of Waterloo
What Is Algebra?: BBC
Ten Simple Rules for Mathematical Writing: Ohio State University
Practical Algebra Lessons: Purplemath
Topics in Geometry: Massachusetts Institute of Technology
The Geometry Junkyard: All Topics: Donald Bren School of Information and Computer Sciences
Calculus I: Lamar University
Business Math for Financial Management: The Balance Small Business
What Is Mathematics: Life Science
What Is Mathematics Education?: University of California, Berkeley
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14 May 2024

Why mathematics is set to be revolutionized by AI

Thomas Fink 0

Thomas Fink is the director of the London Institute for Mathematical Sciences, UK.

You can also search for this author in PubMed Google Scholar

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Giving birth to a conjecture — a proposition that is suspected to be true, but needs definitive proof — can feel to a mathematician like a moment of divine inspiration. Mathematical conjectures are not merely educated guesses. Formulating them requires a combination of genius, intuition and experience. Even a mathematician can struggle to explain their own discovery process. Yet, counter-intuitively, I think that this is the realm in which machine intelligence will initially be most transformative.

In 2017, researchers at the London Institute for Mathematical Sciences, of which I am director, began applying machine learning to mathematical data as a hobby. During the COVID-19 pandemic, they discovered that simple artificial intelligence (AI) classifiers can predict an elliptic curve’s rank 1 — a measure of its complexity. Elliptic curves are fundamental to number theory, and understanding their underlying statistics is a crucial step towards solving one of the seven Millennium Problems, which are selected by the Clay Mathematics Institute in Providence, Rhode Island, and carry a prize of US$1 million each. Few expected AI to make a dent in this high-stakes arena.

AI now beats humans at basic tasks — new benchmarks are needed, says major report

AI has made inroads in other areas, too. A few years ago, a computer program called the Ramanujan Machine produced new formulae for fundamental constants 2 , such as π and e . It did so by exhaustively searching through families of continued fractions — a fraction whose denominator is a number plus a fraction whose denominator is also a number plus a fraction and so on. Some of these conjectures have since been proved, whereas others remain open problems.

Another example pertains to knot theory, a branch of topology in which a hypothetical piece of string is tangled up before the ends are glued together. Researchers at Google DeepMind, based in London, trained a neural network on data for many different knots and discovered an unexpected relationship between their algebraic and geometric structures 3 .

How has AI made a difference in areas of mathematics in which human creativity was thought to be essential?

First, there are no coincidences in maths. In real-world experiments, false negatives and false positives abound. But in maths, a single counterexample leaves a conjecture dead in the water. For example, the Pólya conjecture states that most integers below any given integer have an odd number of prime factors. But in 1960, it was found that the conjecture does not hold for the number 906,180,359. In one fell swoop, the conjecture was falsified.

Second, mathematical data — on which AI can be trained — are cheap. Primes, knots and many other types of mathematical object are abundant. The On-Line Encyclopedia of Integer Sequences (OEIS) contains almost 375,000 sequences — from the familiar Fibonacci sequence (1, 1, 2, 3, 5, 8, 13, ...) to the formidable Busy Beaver sequence (0, 1, 4, 6, 13, …), which grows faster than any computable function. Scientists are already using machine-learning tools to search the OEIS database to find unanticipated relationships.

DeepMind AI outdoes human mathematicians on unsolved problem

AI can help us to spot patterns and form conjectures. But not all conjectures are created equal. They also need to advance our understanding of mathematics. In his 1940 essay A Mathematician’s Apology , G. H. Hardy explains that a good theorem “should be one which is a constituent in many mathematical constructs, which is used in the proof of theorems of many different kinds”. In other words, the best theorems increase the likelihood of discovering new theorems. Conjectures that help us to reach new mathematical frontiers are better than those that yield fewer insights. But distinguishing between them requires an intuition for how the field itself will evolve. This grasp of the broader context will remain out of AI’s reach for a long time — so the technology will struggle to spot important conjectures.

But despite the caveats, there are many upsides to wider adoption of AI tools in the maths community. AI can provide a decisive edge and open up new avenues for research.

Mainstream mathematics journals should also publish more conjectures. Some of the most significant problems in maths — such as Fermat’s Last Theorem, the Riemann hypothesis, Hilbert’s 23 problems and Ramanujan’s many identities — and countless less-famous conjectures have shaped the course of the field. Conjectures speed up research by pointing us in the right direction. Journal articles about conjectures, backed up by data or heuristic arguments, will accelerate discovery.

Last year, researchers at Google DeepMind predicted 2.2 million new crystal structures 4 . But it remains to be seen how many of these potential new materials are stable, can be synthesized and have practical applications. For now, this is largely a task for human researchers, who have a grasp of the broad context of materials science.

Similarly, the imagination and intuition of mathematicians will be required to make sense of the output of AI tools. Thus, AI will act only as a catalyst of human ingenuity, rather than a substitute for it.

Nature 629 , 505 (2024)

doi: https://doi.org/10.1038/d41586-024-01413-w

He, Y.-H., Lee, K.-H., Oliver, T. & Pozdnyakov, A. Preprint at arXiv https://doi.org/10.48550/arXiv.2204.10140 (2024).

Raayoni, G. et al. Nature 590 , 67–73 (2021).

Article PubMed Google Scholar

Davies, A. et al. Nature 600 , 70–74 (2021).

Merchant, A. et al. Nature 624 , 80–85 (2023).

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166 Extraordinary Math Research Topics For Your Papers

$math research topics$

Math research topics cover various genres from which students can choose. Many people think that a research project on a math topic is dull. However, mathematics can be a wonderful and vivid field. Since it’s a universal language, mathematics can describe anything and everything, from galaxies that orbit each other to music. However, the broad nature of this study field also makes selecting a research paper difficult. That’s because learners want to pick interesting topics that will impress educators to award them top scores. This article lists the best math research paper topics. It’s useful because it inspires students to select or customize topics for their academic essays without much struggle.

What Are The Different Types Of Math?

As hinted, math covers several genres. Here are the primary types of mathematics:

Geometry: It’s a math branch that deals with the shapes, size, and relative position of figures. Many people consider geometry a practical math branch because it examines figures, shapes, sizes, and features of various entities, including parts like solids, lines, surfaces, lines, and angles. Algebra: It assists in solving equations and manipulating symbols. This branch helps students represent unknown quantities with alphabets and use them alongside numbers. Calculus: This area is vital in determining rates of change, such as velocity and acceleration. Arithmetic: Arithmetic is the most common and oldest math branch, encompassing basis number operations. These operations include subtraction, addition, divisions, and multiplications, and some schools shorten it as BODMAS. Statistics and Probability: They help analyze numerical data to make predictions. Probability is about chances, while statistics entails handling different data using various techniques. Trigonometry: It assists in calculating angles and distances between points. It mainly deals with triangles’ relationships, sides, and curves.

Now that you understand the types of mathematics, it’s easier to select a suitable research topic. The following are some of the best topic ideas in math.

Undergraduate Math Research Topics

Maybe you’re pursuing your undergraduate studies. However, you have challenges comprehending math topics, yet the professor expects you to write a superior paper. In that case, here’s a list of engaging research topics in math to consider for your essays.

An in-depth comprehension of the meaning of discrete random variables in math and their identification
Math evolution- Comprehending the Gauss-Markov
Primary math theorems- Investigating how they work
Continuous stochastic process- Exploring its role in the math process
Analyzing the Dempster-Shafer theory
The application of the transferable belief model
Exploring the use of math in artificial intelligence
The application of mathematics in daily life
Algebra and its history
Math and culture- What’s the relationship?
How drawing and painting could help with mathematics
Ways to boost math interest among learners
The social and political significance of learning mathematics
Circles and their relevance in mathematics
Challenges to math learning in public schools
Prove the use of F-Algebras
Understanding the meaning of abstract algebra
Discuss geometry and algebra
How acute square triangulation works
Discuss the essence of right triangles
Why non-Euclidean geometry should be compulsory for math students
Investigating number problems
Discuss the meaning of Dirac manifolds
How geometry influences chemistry and physics
Riemannian manifolds’ application in the Euclidean space

These are exciting math topics for undergraduate students. Nevertheless, prepare adequate time and resources to investigate any of these titles to draft a winning essay. You might have to provide theoretical and practical assessments when writing your essay.

Math Research Topics for High School Learners

Maybe your high school teacher asked you to write a research paper. Choosing a familiar topic is an excellent way to get a high grade. Here are some of the best math research paper topics for high school.

How to draw a chart representing the financial analysis of a prominent company over the last five years
How to solve a matrix- The vital principles and formulas to embrace
Exploring various techniques for solving finance and mathematical gaps
Discount factor- Why it’s crucial for learners and ways to achieve it
Calculating the interest rate and its essence in the banking industry
Why imaginary numbers are important
Investigating the application of math in the workplace
Explain why learners hate mathematics teachers
What makes math a complex subject?
Is making math compulsory in high school a good thing?
How to solve a dice question from a probability perspective
Understanding the Binomial theorem and its essence
Investigating Egyptian mathematics
Hyperbola- Understanding it and its use in math
When should students use calculators in class?
How to solve linear equations
Is the Pythagoras theorem important in math?
The interdependence between math and art
Philosophy’s role in math
Numerical data overview

High school learners can pick any of these titles and develop them into an essay. Nevertheless, they should prepare to spend some time investigating their topics to write pieces that will impress their educators. Titles that address math history and its influence on education can also suit high school students. However, learners should select titles that fulfil the academic requirements set by the educators.

Applied Math Research Topics

As a branch, applied math deals with mathematical methods and their real-life applications. These methods are manifest in engineering, finance, medicine, biology, physics, and others. Here are some of the exciting topics in this field.

Dimensions for examining fingerprints
Computer tomography and its significance
Step-stress modelling- What is its importance?
Explain the essence of data mining- How does it benefit the banking sector?
A detailed examination of nonlinear models
How genes discovery helps determine unhealthy and healthy patients
Algorithms and their role in probabilistic modelling
Mathematicians and their importance in robots’ development
Mathematicians’ role in crime prevention and data analysis
The essence of Law of Motion by Isaac in real life
The importance of math in energy conservation
Math and its role in quantum theory
Analyzing the Lorentz symmetry features
Evaluating the processing of the statistical signal in detail
Explain the achievement of Galilean Transformation

These are exciting ideas to explore when writing a research paper in applied math. Nevertheless, take your time to carefully and extensively research your preferred title to write a high-quality essay. Students should also note that some topics in this category require specialized knowledge to write superior papers.

It’s a challenge to write a paper for a high grade. Sometimes every student need a professional help with college paper writing. Therefore, don’t be afraid to hire a writer to complete your assignment. Just write a message “Please, write custom research paper for me” and get time to relax. Contact us today and get a 100% original paper.

Interesting Math Research Topics

Maybe you’re among the learners that prefer working with exciting ideas. In that case, this category has topics that will interest you.

The uses of numerical analysis in machine learning
Foundations and philosophical problems
Convex versus Concave in geometry
Homological algebra- What is its purpose?
Is math useful in cryptography
Probability theory and random variable
Functional analysis- What are its four conditions?
Vector calculus versus multivariable
Mathematics and logicist definitions
Ways to apply the number theory in daily life
Studying complex math equations
How to calculate mode, median, and mean
Understanding the meaning of the Scholz conjecture
The definition of the past correspondence problem
Computational maths- What are its classes?
Multiplication table and its importance
What the Boolean satisfiability problem means for a learner
Understanding the linear speedup theory in mathematics
The Turing machine description
Understanding the Markov algorithm
Investigating the similarities and differences between Buchi automation and Pushdown automation
What is the meaning of Tree automation?
Describing the enclosing sphere method and its use in combinations
Egyptian pyramids and calculus
Analyzing De Finetti theorem in statistics and probability
Examining the congruence meaning in math
Application and purpose of calculus in the banking industry
Jean d’Alembert’s most famous works
Boolean algebra- What are its essential elements
Isaac Newton- His contribution, life, and time in math
Understanding the meaning of Sphericon
What is the purpose of Martingales?
Gauss times, energy, and contributions to math
Jakob Bernoulli- Exploring his famous works
A brief history of math

Some learners think writing a math essay is complex and tedious. However, you can find a topic you will enjoy working with throughout the project. These are exciting ideas to explore in research papers. However, prepare to spend sufficient time investigating your chosen title to write a winning paper, although these are generally relaxing titles for math papers and essays.

Math Research Topics for Middle School

Some middle school students worry about the math topics for their research. However, they can choose unique titles that will impress their teachers. Here are some of these ideas.

The impacts of standard exam curriculum on math education
Why is learning math so tricky?
What is the meaning of the commutative ring in algebra?
The Artin-Wedderburn theorem and its meaning
How monopolists and epimorphisms differ
Understanding the Jacobson density theorem
How linear approximations work
Root and ratio test definition
Statistics role in business
Economic lot scheduling- What does it mean?
Causes of the stock market crash
How many traders contribute to the New York Stock Exchange
The history of revenue management
Financial signs of an excellent investment
Depreciation and its odds
How a poor currency can benefit a country
How math helps with debt amortization
Ways to calculate a person’s net worth
Distinctions in algebra, trigonometry, and calculus
Discussing the beginning of calculus
The essence of stochastic in math
The meaning of limits in math
Ways to identify a critical point in a graph
Nonstandard analysis- What does it mean in the probability theory?
Continuous function description and meaning
Calculus- What are its primary principles?
Pythagoras theorem- What are its central tenets?
Calculus applications in finance
Theorem value in math
The application of linear approximations

This list has some of the best titles for middle school learners. But they also require some research to write superior essays. However, finding information on such topics is relatively easy, making them suitable for middle school students.

Math Research Topics for College Students

Maybe you’re pursuing college studies and need a title for a math research paper. In that case, here are exciting titles to consider for your essay.

What is the purpose of n-dimensional spaces?
Card counting- How does it work?
How continuous probability and discrete distribution differ
Understanding encryption- How Does it work?
Extremal problems- Investigating them in discrete geometry
The Mobius strip- Examining the topology
Why can a math problem be unsolvable?
Comparing different statistical methods
Explain the vital number theory concepts
Analyzing the polynomial functions’ degrees
Ways to divide complex numbers
Describe the prize problems with the millennium
The reasons for the unsolved Riemann hypothesis
Methods of solving Sudoku with math
Explain the fractals formation
Describe the evolution of math
Explore different types of Tower of Hanoi solutions
Discuss the uses of Napier’s bones
With examples, explain the chaos theory
Why are mathematical equations important all the time?
Fisher’s fundamental theorem and natural selection- Why are they important?

College professors expect students to draft papers with relevant and valuable information. These are relevant titles for college students. However, they require extensive research to write winning papers.

Cool Math Topics to Research

Maybe you don’t need a complex topic for your research paper. In that case, consider any of these ideas for your essay. If you have a problem writing even with these topics and you’re thinking: “solve my math for me,” you can always reach out to our service.

How contemporary architectural designs use geometry
What makes some math equations complex?
Ways to solve the Rubik’s cube
Discuss the meaning of prescriptive statistical and predictive analysis
Understanding the purpose of the chaos theory
What limits calculus?- Provide relevant examples
A comparison of universal and abstract algebra- How do they differ?
The relationship between probability and card tricks
Pascal’s Triangle- What does it mean?
Mobius strip- What are its features in geometry?
Multiple probability ideas- A brief overview
Discuss the meaning of the Golden Ration in Renaissance period paintings
How checkers and chess matter in understanding mathematics
Ways to measure infinity
Evaluating the Georg Contor theory
Are hexagons the most balanced shapes in the world?
The Koch snowflake- Explain the iterations
The history of various number types and their use
Game theory use in social science
Five math types with significant benefits in computer science

These are some of the most excellent math education research topics. However, they also require extensive research to write high-quality papers.

Enlist the Best College Research Paper Writing Service

Perhaps, you have a topic for your paper but not the time to write a winning piece. Maybe you’re not confident in your research, analytical, and writing skills. Thus, you’re unsure that you can write an essay that will compel your educator to award you the highest grade in your class. Well, you’re not the only one. Many students seek cheap research papers due to varied reasons. Whether it’s limited time and resources or a lack of the necessary skills and experience in academic paper writing, our crew can help you. We offer affordable college paper writing services and help in various math branches. Our experts can assist you if you need help with math research topics for high school students, college, or undergraduates. We are a professional team with a reputation for providing the best-rated academic writing assistance. Whether in university, college, or high school, our crew will offer the service you need to excel academically. Contact us now for cheap and reliable help with your academic essays.

202 Math Research Topics: List To Vary Your Ideas

$202 Math Research Topics$

Mathematics is an exceptional field of study dealing primarily with numbers. It also deals with structures, formulas, shapes, spaces, and quantities of where they are contained.

Maths encompasses different types of computations that are applied in the real world.

Math requires a lot of analysis. This is why there are different types of maths. They all encompass different subjects and deal with different things. What are the types of maths?

Arithmetic This is perhaps the commonest type or branch of maths. It is one of the oldest and it encompasses basic numbers operations. These are addition, subtraction, multiplication, and divisions; in some schools, the short word for it is BODMAS. This is known as the Bracket of Division, Multiplication, Addition, and Subtraction. Algebra This is where unknown quantities are represented by alphabets and used along with numbers. The letters these unknown quantities are represented by are usually A, B, X, and Y, and they could also be symbols. Geometry This is considered one of the practical branches of maths as it examines sizes, shapes, figures, and the features of these entities. The most common parts of geometry are lines, points, solids, surfaces, and angles.

There are many other types but the above are the most popular. Others are trigonometry, topology, mathematical analysis, calculus, probability, statistics, and a few others.

As many students find it hard to develop maths research topics on their own, this is a chance for you. It’s okay to be worked up when you can’t find undergraduate math research topics that fit your project, essay or paper choices. This article will provide custom maths education research topics for your use. Before that, how do you structure your math essay or paper?

How to Structure Your Math Essay or Paper

Structuring your essay or paper may require that you’ve been reading critical math journals. Reading them could have made it easy to understand how to structure your paper. However, you don’t have to worry if you haven’t. Structuring your paper as expected is an essential part of writing and you’ll know about it in this section. Before you learn that, how do you choose a topic?

Choosing a Topic to Discuss

One of the difficult yet significant parts of any math essay or paper is choosing your topic. This is because you need to solve a problem or engage in a subject that has got less attention. You also need to understand the background to the subject you want to discuss as you can’t write blindly.

You must also be able to articulate your thoughts well as you must show visible knowledge before you commence the research and writing. How do you go about this? You can consider reading existing research. You can even take notes during classes to see the areas you think more work needs to be done.

After choosing your topic, conduct your research to see if you can investigate the sphere. If you can, you need to structure your research thus:

The Background This includes the discussion on what the essay is about. Depending on what you’re writing about, you need to discuss the primary concepts, including the history of some terms, where essential, in this section. This section is more like general information about the subject you want to discuss with your paper. This helps your readers familiarize themselves with your intended discussion. The Introduction This is where the main ideas behind your essays (and the solutions you hope to proffer) are tended to the readers. This is where you also explain the symbols you’ll use and the principles which are required in your essay. Aside from this, you need to state the basic issues, the solutions you could offer, the laws which are essential to discuss to make your work comprehensible. The Main Body This is where you elaborate on your findings. You need to state the research problem, the formulas, the theories you’ll use in tackling the problem, and many other things. You also need to introduce different sections of maths into the main body which is divided by paragraphs and/or chapters as well as mathematical analysis where needed. Implications This is the last part of your essay or paper. This is where you share the insights of your research with your readers. You offer short explanations of the things you have discussed. If you have treated a subject in applied mathematics, this is where you give summaries of how math is connected to human life and the strategic importance of these to people.

By adhering to this structure, you would have crafted the best rated and high-quality maths paper. Furthermore, remember you always have an option to get help with dissertations and save your time. Since it is sometimes challenging to choose cool maths topics to research on your own, these are some for you:

Research Topics in Math

Math is a broad subject. There is a study of the history of math as well as its influence in education, amongst many other sub-sections. If you’d like to create stunning research, you may choose to discuss any of these research topics in math to fulfill one of your academic requirements:

What are the distinctions between commutative and noncommutative algebra?
Discuss the methods of factoring quadratics
Types of sequences and your understanding of them
Partial fractions: what are they and how do they work?
Logarithms: what are they and how do they work?
An overview of Gaussian elimination
An overview of Brun’s constant relevant
A description of the effect of dyscalculia on daily student lives
Describe Descartes’s Dukes of Signs and their application
Greeks and geometry: discuss
Describe Euler’s formula
The progression in the study of math
Congruence meaning and methods
Describe the correlation of CT scans to geometry
Hypercubes and how they work
The basis of Cramer’s rule
The examination of Archimedean solids
Projective geometry and why it’s studied
Types of Transformations and the available types
Picasso’s works and the application of geometry
Difference between the conventional and unconventional approaches to teaching
Math education and the process of Improvement in the US
Rhombicosidodecahedron and how it operates in real life
What are the STEM career fields and why are they important?
Why women are needed in STEM
The goals of teaching maths
How to teach maths to special students
The correlation between maths and accounting
The distinction between computer programming and applied maths
Applied maths and its dynamics
Processes of solving Heesch’s problem
Why should kids learn equations?
History of calculus
Why there is a need for math camps in schools
The need for more maths competition in the US
Methods of draining flight schedule for a country
Why are some math problems unsolved?
Discuss the consequences of the gender gap in math students
Encryption and prime numbers: how do they apply?
The significance of maths in day to day living.

Undergraduate Math Research Topics

As an undergraduate, you may also have a difficult time wrapping your head around math research topics. You may need to offer both practical and theoretical assessments while writing your paper or essay. The following are undergraduate math research topics:

Show the proofs of what F-algebras are used
Abstract algebra, what does it mean?
Algebra and geometry: discuss
Acute square triangulation: how it works
Right triangles: discuss their importance
Discuss number problems
Why every math student should study non-Euclidean geometry
Dirac manifolds and what it means
Influence of geometry in physics, chemistry, and others
The application of Riemannian manifolds in the Euclidean space
How to improve your mathematical thinking ability
Technology in maths: how is it used?
Studies of maths in Europe
Math anxiety and what it truly means
Standardized testing and the goals of such
Challenges of learning maths from public schools
The significance of circles in maths
The political and social significance of learning maths
Research into how to increase student interest in maths
How painting and drawing could help with maths
Relationship of culture and maths
History of algebra
Role of maths in everyday life
How math is used in Artificial intelligence
The transferable belief model and its application
An analysis of the Dempster-Shafer theory
The role of continuous stochastic process in mathematics
The major math theorems: discuss how they work
Understanding the Gauss-Markov: The Evolution of maths
Discrete random variable: an in-depth understanding of what it means in math and how to identify one.

Math Research Topics for High School Students

As a high school student writing a research paper, one way to get high grades is to write what you know. If you know any math research paper topics for high school, they are the topics you should pick. You can consider:

Hyperbola: what it is and how it’s used in math
When to use a calculator in class
How to find solutions to linear equations
The need for Pythagoras theorem in maths
The role of art in maths and vice versa
Role of philosophy in maths
An overview of numerical data
Egyptian mathematics explained
Binomial theorem and its importance
Probability, and how to solve a question on dice
Why is math made compulsory in schools?
Why do students hate maths?
Why do students hate math teachers?
How is math applied in the workplace?
What are imaginary numbers and why are they needed
How to calculate the interest rate and what is their importance in the banking sector?
Discount factor: how is it achieved and why is it important for students?
Types of techniques to be used while finding solutions to mathematical and finance gaps
Solving a matrix: what are the important formulas and principles to embrace?
How to create a chart on a company’s financial analysis for the past 5 years.

Interesting Math Research Topics

Writing a mathematical essay may seem complex to you if you can’t find simple topics to write about. There are many easy topics which are also general in maths. If you want to choose a relaxing topic for your math essay or paper, you can write about the following:

The basic elements of Boolean algebra
The life, time, and contribution of Isaac Newton to maths
Sphericon and what it means
Martingales and what they mean
Hyperboloid and importance in geometry
Describe the life, times, and contribution of Gauss to maths
The most famous work of Jakob Bernoulli
The most famous work of Jean d’Alembert
Meaning and application of calculus in the banking field
The meaning of congruence in math
Analysis of De Finetti theorem in probability and statistics
Describe Egyptian pyramids in concert with calculus
Describe the enclosing sphere technique as used in combinatorics
Tree automation meaning
Pushdown automaton and Buchi automaton: differences and similarities
What is the Markov algorithm?
Describe what a Turing machine is
What is the linear speedup theory in math?
The Boolean satisfiability problem and what it means for students
Why is the multiplication table important?
Computational maths and its classes
What does the post correspondence problem mean?
What does the Scholz conjecture mean?
How to calculate mean, median, and mode
A study of the most difficult equations in math.

Cool Math Topics to Research

As a student of any level, you may love to create math topics that are not exactly complex. These are topics that lean on the history of maths, math education research topics, and others. Consider these math research topics for college students for your next essay or paper:

Discuss what the Golden Ratio means in the paintings of the Renaissance period
How to learn math
An overview of the multiple ideas to probability
How chess and checkers is essential in understanding mathematics
How Pythagorean theorem is applied in real-life maths
How to measure infinity
The features of Mobius strip in geometry
Describe what is meant by the Pascal’s Triangle
Evaluate the Georg Cantor set theory
What is the history of the number types?
How does probability relate to card tricks?
Compare and contrast abstract and universal algebra
Describe Euclid’s role in the evolution of maths
Evaluate the role of Indians in maths
Explain the limits of calculus
Discuss what predictive and prescriptive statistical analysis means
What does chaos theory mean?
Explain how to solve the Rubik’s Cube
Why are some math equations so complex?
How is geometry used in contemporary architectural designs?

Math Research Topics for Middle School

It’s okay to be worried about math topics for your research as a middle school student. There are still different unique topics that are rebranded from existing ones. You can find some of the right math research paper topics for you here:

The role of statistics in business
Definition of economic lot scheduling
Why stock market crash
The contribution of many traders in the New York Stock Exchange
Revenue management and its history
What are the financial indicators of a good investment?
What are the odds of depreciation?
How can any country benefit from the poor currency?
Describe debt amortization and how math helps
How to calculate net worth
Distinctions in calculus, trigonometry, and algebra
How did calculus start?
How did trigonometry start?
Why is Ito stochastic important in math?
What do limits in math mean?
How to know critical points in graphs
What does nonstandard analysis in the probability theory mean?
Describe continuous function
The main principles of calculus
The main principles of Pythagoras theorem
Application of calculus in finance
Value theorem in math
Ratio and root test definition
Linear approximations and how they work
What is the Jacobson density theorem?
Similarities and differences between epimorphisms and monopolists
What does the Artin-Wedderburn theorem mean?
Commutative ring and its meaning in algebra
How difficult is it to teach maths?
How standards examination curriculum affects math education.

Applied Math Research Topics

Applied math is a branch which deals with the application of mathematical methods in real life. These are manifested by applications in finance, physics, engineering, biology, medicine, and others. Through specialized knowledge, applied math is made possible. These are some topics for you in this area:

How discovering genes can help determine healthy and unhealthy patients
Role of algorithms in probabilistic modeling
The need for mathematicians in developing robots
The role of mathematicians in crime data analysis and prevention
How did Isaac’s Laws of Motion help in real life?
How math helped with energy conservation
The role of math in quantum theory
Analyze the features of the Lorentz symmetry
Evaluate statistical signal processing in details
Discuss how Galilean Transformation was achieved
Examine nonlinear models
Elucidate on the importance of data mining in banking
The importance of step-stress modeling
The significance of computer tomography
What are the dimensions used in examining fingerprints?

Math Research Topics for College Students

As college students, you are at a critical level. You need maths topics for your essays and paper. You may also need them to prepare for your exams. These are some math research topics for you:

Evolution of mathematics
Explore the varieties of the Tower of Hanoi solutions
Discuss how to use Napier’s bones
Give examples of chaos theory and explain
Discuss the important mathematical equations of all times
Examine the nitty-gritty of barcodes
What is the Traveling Salesman Problem?
Natural selection and Fisher’s fundamental theorem of understanding it
The Influence of math in biology
The Influence of math in chemistry
What is quantum computing?
How to solve extremal problems in maths
Analyze the meaning of fractals
Discuss Einstein’s field equation theory
Who created computer vision and object recognition?
Five formulas and how they are applied
Give three approaches to understanding maths
Explain the origin and importance of algebra
What do you know about the Fibonacci sequence?
Trace the origin of math
How does math help in geography?
What does the operator spaces notion mean?

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Mathematics Theses, Projects, and Dissertations

Theses/projects/dissertations from 2024 2024.

On Cheeger Constants of Knots , Robert Lattimer

Information Based Approach for Detecting Change Points in Inverse Gaussian Model with Applications , Alexis Anne Wallace

Theses/Projects/Dissertations from 2023 2023

DNA SELF-ASSEMBLY OF TRAPEZOHEDRAL GRAPHS , Hytham Abdelkarim

An Exposition of the Curvature of Warped Product Manifolds , Angelina Bisson

Jackknife Empirical Likelihood Tests for Equality of Generalized Lorenz Curves , Anton Butenko

MATHEMATICS BEHIND MACHINE LEARNING , Rim Hammoud

Statistical Analysis of Health Habits for Incoming College Students , Wendy Isamara Lizarraga Noriega

Reverse Mathematics of Ramsey's Theorem , Nikolay Maslov

Distance Correlation Based Feature Selection in Random Forest , Jose Munoz-Lopez

Constructing Hyperbolic Polygons in the Poincaré Disk , Akram Zakaria Samweil

KNOT EQUIVALENCE , Jacob Trubey

Theses/Projects/Dissertations from 2022 2022

SYMMETRIC GENERATIONS AND AN ALGORITHM TO PROVE RELATIONS , Diddier Andrade

The Examination of the Arithmetic Surface (3, 5) Over Q , Rachel J. Arguelles

Error Terms for the Trapezoid, Midpoint, and Simpson's Rules , Jessica E. Coen

de Rham Cohomology, Homotopy Invariance and the Mayer-Vietoris Sequence , Stacey Elizabeth Cox

Symmetric Generation , Ana Gonzalez

SYMMETRIC PRESENTATIONS OF FINITE GROUPS AND RELATED TOPICS , Samar Mikhail Kasouha

Simple Groups and Related Topics , Simrandeep Kaur

Homomorphic Images and Related Topics , Alejandro Martinez

LATTICE REDUCTION ALGORITHMS , Juan Ortega

THE DECOMPOSITION OF THE SPACE OF ALGEBRAIC CURVATURE TENSORS , Katelyn Sage Risinger

Verifying Sudoku Puzzles , Chelsea Schweer

AN EXPOSITION OF ELLIPTIC CURVE CRYPTOGRAPHY , Travis Severns

Theses/Projects/Dissertations from 2021 2021

Non-Abelian Finite Simple Groups as Homomorphic Images , Sandra Bahena

Matroids Determinable by Two Partial Representations , Aurora Calderon Dojaquez

SYMMETRIC REPRESENTATIONS OF FINITE GROUPS AND RELATED TOPICS , Connie Corona

Symmetric Presentation of Finite Groups, and Related Topics , Marina Michelle Duchesne

MEASURE AND INTEGRATION , JeongHwan Lee

A Study in Applications of Continued Fractions , Karen Lynn Parrish

Partial Representations for Ternary Matroids , Ebony Perez

Theses/Projects/Dissertations from 2020 2020

Sum of Cubes of the First n Integers , Obiamaka L. Agu

Permutation and Monomial Progenitors , Crystal Diaz

Tile Based Self-Assembly of the Rook's Graph , Ernesto Gonzalez

Research In Short Term Actuarial Modeling , Elijah Howells

Hyperbolic Triangle Groups , Sergey Katykhin

Exploring Matroid Minors , Jonathan Lara Tejeda

DNA COMPLEXES OF ONE BOND-EDGE TYPE , Andrew Tyler Lavengood-Ryan

Modeling the Spread of Measles , Alexandria Le Beau

Symmetric Presentations and Related Topics , Mayra McGrath

Minimal Surfaces and The Weierstrass-Enneper Representation , Evan Snyder

ASSESSING STUDENT UNDERSTANDING WHILE SOLVING LINEAR EQUATIONS USING FLOWCHARTS AND ALGEBRAIC METHODS , Edima Umanah

Excluded minors for nearly-paving matroids , Vanessa Natalie Vega

Theses/Projects/Dissertations from 2019 2019

Fuchsian Groups , Bob Anaya

Tribonacci Convolution Triangle , Rosa Davila

VANISHING LOCAL SCALAR INVARIANTS ON GENERALIZED PLANE WAVE MANIFOLDS , Brian Matthew Friday

Analogues Between Leibniz's Harmonic Triangle and Pascal's Arithmetic Triangle , Lacey Taylor James

Geodesics on Generalized Plane Wave Manifolds , Moises Pena

Algebraic Methods for Proving Geometric Theorems , Lynn Redman

Pascal's Triangle, Pascal's Pyramid, and the Trinomial Triangle , Antonio Saucedo Jr.

THE EFFECTIVENESS OF DYNAMIC MATHEMATICAL SOFTWARE IN THE INSTRUCTION OF THE UNIT CIRCLE , Edward Simons

CALCULUS REMEDIATION AS AN INDICATOR FOR SUCCESS ON THE CALCULUS AP EXAM , Ty Stockham

Theses/Projects/Dissertations from 2018 2018

PROGENITORS, SYMMETRIC PRESENTATIONS AND CONSTRUCTIONS , Diana Aguirre

Monomial Progenitors and Related Topics , Madai Obaid Alnominy

Progenitors Involving Simple Groups , Nicholas R. Andujo

Simple Groups, Progenitors, and Related Topics , Angelica Baccari

Exploring Flag Matroids and Duality , Zachary Garcia

Images of Permutation and Monomial Progenitors , Shirley Marina Juan

MODERN CRYPTOGRAPHY , Samuel Lopez

Progenitors, Symmetric Presentations, and Related Topics , Joana Viridiana Luna

Symmetric Presentations, Representations, and Related Topics , Adam Manriquez

Toroidal Embeddings and Desingularization , LEON NGUYEN

THE STRUGGLE WITH INVERSE FUNCTIONS DOING AND UNDOING PROCESS , Jesus Nolasco

Tutte-Equivalent Matroids , Maria Margarita Rocha

Symmetric Presentations and Double Coset Enumeration , Charles Seager

MANUAL SYMMETRIC GENERATION , Joel Webster

Theses/Projects/Dissertations from 2017 2017

Investigation of Finite Groups Through Progenitors , Charles Baccari

CONSTRUCTION OF HOMOMORPHIC IMAGES , Erica Fernandez

Making Models with Bayes , Pilar Olid

An Introduction to Lie Algebra , Amanda Renee Talley

SIMPLE AND SEMI-SIMPLE ARTINIAN RINGS , Ulyses Velasco

CONSTRUCTION OF FINITE GROUP , Michelle SoYeong Yeo

Theses/Projects/Dissertations from 2016 2016

Upset Paths and 2-Majority Tournaments , Rana Ali Alshaikh

Regular Round Matroids , Svetlana Borissova

GEODESICS IN LORENTZIAN MANIFOLDS , Amir A. Botros

REALIZING TOURNAMENTS AS MODELS FOR K-MAJORITY VOTING , Gina Marie Cheney

Solving Absolute Value Equations and Inequalities on a Number Line , Melinda A. Curtis

BIO-MATHEMATICS: INTRODUCTION TO THE MATHEMATICAL MODEL OF THE HEPATITIS C VIRUS , Lucille J. Durfee

ANALYSIS AND SYNTHESIS OF THE LITERATURE REGARDING ACTIVE AND DIRECT INSTRUCTION AND THEIR PROMOTION OF FLEXIBLE THINKING IN MATHEMATICS , Genelle Elizabeth Gonzalez

LIFE EXPECTANCY , Ali R. Hassanzadah

PLANAR GRAPHS, BIPLANAR GRAPHS AND GRAPH THICKNESS , Sean M. Hearon

A Dual Fano, and Dual Non-Fano Matroidal Network , Stephen Lee Johnson

Mathematical Reasoning and the Inductive Process: An Examination of The Law of Quadratic Reciprocity , Nitish Mittal

The Kauffman Bracket and Genus of Alternating Links , Bryan M. Nguyen

Probabilistic Methods In Information Theory , Erik W. Pachas

THINKING POKER THROUGH GAME THEORY , Damian Palafox

Indicators of Future Mathematics Proficiency: Literature Review & Synthesis , Claudia Preciado

Ádám's Conjecture and Arc Reversal Problems , Claudio D. Salas

AN INTRODUCTION TO BOOLEAN ALGEBRAS , Amy Schardijn

The Evolution of Cryptology , Gwendolyn Rae Souza

Theses/Projects/Dissertations from 2015 2015

SYMMETRIC PRESENTATIONS AND RELATED TOPICS , Mashael U. Alharbi

Homomorphic Images And Related Topics , Kevin J. Baccari

Geometric Constructions from an Algebraic Perspective , Betzabe Bojorquez

Discovering and Applying Geometric Transformations: Transformations to Show Congruence and Similarity , Tamara V. Bonn

Symmetric Presentations and Generation , Dustin J. Grindstaff

HILBERT SPACES AND FOURIER SERIES , Terri Joan Harris Mrs.

SYMMETRIC PRESENTATIONS OF NON-ABELIAN SIMPLE GROUPS , Leonard B. Lamp

Simple Groups and Related Topics , Manal Abdulkarim Marouf Ms.

Elliptic Curves , Trinity Mecklenburg

A Fundamental Unit of O_K , Susana L. Munoz

CONSTRUCTIONS AND ISOMORPHISM TYPES OF IMAGES , Jessica Luna Ramirez

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A Research Guide
Research Paper Topics

25 Maths Research Paper Topics

Useful information: Do research papers have a thesis statement?

A List of 25 Research Topics in Mathematics

The history of mathematics
Greek math theories and inventions
The math of ancient great buildings
The math of Universe. Universal constants
Astronomy and math. How can we know about what we have never seen?
The greatest mathematicians and their role in the history
The greatest math invention in history
Euclidean and non-Euclidean geometries. Going beyond the space we used to
Unsolved problems in math
Math and Quantum theory
Math and Philosophy
Art and math: are they connected?
Number theory
Math and the AI concepts
Math in nature
Math in our daily life
Math and Probabilities
Fundamental mathematical theorems
Sports and math
Is Math unique for humans only?
STEM Education: why math is so important?
Math and formal logic
The math of time
Math and gender

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Ivan Specht decided to employ his love of math during pandemic, which led to contact-tracing app, papers, future path

Part of the commencement 2024 series.

A collection of stories covering Harvard University’s 373rd Commencement.

Ivan Specht started at Harvard on track to study pure mathematics. But when COVID-19 sent everyone home, he began wishing the math he was doing had more relevance to what was happening in the world.

Specht, a New York City native, expanded his coursework, arming himself with statistical modeling classes, and began to “fiddle around” with simulating ways diseases spread through populations. He got hooked. During the pandemic, he became one of only two undergraduates to serve on Harvard’s testing and tracing committee, eventually developing a prototype contact-tracing app called CrimsonShield.

Specht took his curiosity for understanding disease propagation to the lab of computational geneticist Pardis Sabeti , professor in Organismic and Evolutionary Biology at Harvard and member of the Broad Institute, known for her work sequencing the Ebola virus in 2014 . Specht, now a senior, has since co-authored several studies around new statistical methods for analyzing the spread of infectious diseases, with plans to continue that work in graduate school.

“Ivan is absolutely brilliant and a joy to work with, and his research accomplishments already as an undergraduate are simply astounding,” Sabeti said. “He is operating at the level of a seasoned postdoc.”

His senior thesis, “Reconstructing Viral Epidemics: A Random Tree Approach,” described a statistical model aimed at tackling one of the most intractable problems that plague infectious disease researchers: determining who transmitted a given pathogen to whom during a viral outbreak. Specht was co-advised by computer science Professor Michael Mitzenmacher, who guided the statistical and computational sections of his thesis, particularly in deriving genomic frequencies within a host using probabilistic methods.

Specht said the pandemic made clear that testing technology could provide valuable information about who got sick, and even what genetic variant of a pathogen made them sick. But mapping paths of transmission was much more challenging because that process was completely invisible. Such information, however, could provide crucial new details into how and where transmission occurred and be used to test things such as vaccine efficacy or the effects of closing schools.

Specht’s work exploited the fact that viruses leave clues about their transmission path in their phylogenetic trees, or lines of evolutionary descent from a common ancestor. “It turns out that genome sequences of viruses provide key insight into that underlying network,” said the joint mathematics and statistics concentrator.

Uncovering this transmission network goes to the heart of how single-stranded RNA pathogens survive: Once they infect their host, they mutate, producing variants that are marked by slightly different genetic barcodes. Specht’s statistical model determines how the virus spreads by tracking the frequencies of different viral variants observed within a host.

As the centerpiece of his thesis, he reconstructed a dataset of about 45,000 SARS-CoV-2 genomes across Massachusetts, providing insights into how outbreaks unfolded across the state.

Specht will take his passion for epidemiological modeling to graduate school at Stanford University, with an eye toward helping both researchers and communities understand and respond to public health crises.

A graphic designer with experience in scientific data visualization, Specht is focused not only on understanding outbreaks, but also creating clear illustrations of them. For example, his thesis contains a creative visual representation of those 45,000 Massachusetts genomes, with colored dots representing cases, positioned nearby other “dots” they are likely to have infected.

Specht’s interest in graphics began in middle school when, as an enthusiast of trains and mass transit, he started designing imagined subway maps for cities that lack actual subways, like Austin, Texas . At Harvard, he designed an interactive “subway map” depicting a viral outbreak.

As a member of the Sabeti lab, Specht taught an infectious disease modeling course to master’s and Ph.D. students at University of Sierra Leone last summer. His outbreak analysis tool is also now being used in an ongoing study of Lassa fever in that region. And he co-authored two chapters of a textbook on outbreak science in collaboration with the Moore Foundation.

Over the past three years, Specht has been lead author of a paper in Scientific Reports and another in Cell Patterns , and co-author on two others, including a cover story in Cell . His first lead-author paper, “The case for altruism in institutional diagnostic testing,” showed that organizations like Harvard should allocate COVID-19 testing capacity to their surrounding communities, rather than monopolize it for themselves. That work was featured in The New York Times .

During his time at Harvard, Specht lived in Quincy House and was design editor of the Harvard Advocate, the University’s undergraduate literary magazine. In his free time he also composes music, and he still considers himself a mass transit enthusiast.

In the acknowledgements section of his thesis, he credited Sabeti with opening his eyes to the “many fascinating problems at the intersection of math, statistics, and computational biology.”

“I could fill this entire thesis with reasons I am grateful for Professor Sabeti, but I think they can be summarized by the sense of wonder and inspiration I feel every time I set foot in her lab.”

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Cities as Engines of Opportunities: Evidence from Brazil

Are developing-world cities engines of opportunities for low-wage earners? In this study, we track a cohort of young low-income workers in Brazil for thirteen years to explore the contribution of factors such as industrial structure and skill segregation on upward income mobility. We find that cities in the south of Brazil are more effective engines of upward mobility than cities in the north and that these differences appear to be primarily related to the exposure of unskilled workers to skilled co-workers, which in turn reflects industry composition and complexity. Our results suggest that the positive effects of urbanization depend on the skilled and unskilled working together, a form of integration that is more prevalent in the cities of southern Brazil than in northern cities. This segregation, which can decline with specialization and the division of labor, may hinder the ability of Brazil's northern cities to offer more opportunities for escaping poverty.

We acknowledge the support of Cristian Jara-Figueroa in the initial conceptualization of the empirical strategy. Barza and Viarengo gratefully acknowledges the financial support received from the Swiss National Science Foundation (Principal Investigator: Prof. Dr. Martina Viarengo; Research Grant n. 100018-176454). Hidalgo acknowledges the support of the Agence Nationale de la Recherche grant number ANR-19-P3IA-0004, the 101086712-LearnData-HORIZON-WIDERA-2022-TALENTS-01 financed by European Research Executive Agency (REA) (https://cordis.europa.eu/project/id/101086712), IAST funding from the French National Research Agency (ANR) under grant ANR-17-EURE-0010 (Investissements d'Avenir program), and the European Lighthouse of AI for Sustainability [grant number 101120237-HOR-IZON-CL4-2022-HUMAN-02]. The usual caveats apply. The views expressed herein are those of the authors and do not necessarily reflect the views of the National Bureau of Economic Research.

I have received speaking fees from organizations that organize members that invest in real estate markets, including the National Association of Real Estate Investment Managers, the Pension Real Estate Association and the Association for International Real Estate Investors.

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Pure Mathematics Research

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251+ Math Research Topics [2024 Updated]
251+ Math Research Topics: Beginners To Advanced. Prime Number Distribution in Arithmetic Progressions. Diophantine Equations and their Solutions. Applications of Modular Arithmetic in Cryptography. The Riemann Hypothesis and its Implications. Graph Theory: Exploring Connectivity and Coloring Problems.
181 Math Research Topics
If you are an undergraduate looking for some research topics for your next math paper, you will surely appreciate our list of interesting undergraduate math research topics: Methods to count discrete objects. The origins of Greek symbols in mathematics. Methods to solve simultaneous equations. Real-world applications of the theorem of Pythagoras.
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Jul 2024. John Peter Lawton. Concept image, and its interaction with formal mathematics, is central to the learning of geometry. This paper discusses findings from a survey of teachers which seeks ...
Mathematics
math.MP is an alias for math-ph. Articles in this category focus on areas of research that illustrate the application of mathematics to problems in physics, develop mathematical methods for such applications, or provide mathematically rigorous formulations of existing physical theories. Submissions to math-ph should be of interest to both ...
Pure mathematics
Pure mathematics uses mathematics to explore abstract ideas, mathematics that does not necessarily describe a real physical system. This can include developing the fundamental tools used by ...
Research
In applied mathematics, we look for important connections with other disciplines that may inspire interesting and useful mathematics, and where innovative mathematical reasoning may lead to new insights and applications. Combinatorics. Computational Biology. Physical Applied Mathematics. Computational Science & Numerical Analysis.
Future themes of mathematics education research: an ...
In this paper, we summarize the responses to these two questions. Similar to Sfard's approach, we start by synthesizing the voices of the respondents before formulating our own views.Some colleagues put forward the idea of formulating a list of key themes or questions, similar to the 23 unsolved mathematical problems that David Hilbert published around 1900 (cf. Schoenfeld, 1999).
Frontiers in Applied Mathematics and Statistics
Computational Methods for Spatial Biomedical Data Analysis. Qiwei Li. Himel Mallick, PhD, FASA. Xiaowei Zhan. Guanyu Hu. 730 views. Explores how the application of mathematics and statistics can drive scientific developments across data science, engineering, finance, physics, biology, ecology, business, medicine, and beyond.
Applied mathematics
Applied mathematics is the application of mathematical techniques to describe real-world systems and solve technologically relevant problems. This can include the mechanics of a moving body, the ...
Home
Research in the Mathematical Sciences is an international, peer-reviewed journal encompassing the full scope of theoretical and applied mathematics, as well as theoretical computer science. Encourages submission of longer articles for more complex and detailed analysis and proofing of theorems. Publishes shorter research communications (Letters ...
Trends in mathematics education and insights from a meta ...
Regarding research topics in the most cited papers, the dominant topics were mathematics achievement, content knowledge, working memory, learning disabilities, and educational technologies. ... Prominent research topics in mathematics education review studies are digital technologies, technology-enhanced approaches (e.g. flipped classrooms ...
Research in Mathematics
Research in Mathematics is a broad open access journal publishing all aspects of mathematics including pure, applied, and interdisciplinary mathematics, and mathematical education and other fields. The journal primarily publishes research articles, but also welcomes review and survey articles, and case studies. Topics include, but are not limited to:
Research Areas
Department members engage in cutting-edge research on a wide variety of topics in mathematics and its applications. Topics continually evolve to reflect emerging interests and developments, but can roughly grouped into the following areas. Algebra, Combinatorics, and Geometry Algebra, combinatorics, and geometry are areas of very active research at the University of Pittsburgh.
Mathematics Research Paper Topics
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Research in Mathematics
Research in Mathematics is a broad open access journal publishing all aspects of mathematics including pure, applied, and interdisciplinary mathematics, and mathematical education and other fields. The journal primarily publishes research articles, but also welcomes review and survey articles, and case studies. Topics include, but are not limited to:

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Mathematics (since February 1992)

Categories within Mathematics

Trends in mathematics education and insights from a meta-review and bibliometric analysis of review studies

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1 Introduction

2 Literature review studies and review typologies– background information

2.1 Literature review typologies

2.1.1 Seminal work by Grant and Booth ( 2009 ) on the discourse of literature review typologies

2.1.2 Further development of the review typologies

2.2 Advancements in guidelines and protocols for review studies

2.3 Literature reviews in mathematics education

3 Methodology

3.1.1 Identification

3.1.2 Screening

3.1.3 Included

3.2 Data analysis

4.1 Overview of review studies in mathematics education (RQ1)

4.2 Results of the bibliometric analysis (RQ2–RQ5)

4.2.1 Co-authorship analysis

Co-authorship and author analysis

Co-authorship and country analysis

4.2.2 Co-occurrence analysis

Co-occurrence analysis based on author keywords

4.2.3 Citation analysis

5 Discussion, conclusions, and limitations

5.1 Insights from the meta-review and implications

5.2 Insights from the bibliometric analyses and implications

5.3 Limitations and conclusion

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Research Areas

Algebra, Combinatorics, and Geometry

Analysis and Partial Differential Equations

Applied Analysis

Mathematical Biology

Mathematical Finance

Numerical Analysis and Scientific Computing

Topology and Differential Geometry

Mathematics Research Paper Topics

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260 Interesting Math Topics for Essays & Research Papers

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