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Theses and Dissertations (Mathematics Education)

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• The challenges faced by Grade 7 Mathematics teachers in integrating digital technologies to teach data handling  Paulus, Johannes Natangwe ( 2023-12 ) This study explored the challenges faced by mathematics teachers in integrating digital technologies in teaching Data handling in Grade 7 in Ohangwena Region, Namibia. In this digital era, it is crucial for teachers to ...
• Exploring the TVET college lecturers’ perspectives on the usage of problem-centred teaching in level 4 Calculus  Ndlovu, Jesca ( 2023-12 ) This study explored the perspectives of Technical and Vocational Education and Training (TVET) college lecturers on the usage of problem-based learning as a teaching method in teaching level 4 Calculus. Achievement in ...
• Exploring Grade 10 teachers’ mathematical discourses during Euclidean geometry lessons in Johannesburg East District, South Africa  Kyabuntu, Kambila Joxe ( 2023-11-29 ) The current study sought to investigate the mathematical discourses used by Grade 10 teachers during Euclidean geometry lessons. To explore and understand teachers’ classroom discourses during Euclidean geometry lessons, ...
• Industrial mathematics curriculum development for Ethiopian Science and Technology universities  Zewdie Woldeamanuel Habte ( 2023-09 ) This study aimed to examine the development and implementation of the new industrial mathematics curriculum for Ethiopian Science and Technology universities. Ethiopia is in the process of transforming to industry led ...
• The impact of 8Ps learning model on the mathematical problem-solving performance of grade 12 learners in the concept of stationary points in differential calculus  Omoniyi, Adebayo Akinyinka ( 2022-11-11 ) Noting the centrality of problem solving to Mathematics and its capability to enhance learner performance in the subject, the study measured the impact of the use of 8Ps learning model on the mathematical problem-solving ...
• Enhancing mathematics teachers' professional development for creative teaching in Addis Ababa secondary schools  Anwar Seid Al-amin ( 2023-09-25 ) The Ethiopian education system is imported from the West, and the traditional method of instruction (pouring information) in the ICT revolution era wastes time and resources. Learners can get more information about mathematics ...
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• Teachers improvement of mathematics achievements in rural schools of Mopani District : implications for professional development  Sambo, Sosa Isaac ( 2023-01-01 ) Throughout the globe, there is an outcry that learners’ performance in mathematics is below the expected standard. Hence, teachers need teacher development to improve their skills and knowledge in the subject. The purpose ...
• Grade 10 learners’ academic experiences of learning parabolic functions in schools of Vhembe district of Limpopo Province  Mudau, Takalani Lesley ( 2022-11-22 ) The objective of this study was to determine Grade 10 learners' academic performance in learning parabola functions. Furthermore, the study sought to unearth errors that learners make when learning parabola functions and ...
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• The impact of technology integration in teaching grade 11 Euclidean geometry based on van Hiele’s model  Bediako, Adjei ( 2021-10-10 ) This quantitative study reports on the impact of using GeoGebra software to teach Grade 11 geometry through van Hieles’ levels theory, merged with some elements of the Technological Pedagogical Content Knowledge framework. ...
• A framework towards improved instruction of probability to grade seven students : a case of South African schools in Mpumalanga province  Kodisang, Sophy Mamanyena ( 2022-02-03 ) This empirical phenomenological study explored teachers’ conceptual understanding of probability to gain insights into how this understanding enhanced their instructional classroom practice. The study was motivated by the ...
• The use and effect of Geogebra software in Calculus at Wachemo University, Ethiopia : an investigation  Tola Bekene Bedada ( 2021-08 ) With the rapid growth of technology in the 21st century, traditional teaching and learning methods are considered outdated and not suitable for the active learning processes of the constructivist learning approach. The ...

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251+ Math Research Topics [2024 Updated]

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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Research In Mathematics Education: Some Issues and Some Emerging Influences

2001, Research in Mathematics Education

Related Papers

Canadian Journal of Science, Mathematics and Technology Education

Soudeh Oladi

Despite widespread calls for evidence-based research in education, this strategy has heretofore generated a surprisingly small return on the related financial investment. Some scholars have suggested that the situation follows from a mismatch between education as an assumed field of study and applied empirical research methods. This article’s analysis of evidence-based recommendations in mathematics education is based on a critique that evidence-based research recommendations for classroom practice simply advance analytic claims that are conceptually connected to the particular practice under investigation.

John Selden

Jagdish M , Anna Sfard

Plenary Lecture based on the work of Survey Team 1, presented at the International Congress on Mathematics Education (ICME -10, Copenhagen) I did not co-author this paper, but helped in the research and data analysis which was used by the author of this paper. Dr Sfard is the sole author of this paper.

Caitlin Furlong

In initial teacher training, is there a bridge between theory and practice and, more importantly, does this bridge hold up when students find themselves in the labour market? For several years, this question has been at the heart of the work of authors who have studied the integration of research in initial training and more precisely in initial teacher training. At the Universite de Moncton , undergraduate students at the faculty of education take one research course during their studies. However, that course alone doesn’t seem to be enough to get students to really incorporate research both in their other courses and in their practicum. Therefore, in order to integrate research in initial teacher training, some changes were made to the mathematics education course. Our goal was both to have students develop a positive attitude towards research and to carry out their own research. In order to do that, the work that they had to do was organized to achieve all the learning outcomes ...

Paola Valero

1. Tennessee Technological University Mathematics Department, Technical Report No. 2002-2.

ANNIE SELDEN

"There are no proofs in mathematics education." While this is true, claims are made in mathematics education research and evidence is provided for them. In this talk, I will explore the nature of such research, the kinds of claims and evidence, and what such research might have to offer teachers of mathematics, especially at the undergraduate level. Along the way, I will point out differences between the ways research is done in the two fields.

Edrine Mutebi CFA

Mutebi Edrine

Cambridge Journal of Education

Marja Van den Heuvel-Panhuizen

CMESG/GCEDM Proceedings 2003

Anna Sierpinska

Athanassios Strantzalos

DOI: 10.13140/RG.2.2.21419.59681 Teaching- and Research-Methods of Critical Mathematics Education (CME) have to deal with the dichotomy of the social and the individualist aspect of collaborative learning (Nunes and Bryant, 1996; Lerman, 2001; Valero, 2002). Collaboration refers mostly to the formulation and elaboration of a “dialogical learning framework” (discourse) (Civil & Planas, 2004) within which learning happens as the adoption of certain norms, values and notions of importance. The above give rise to elaborations of “social interactions” as tools to interpret the “classroom dialectics”. To that, let us consider tutors and learners as “active social individuals” whose engagement in social interactions abides to principles of “autonomies” and “heteronomies” (Castoriades in: Straume, 2016) defined against an established collection of normative regulations (the instituted society, (ibid.)): these consist also of “established epistemologies” or, in our frame, “established pedagogical contexts and methods”. Within the same contextual trading of the educational frame, Critical Educational Research and, especially, Emancipatory/Transformational Action Research (AR) tend towards the “(self-) institutionalising society” (ibid.) of Learning, that conceptualizes and contains the collective potentials of its autonomous members, preferably “breaking the didactical contracts along the way” (Brousseau, 1997; Brousseau et al., 2014). Diminishing the “autonomous potential” in these dialectical scheme is one of the main reasons of criticism towards Critical Pedagogies, as e.g. in (Giroux, 1983), and supports tendencies towards “social (establishment) reproduction”. It is of no surprise that classical Mathematical Pedagogies tend to adopt Socio-Cultural aspects that support norms and questions of diverse educational-political establishments, be it the cognitive-skills-approach (Freudenthal, 1981; Stinson et al., 20012; Bishop, 2008; Schoenfeld, 2013; Mason, 1998; Kinard & Kozulin, 2008), or CME (Winter, 1996; Elliott, 1994; Skovsmose, 1994; Stinson et al., 2012; Bishop, 2008; Valero, 2002); even if mathematics teachers usually have no means of describing the corresponding demands and principles (Bishop, 2008). In the above sketched conceptual frame, we shall try to describe the position and potential impact of Teacher-Researchers that engage in Transformational and Emancipatory AR on Teaching and Curriculum, and comment on the sought-for characteristics – both educational and civilian – that would facilitate the intervention of the active practitioners in the context of the established pedagogies themselves via critical curriculum research. Let us add to these the need – raised by the engagement in AR-procedures – to learn to “observe in a critical and, at the same time, self-reflecting manner” the procedures of learning themselves; a need that is preferably supported in ME, given its metacognitive aspects.

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Home > Physical and Mathematical Sciences > Mathematics Education > Theses and Dissertations

Mathematics Education Theses and Dissertations

Theses/dissertations from 2024 2024.

New Mathematics Teachers' Goals, Orientations, and Resources that Influence Implementation of Principles Learned in Brigham Young University's Teacher Preparation Program , Caroline S. Gneiting

Theses/Dissertations from 2023 2023

Impact of Applying Visual Design Principles to Boardwork in a Mathematics Classroom , Jennifer Rose Canizales

Practicing Mathematics Teachers' Perspectives of Public Records in Their Classrooms , Sini Nicole White Graff

Parents' Perceptions of the Importance of Teaching Mathematics: A Q-Study , Ashlynn M. Holley

Engagement in Secondary Mathematics Group Work: A Student Perspective , Rachel H. Jorgenson

Theses/Dissertations from 2022 2022

Understanding College Students' Use of Written Feedback in Mathematics , Erin Loraine Carroll

Identity Work to Teach Mathematics for Social Justice , Navy B. Dixon

Developing a Quantitative Understanding of U-Substitution in First-Semester Calculus , Leilani Camille Heaton Fonbuena

The Perception of At-Risk Students on Caring Student-Teacher Relationships and Its Impact on Their Productive Disposition , Brittany Hopper

Variational and Covariational Reasoning of Students with Disabilities , Lauren Rigby

Structural Reasoning with Rational Expressions , Dana Steinhorst

Student-Created Learning Objects for Mathematics Renewable Assignments: The Potential Value They Bring to the Broader Community , Webster Wong

Theses/Dissertations from 2021 2021

Emotional Geographies of Beginning and Veteran Reformed Teachers in Mentor/Mentee Relationships , Emily Joan Adams

You Do Math Like a Girl: How Women Reason Mathematically Outside of Formal and School Mathematics Contexts , Katelyn C. Pyfer

Developing the Definite Integral and Accumulation Function Through Adding Up Pieces: A Hypothetical Learning Trajectory , Brinley Nichole Stevens

Theses/Dissertations from 2020 2020

Mathematical Identities of Students with Mathematics Learning Dis/abilities , Emma Lynn Holdaway

Teachers' Mathematical Meanings: Decisions for Teaching Geometric Reflections and Orientation of Figures , Porter Peterson Nielsen

Student Use of Mathematical Content Knowledge During Proof Production , Chelsey Lynn Van de Merwe

Theses/Dissertations from 2019 2019

Making Sense of the Equal Sign in Middle School Mathematics , Chelsea Lynn Dickson

Developing Understanding of the Chain Rule, Implicit Differentiation, and Related Rates: Towards a Hypothetical Learning Trajectory Rooted in Nested Multivariation , Haley Paige Jeppson

Secondary Preservice Mathematics Teachers' Curricular Reasoning , Kimber Anne Mathis

“Don’t Say Gay. We Say Dumb or Stupid”: Queering ProspectiveMathematics Teachers’ Discussions , Amy Saunders Ross

Aspects of Engaging Problem Contexts From Students' Perspectives , Tamara Kay Stark

Theses/Dissertations from 2018 2018

Addressing Pre-Service Teachers' Misconceptions About Confidence Intervals , Kiya Lynn Eliason

How Teacher Questions Affect the Development of a Potential Hybrid Space in a Classroom with Latina/o Students , Casandra Helen Job

Teacher Graphing Practices for Linear Functions in a Covariation-Based College Algebra Classroom , Konda Jo Luckau

Principles of Productivity Revealed from Secondary Mathematics Teachers' Discussions Around the Productiveness of Teacher Moves in Response to Teachable Moments , Kylie Victoria Palsky

Theses/Dissertations from 2017 2017

Curriculum Decisions and Reasoning of Middle School Teachers , Anand Mikel Bernard

Teacher Response to Instances of Student Thinking During Whole Class Discussion , Rachel Marie Bernard

Kyozaikenkyu: An In-Depth Look into Japanese Educators' Daily Planning Practices , Matthew David Melville

Analysis of Differential Equations Applications from the Coordination Class Perspective , Omar Antonio Naranjo Mayorga

Theses/Dissertations from 2016 2016

The Principles of Effective Teaching Student Teachershave the Opportunity to Learn in an AlternativeStudent Teaching Structure , Danielle Rose Divis

Insight into Student Conceptions of Proof , Steven Daniel Lauzon

Theses/Dissertations from 2015 2015

Teacher Participation and Motivation inProfessional Development , Krystal A. Hill

Student Evaluation of Mathematical Explanations in anInquiry-Based Mathematics Classroom , Ashley Burgess Hulet

English Learners' Participation in Mathematical Discourse , Lindsay Marie Merrill

Mathematical Interactions between Teachers and Students in the Finnish Mathematics Classroom , Paula Jeffery Prestwich

Parents and the Common Core State Standards for Mathematics , Rebecca Anne Roberts

Examining the Effects of College Algebra on Students' Mathematical Dispositions , Kevin Lee Watson

Problems Faced by Reform Oriented Novice Mathematics Teachers Utilizing a Traditional Curriculum , Tyler Joseph Winiecke

Academic and Peer Status in the Mathematical Life Stories of Students , Carol Ann Wise

Theses/Dissertations from 2014 2014

The Effect of Students' Mathematical Beliefs on Knowledge Transfer , Kristen Adams

Language Use in Mathematics Textbooks Written in English and Spanish , Kailie Ann Bertoch

Teachers' Curricular Reasoning and MKT in the Context of Algebra and Statistics , Kolby J. Gadd

Mathematical Telling in the Context of Teacher Interventions with Collaborative Groups , Brandon Kyle Singleton

An Investigation of How Preservice Teachers Design Mathematical Tasks , Elizabeth Karen Zwahlen

Theses/Dissertations from 2013 2013

Student Understanding of Limit and Continuity at a Point: A Look into Four Potentially Problematic Conceptions , Miriam Lynne Amatangelo

Exploring the Mathematical Knowledge for Teaching of Japanese Teachers , Ratu Jared R. T. Bukarau

Comparing Two Different Student Teaching Structures by Analyzing Conversations Between Student Teachers and Their Cooperating Teachers , Niccole Suzette Franc

Professional Development as a Community of Practice and Its Associated Influence on the Induction of a Beginning Mathematics Teacher , Savannah O. Steele

Types of Questions that Comprise a Teacher's Questioning Discourse in a Conceptually-Oriented Classroom , Keilani Stolk

Theses/Dissertations from 2012 2012

Student Teachers' Interactive Decisions with Respect to Student Mathematics Thinking , Jonathan J. Call

Manipulatives and the Growth of Mathematical Understanding , Stacie Joyce Gibbons

Learning Within a Computer-Assisted Instructional Environment: Effects on Multiplication Math Fact Mastery and Self-Efficacy in Elementary-Age Students , Loraine Jones Hanson

Mathematics Teacher Time Allocation , Ashley Martin Jones

Theses/Dissertations from 2011 2011

How Student Positioning Can Lead to Failure in Inquiry-based Classrooms , Kelly Beatrice Campbell

Teachers' Decisions to Use Student Input During Class Discussion , Heather Taylor Toponce

A Conceptual Framework for Student Understanding of Logarithms , Heather Rebecca Ambler Williams

Theses/Dissertations from 2010 2010

Growth in Students' Conceptions of Mathematical Induction , John David Gruver

Contextualized Motivation Theory (CMT): Intellectual Passion, Mathematical Need, Social Responsibility, and Personal Agency in Learning Mathematics , Janelle Marie Hart

Thinking on the Brink: Facilitating Student Teachers' Learning Through In-the-Moment Interjections , Travis L. Lemon

Understanding Teachers' Change Towards a Reform-Oriented Mathematics Classroom , Linnae Denise Williams

Theses/Dissertations from 2009 2009

A Comparison of Mathematical Discourse in Online and Face-to-Face Environments , Shawn D. Broderick

The Influence of Risk Taking on Student Creation of Mathematical Meaning: Contextual Risk Theory , Erin Nicole Houghtaling

Uncovering Transformative Experiences: A Case Study of the Transformations Made by one Teacher in a Mathematics Professional Development Program , Rachelle Myler Orsak

Theses/Dissertations from 2008 2008

Student Teacher Knowledge and Its Impact on Task Design , Tenille Cannon

How Eighth-Grade Students Estimate with Fractions , Audrey Linford Hanks

Similar but Different: The Complexities of Students' Mathematical Identities , Diane Skillicorn Hill

Choose Your Words: Refining What Counts as Mathematical Discourse in Students' Negotiation of Meaning for Rate of Change of Volume , Christine Johnson

Mathematics Student Teaching in Japan: A Multi-Case Study , Allison Turley Shwalb

Theses/Dissertations from 2007 2007

Applying Toulmin's Argumentation Framework to Explanations in a Reform Oriented Mathematics Class , Jennifer Alder Brinkerhoff

What Are Some of the Common Traits in the Thought Processes of Undergraduate Students Capable of Creating Proof? , Karen Malina Duff

Probing for Reasons: Presentations, Questions, Phases , Kellyn Nicole Farlow

One Problem, Two Contexts , Danielle L. Gigger

The Main Challenges that a Teacher-in-Transition Faces When Teaching a High School Geometry Class , Greg Brough Henry

Discovering the Derivative Can Be "Invigorating:" Mark's Journey to Understanding Instantaneous Velocity , Charity Ann Gardner Hyer

Theses/Dissertations from 2006 2006

How a Master Teacher Uses Questioning Within a Mathematical Discourse Community , Omel Angel Contreras

Determining High School Geometry Students' Geometric Understanding Using van Hiele Levels: Is There a Difference Between Standards-based Curriculum Students and NonStandards-based Curriculum Students? , Rebekah Loraine Genz

The Nature and Frequency of Mathematical Discussion During Lesson Study That Implemented the CMI Framework , Andrew Ray Glaze

Second Graders' Solution Strategies and Understanding of a Combination Problem , Tiffany Marie Hessing

What Does It Mean To Preservice Mathematics Teachers To Anticipate Student Responses? , Matthew M. Webb

Theses/Dissertations from 2005 2005

Fraction Multiplication and Division Image Change in Pre-Service Elementary Teachers , Jennifer J. Cluff

An Examination of the Role of Writing in Mathematics Instruction , Amy Jeppsen

Theses/Dissertations from 2004 2004

Reasoning About Motion: A Case Study , Tiffini Lynn Glaze

Theses/Dissertations from 2003 2003

An Analysis of the Influence of Lesson Study on Preservice Secondary Mathematics Teachers' View of Self-As Mathematics Expert , Julie Stafford

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Research Topics & Ideas: Education

170+ Research Ideas To Fast-Track Your Project

If you’re just starting out exploring education-related topics for your dissertation, thesis or research project, you’ve come to the right place. In this post, we’ll help kickstart your research topic ideation process by providing a hearty list of research topics and ideas , including examples from actual dissertations and theses..

PS – This is just the start…

We know it’s exciting to run through a list of research topics, but please keep in mind that this list is just a starting point . To develop a suitable education-related research topic, you’ll need to identify a clear and convincing research gap , and a viable plan of action to fill that gap.

If this sounds foreign to you, check out our free research topic webinar that explores how to find and refine a high-quality research topic, from scratch. Alternatively, if you’d like hands-on help, consider our 1-on-1 coaching service .

Overview: Education Research Topics

• How to find a research topic (video)
• List of 50+ education-related research topics/ideas
• List of 120+ level-specific research topics 
• Examples of actual dissertation topics in education
• Tips to fast-track your topic ideation (video)
• Free Webinar : Topic Ideation 101
• Where to get extra help

Education-Related Research Topics & Ideas

Below you’ll find a list of education-related research topics and idea kickstarters. These are fairly broad and flexible to various contexts, so keep in mind that you will need to refine them a little. Nevertheless, they should inspire some ideas for your project.

• The impact of school funding on student achievement
• The effects of social and emotional learning on student well-being
• The effects of parental involvement on student behaviour
• The impact of teacher training on student learning
• The impact of classroom design on student learning
• The impact of poverty on education
• The use of student data to inform instruction
• The role of parental involvement in education
• The effects of mindfulness practices in the classroom
• The use of technology in the classroom
• The role of critical thinking in education
• The use of formative and summative assessments in the classroom
• The use of differentiated instruction in the classroom
• The use of gamification in education
• The effects of teacher burnout on student learning
• The impact of school leadership on student achievement
• The effects of teacher diversity on student outcomes
• The role of teacher collaboration in improving student outcomes
• The implementation of blended and online learning
• The effects of teacher accountability on student achievement
• The effects of standardized testing on student learning
• The effects of classroom management on student behaviour
• The effects of school culture on student achievement
• The use of student-centred learning in the classroom
• The impact of teacher-student relationships on student outcomes
• The achievement gap in minority and low-income students
• The use of culturally responsive teaching in the classroom
• The impact of teacher professional development on student learning
• The use of project-based learning in the classroom
• The effects of teacher expectations on student achievement
• The use of adaptive learning technology in the classroom
• The impact of teacher turnover on student learning
• The effects of teacher recruitment and retention on student learning
• The impact of early childhood education on later academic success
• The impact of parental involvement on student engagement
• The use of positive reinforcement in education
• The impact of school climate on student engagement
• The role of STEM education in preparing students for the workforce
• The effects of school choice on student achievement
• The use of technology in the form of online tutoring

Level-Specific Research Topics

Looking for research topics for a specific level of education? We’ve got you covered. Below you can find research topic ideas for primary, secondary and tertiary-level education contexts. Click the relevant level to view the respective list.

Research Topics: Pick An Education Level

Primary education.

• Investigating the effects of peer tutoring on academic achievement in primary school
• Exploring the benefits of mindfulness practices in primary school classrooms
• Examining the effects of different teaching strategies on primary school students’ problem-solving skills
• The use of storytelling as a teaching strategy in primary school literacy instruction
• The role of cultural diversity in promoting tolerance and understanding in primary schools
• The impact of character education programs on moral development in primary school students
• Investigating the use of technology in enhancing primary school mathematics education
• The impact of inclusive curriculum on promoting equity and diversity in primary schools
• The impact of outdoor education programs on environmental awareness in primary school students
• The influence of school climate on student motivation and engagement in primary schools
• Investigating the effects of early literacy interventions on reading comprehension in primary school students
• The impact of parental involvement in school decision-making processes on student achievement in primary schools
• Exploring the benefits of inclusive education for students with special needs in primary schools
• Investigating the effects of teacher-student feedback on academic motivation in primary schools
• The role of technology in developing digital literacy skills in primary school students
• Effective strategies for fostering a growth mindset in primary school students
• Investigating the role of parental support in reducing academic stress in primary school children
• The role of arts education in fostering creativity and self-expression in primary school students
• Examining the effects of early childhood education programs on primary school readiness
• Examining the effects of homework on primary school students’ academic performance
• The role of formative assessment in improving learning outcomes in primary school classrooms
• The impact of teacher-student relationships on academic outcomes in primary school
• Investigating the effects of classroom environment on student behavior and learning outcomes in primary schools
• Investigating the role of creativity and imagination in primary school curriculum
• The impact of nutrition and healthy eating programs on academic performance in primary schools
• The impact of social-emotional learning programs on primary school students’ well-being and academic performance
• The role of parental involvement in academic achievement of primary school children
• Examining the effects of classroom management strategies on student behavior in primary school
• The role of school leadership in creating a positive school climate Exploring the benefits of bilingual education in primary schools
• The effectiveness of project-based learning in developing critical thinking skills in primary school students
• The role of inquiry-based learning in fostering curiosity and critical thinking in primary school students
• The effects of class size on student engagement and achievement in primary schools
• Investigating the effects of recess and physical activity breaks on attention and learning in primary school
• Exploring the benefits of outdoor play in developing gross motor skills in primary school children
• The effects of educational field trips on knowledge retention in primary school students
• Examining the effects of inclusive classroom practices on students’ attitudes towards diversity in primary schools
• The impact of parental involvement in homework on primary school students’ academic achievement
• Investigating the effectiveness of different assessment methods in primary school classrooms
• The influence of physical activity and exercise on cognitive development in primary school children
• Exploring the benefits of cooperative learning in promoting social skills in primary school students

Secondary Education

• Investigating the effects of school discipline policies on student behavior and academic success in secondary education
• The role of social media in enhancing communication and collaboration among secondary school students
• The impact of school leadership on teacher effectiveness and student outcomes in secondary schools
• Investigating the effects of technology integration on teaching and learning in secondary education
• Exploring the benefits of interdisciplinary instruction in promoting critical thinking skills in secondary schools
• The impact of arts education on creativity and self-expression in secondary school students
• The effectiveness of flipped classrooms in promoting student learning in secondary education
• The role of career guidance programs in preparing secondary school students for future employment
• Investigating the effects of student-centered learning approaches on student autonomy and academic success in secondary schools
• The impact of socio-economic factors on educational attainment in secondary education
• Investigating the impact of project-based learning on student engagement and academic achievement in secondary schools
• Investigating the effects of multicultural education on cultural understanding and tolerance in secondary schools
• The influence of standardized testing on teaching practices and student learning in secondary education
• Investigating the effects of classroom management strategies on student behavior and academic engagement in secondary education
• The influence of teacher professional development on instructional practices and student outcomes in secondary schools
• The role of extracurricular activities in promoting holistic development and well-roundedness in secondary school students
• Investigating the effects of blended learning models on student engagement and achievement in secondary education
• The role of physical education in promoting physical health and well-being among secondary school students
• Investigating the effects of gender on academic achievement and career aspirations in secondary education
• Exploring the benefits of multicultural literature in promoting cultural awareness and empathy among secondary school students
• The impact of school counseling services on student mental health and well-being in secondary schools
• Exploring the benefits of vocational education and training in preparing secondary school students for the workforce
• The role of digital literacy in preparing secondary school students for the digital age
• The influence of parental involvement on academic success and well-being of secondary school students
• The impact of social-emotional learning programs on secondary school students’ well-being and academic success
• The role of character education in fostering ethical and responsible behavior in secondary school students
• Examining the effects of digital citizenship education on responsible and ethical technology use among secondary school students
• The impact of parental involvement in school decision-making processes on student outcomes in secondary schools
• The role of educational technology in promoting personalized learning experiences in secondary schools
• The impact of inclusive education on the social and academic outcomes of students with disabilities in secondary schools
• The influence of parental support on academic motivation and achievement in secondary education
• The role of school climate in promoting positive behavior and well-being among secondary school students
• Examining the effects of peer mentoring programs on academic achievement and social-emotional development in secondary schools
• Examining the effects of teacher-student relationships on student motivation and achievement in secondary schools
• Exploring the benefits of service-learning programs in promoting civic engagement among secondary school students
• The impact of educational policies on educational equity and access in secondary education
• Examining the effects of homework on academic achievement and student well-being in secondary education
• Investigating the effects of different assessment methods on student performance in secondary schools
• Examining the effects of single-sex education on academic performance and gender stereotypes in secondary schools
• The role of mentoring programs in supporting the transition from secondary to post-secondary education

Tertiary Education

• The role of student support services in promoting academic success and well-being in higher education
• The impact of internationalization initiatives on students’ intercultural competence and global perspectives in tertiary education
• Investigating the effects of active learning classrooms and learning spaces on student engagement and learning outcomes in tertiary education
• Exploring the benefits of service-learning experiences in fostering civic engagement and social responsibility in higher education
• The influence of learning communities and collaborative learning environments on student academic and social integration in higher education
• Exploring the benefits of undergraduate research experiences in fostering critical thinking and scientific inquiry skills
• Investigating the effects of academic advising and mentoring on student retention and degree completion in higher education
• The role of student engagement and involvement in co-curricular activities on holistic student development in higher education
• The impact of multicultural education on fostering cultural competence and diversity appreciation in higher education
• The role of internships and work-integrated learning experiences in enhancing students’ employability and career outcomes
• Examining the effects of assessment and feedback practices on student learning and academic achievement in tertiary education
• The influence of faculty professional development on instructional practices and student outcomes in tertiary education
• The influence of faculty-student relationships on student success and well-being in tertiary education
• The impact of college transition programs on students’ academic and social adjustment to higher education
• The impact of online learning platforms on student learning outcomes in higher education
• The impact of financial aid and scholarships on access and persistence in higher education
• The influence of student leadership and involvement in extracurricular activities on personal development and campus engagement
• Exploring the benefits of competency-based education in developing job-specific skills in tertiary students
• Examining the effects of flipped classroom models on student learning and retention in higher education
• Exploring the benefits of online collaboration and virtual team projects in developing teamwork skills in tertiary students
• Investigating the effects of diversity and inclusion initiatives on campus climate and student experiences in tertiary education
• The influence of study abroad programs on intercultural competence and global perspectives of college students
• Investigating the effects of peer mentoring and tutoring programs on student retention and academic performance in tertiary education
• Investigating the effectiveness of active learning strategies in promoting student engagement and achievement in tertiary education
• Investigating the effects of blended learning models and hybrid courses on student learning and satisfaction in higher education
• The role of digital literacy and information literacy skills in supporting student success in the digital age
• Investigating the effects of experiential learning opportunities on career readiness and employability of college students
• The impact of e-portfolios on student reflection, self-assessment, and showcasing of learning in higher education
• The role of technology in enhancing collaborative learning experiences in tertiary classrooms
• The impact of research opportunities on undergraduate student engagement and pursuit of advanced degrees
• Examining the effects of competency-based assessment on measuring student learning and achievement in tertiary education
• Examining the effects of interdisciplinary programs and courses on critical thinking and problem-solving skills in college students
• The role of inclusive education and accessibility in promoting equitable learning experiences for diverse student populations
• The role of career counseling and guidance in supporting students’ career decision-making in tertiary education
• The influence of faculty diversity and representation on student success and inclusive learning environments in higher education

Education-Related Dissertations & Theses

While the ideas we’ve presented above are a decent starting point for finding a research topic in education, they are fairly generic and non-specific. So, it helps to look at actual dissertations and theses in the education space to see how this all comes together in practice.

Below, we’ve included a selection of education-related research projects to help refine your thinking. These are actual dissertations and theses, written as part of Master’s and PhD-level programs, so they can provide some useful insight as to what a research topic looks like in practice.

• From Rural to Urban: Education Conditions of Migrant Children in China (Wang, 2019)
• Energy Renovation While Learning English: A Guidebook for Elementary ESL Teachers (Yang, 2019)
• A Reanalyses of Intercorrelational Matrices of Visual and Verbal Learners’ Abilities, Cognitive Styles, and Learning Preferences (Fox, 2020)
• A study of the elementary math program utilized by a mid-Missouri school district (Barabas, 2020)
• Instructor formative assessment practices in virtual learning environments : a posthumanist sociomaterial perspective (Burcks, 2019)
• Higher education students services: a qualitative study of two mid-size universities’ direct exchange programs (Kinde, 2020)
• Exploring editorial leadership : a qualitative study of scholastic journalism advisers teaching leadership in Missouri secondary schools (Lewis, 2020)
• Selling the virtual university: a multimodal discourse analysis of marketing for online learning (Ludwig, 2020)
• Advocacy and accountability in school counselling: assessing the use of data as related to professional self-efficacy (Matthews, 2020)
• The use of an application screening assessment as a predictor of teaching retention at a midwestern, K-12, public school district (Scarbrough, 2020)
• Core values driving sustained elite performance cultures (Beiner, 2020)
• Educative features of upper elementary Eureka math curriculum (Dwiggins, 2020)
• How female principals nurture adult learning opportunities in successful high schools with challenging student demographics (Woodward, 2020)
• The disproportionality of Black Males in Special Education: A Case Study Analysis of Educator Perceptions in a Southeastern Urban High School (McCrae, 2021)

As you can see, these research topics are a lot more focused than the generic topic ideas we presented earlier. So, in order for you to develop a high-quality research topic, you’ll need to get specific and laser-focused on a specific context with specific variables of interest.  In the video below, we explore some other important things you’ll need to consider when crafting your research topic.

Get 1-On-1 Help

If you’re still unsure about how to find a quality research topic within education, check out our Research Topic Kickstarter service, which is the perfect starting point for developing a unique, well-justified research topic.

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66 Comments

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Special education

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Research title related to school of students

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Research title related to students

My field is research measurement and evaluation. Need dissertation topics in the field

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Write on action research topic, using guidance and counseling to address unwanted teenage pregnancy in school

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Thank you for the information.. I would like to request a topic based on school major in social studies

parental involvement and students academic performance

Science education topics?

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How about School management and supervision pls.?

Hi i am an Deputy Principal in a primary school. My wish is to srudy foe Master’s degree in Education.Please advice me on which topic can be relevant for me. Thanks.

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Kindly help me with the research questions on the topic” Effects of workplace conflict on the employees’ job performance”. The effects can be applicable in every institution,enterprise or organisation.

Greetings, I am a student majoring in Sociology and minoring in Public Administration. I’m considering any recommended research topic in the field of Sociology.

I’m a student pursuing Mphil in Basic education and I’m considering any recommended research proposal topic in my field of study

Research Defense for students in senior high

Kindly help me with a research topic in educational psychology. Ph.D level. Thank you.

Project-based learning is a teaching/learning type,if well applied in a classroom setting will yield serious positive impact. What can a teacher do to implement this in a disadvantaged zone like “North West Region of Cameroon ( hinterland) where war has brought about prolonged and untold sufferings on the indegins?

I wish to get help on topics of research on educational administration

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Would like to request for suggestions on a topic in Economics of education,PhD level

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I am PhD student, I am searching my Research topic, It should be innovative,my area of interest is online education,use of technology in education

request suggestion on topic in masters in medical education .

Look at British Library as they keep a copy of all PhDs in the UK Core.ac.uk to access Open University and 6 other university e-archives, pdf downloads mostly available, all free.

May I also ask for a topic based on mathematics education for college teaching, please?

Please I am a masters student of the department of Teacher Education, Faculty of Education Please I am in need of proposed project topics to help with my final year thesis

Am a PhD student in Educational Foundations would like a sociological topic. Thank

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Greetings and Regards I am a doctoral student in the field of philosophy of education. I am looking for a new topic for my thesis. Because of my work in the elementary school, I am looking for a topic that is from the field of elementary education and is related to the philosophy of education.

Masters student in the field of curriculum, any ideas of a research topic on low achiever students

In the field of curriculum any ideas of a research topic on deconalization in contextualization of digital teaching and learning through in higher education

Amazing guidelines

I am a graduate with two masters. 1) Master of arts in religious studies and 2) Master in education in foundations of education. I intend to do a Ph.D. on my second master’s, however, I need to bring both masters together through my Ph.D. research. can I do something like, ” The contribution of Philosophy of education for a quality religion education in Kenya”? kindly, assist and be free to suggest a similar topic that will bring together the two masters. thanks in advance

Hi, I am an Early childhood trainer as well as a researcher, I need more support on this topic: The impact of early childhood education on later academic success.

I’m a student in upper level secondary school and I need your support in this research topics: “Impact of incorporating project -based learning in teaching English language skills in secondary schools”.

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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.

Analysis and Partial Differential Equations

The research of the analysis group covers functional analysis, harmonic analysis, several complex variables, partial differential equations, and analysis on metric and Carnot-Caratheodory spaces.

Applied Analysis

The department is a leader in the analysis of systems of nonlinear differential equations and dynamical systems  that arise in modeling a variety of physical phenomena. They include problems in biology, chemistry, phase transitions, fluid flow, flame propagation, diffusion processes, and pattern formation in nonlinear stochastic partial differential equations.

Mathematical Biology

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.

Numerical Analysis and Scientific Computing

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.

Topology and Differential Geometry

Research in analytic topology continues in the broad area of generalized metric spaces. This group studies relativity theory and differential geometry, with emphasis on twistor methods, as well as geometric and topological aspects of quantum field theory, string theory, and M-theory.

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Posing Researchable Questions in Mathematics and Science Education: Purposefully Questioning the Questions for Investigation

• Published: 07 April 2020
• Volume 18 , pages 1–7, ( 2020 )

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• Jinfa Cai 1 &
• Rachel Mamlok-Naaman 2  

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A Correction to this article was published on 15 May 2020

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Avoid common mistakes on your manuscript.

Perhaps the most obvious example is the set of 23 influential mathematical problems posed by David Hilbert that inspired a great deal of progress in the discipline of mathematics (Hilbert, 1901 -1902). Einstein and Infeld ( 1938 ) claimed that “to raise new questions, new possibilities, to regard old problems from a new angle, requires creative imagination and marks real advance in science” (p. 95). Both Cantor and Klamkin recommended that, in mathematics, the art of posing a question be held as high or higher in value than solving it. Similarly, in the history of science, formulating precise, answerable questions not only advances new discoveries but also gives scientists intellectual excitement (Kennedy, 2005 ; Mosteller, 1980 ).

In research related to mathematics and science education, there is no shortage of evidence for the impact of posing important and researchable questions: Posing new, researchable questions marks real advances in mathematics and science education (Cai et al., 2019a ). Although research in mathematics and science education begins with researchable questions, only recently have researchers begun to purposefully and systematically discuss the nature of researchable questions. To conduct research, we must have researchable questions, but what defines a researchable question? What are the sources of researchable questions? How can we purposefully discuss researchable questions?

This special issue marks effort for the field’s discussion of researchable questions. As the field of mathematics and science education matures, it is necessary to reflect on the field at such a metalevel (Inglis & Foster, 2018 ). Although the authors in this special issue discuss researchable questions from different angles, they all refer to researchable questions as those that can be investigated empirically. For any empirical study, one can discuss its design, its conduct, and how it can be written up for publication. Therefore, researchable questions in mathematics and science education can be discussed with respect to study design, the conduct of research, and the dissemination of that research.

Even though there are many lines of inquiry that we can explore with respect to researchable questions, each exploring the topic from a different angle, we have decided to focus on the following three aspects to introduce this special issue: (1) criteria for selecting researchable questions, (2) sources of researchable questions, and (3) alignment of researchable questions with the conceptual framework as well as appropriate research methods.

Criteria for Selecting Researchable Questions

It is clear that not all researchable questions are worth the effort to investigate. According to Cai et al. ( 2020 ), of all researchable questions in mathematics and science education, priority is given to those that are significant. Research questions are significant if they can advance the fields’ knowledge and understanding about the teaching and learning of science and mathematics. Through an analysis of peer reviews for a research journal, Cai et al. ( 2020 ) provide a window into the field’s frontiers related to significant researchable questions. In an earlier article, Cai et al. ( 2019a ) argued that

The significance of a research question cannot be determined just by reading it. Rather, its significance stands in relation to the knowledge of the field. The justification for the research question itself—why it is a significant question to investigate—must therefore be made clear through an explicit argument that ties the research question to what is and is not already known. (p. 118)

In their analysis, Cai et al. ( 2020 ) provide evidence that many reviews that highlighted issues with the research questions in rejected manuscripts specifically called for authors to make an argument to motivate the research questions, whereas none of the manuscripts that were ultimately accepted (pending revisions) received this kind of comment. Cai et al. ( 2020 ) provide a framework not only for analyzing peer reviews about research questions but also for how to communicate researchable questions in journal manuscript preparations.

Whereas Cai and his colleagues, as editors of a journal, discuss significant research questions from the perspective of peer review and publication, King, Ochsendorf, Solomon, and Sloane ( 2020 ), as program directors at the Directorate for Education and Human Resources at the U.S. National Science Foundation (NSF), discuss fundable research questions for research in mathematics and science education. King et al. ( 2020 ) situate their discussion of fundable research questions in the context of writing successful educational research grant proposals. For them, fundable research questions must be transformative and significant with specific and clear constructs. In addition, they present examples of STEM education research questions from different types of research (Institute of Education Sciences [IES] & NSF, 2013 ) and how the questions themselves direct specific design choices, methodologies, measures, study samples, and analytical models as well as how they can reflect the disciplinary orientations of the researchers.

Hjalmarson and Baker ( 2020 ) take a quite different approach to discussing researchable questions for teacher professional development. They argue for the need to include mathematics specialists (e.g. mathematics coaches or mathematics teacher leaders) for studying teacher learning and development. To Hjalmarson and Baker ( 2020 ), researchable questions related to teacher professional learning should be selected by including mathematics specialists because of their role in connecting research and practice.

Sanchez ( 2020 ) discuss, in particular, the importance of replication studies in mathematics and the kinds of researchable questions that would be productive to explore within this category. With the increased acknowledgement of the importance of replication studies (Cai et al., 2018 ), Sanchez Aguilar has provided a useful typology of fundamental questions that can guide a replication study in mathematics (and science) education.

Schoenfeld ( 2020 ) is very direct in suggesting that researchable questions must advance the field and that these research questions must be meaningful and generative: “What is meant by meaningful is that the answer to the questions posed should matter to either practice or theory in some important way. What is meant by generative is that working on the problem, whether it is ‘solved’ or not, is likely to provide valuable insights” (pp. XX). Schoenfeld calls for researchers to establish research programs—that is, one not only selects meaningful research questions to investigate but also continues in that area of research to produce ongoing insights and further meaningful questions.

Stylianides and Stylianides ( 2020 ) argue that, collectively, researchers can and need to pose new researchable questions. The new researchable questions are worth investigating if they reflect the field’s growing understanding of the web of potentially influential factors surrounding the investigation of a particular area. The argument that Stylianides and Stylianides ( 2020 ) use is very similar to Schoenfeld’s ( 2020 ) generative criteria, but Stylianides and Stylianides ( 2020 ) explicitly emphasize the collective nature of the field’s growing understanding of a particular phenomenon.

Sources of Researchable Questions

Research questions in science and mathematics education arise from multiple sources, including problems of practice, extensions of theory, and lacunae in existing areas of research. Therefore, through a research question’s connections to prior research, it should be clear how answering the question extends the field’s knowledge (Cai et al., 2019a ). Across the papers in this special issue lies a common theme that researchable questions arise from understanding the area under study. Cai et al. ( 2020 ) take the position that the significance of researchable questions must be justified in the context of prior research. In particular, reviewers of manuscripts submitted for publication will evaluate if the study is adequately motivated. In fact, posing significant researchable questions is an iterative process beginning with some broader, general sense of an idea which is potentially fruitful and leading, eventually, to a well-specified, stated research question (Cai et al., 2019a ). Similarly, King et al. ( 2020 ) argue that fundable research questions should be grounded in prior research and make explicit connections to what is known or not known in the given area of study.

Sanchez ( 2020 ) suggest that it is time for the field of mathematics and science education research to seriously consider replication studies. Researchable questions related to replication studies might arise from the examination of the following two questions: (1) Do the results of the original study hold true beyond the context in which it was developed? (2) Are there alternative ways to study and explain an identified phenomenon or finding? Similarly, Hjalmarson and Baker ( 2020 ) specifically suggest two needs related to mathematics specialists in studies of professional development that drive researchable questions: (1) defining practices and hidden players involved in systematic school change and (2) identifying the unit of analysis and scaling up professional development.

Schoenfeld ( 2020 ) uses various examples to illustrate the origin of researchable questions. One of his (perhaps most familiar) examples is his decade-long research on mathematical problem solving. He elaborates on how answering one specific research question leads to another and another. In the context of research on mathematical proof, Stylianides and Stylianides ( 2020 ) also illustrate how researchable questions arise from existing research in the area leading to new researchable questions in the dynamic process of educational research. The arguments and examples in both Schoenfeld ( 2020 ) and Stylianides and Stylianides ( 2020 ) are quite powerful in the sense that this source of researchable questions facilitates the accumulation of knowledge for the given areas of study.

A related source of researchable questions is not discussed in this set of papers—unexpected findings. A potentially powerful source of research questions is the discovery of an unexpected finding when conducting research (Cai et al., 2019b ). Many important advances in scientific research have their origins in serendipitous, unexpected findings. Researchers are often faced with unexpected and perhaps surprising results, even when they have developed a carefully crafted theoretical framework, posed research questions tightly connected to this framework, presented hypotheses about expected outcomes, and selected methods that should help answer the research questions. Indeed, unexpected findings can be the most interesting and valuable products of the study and a source of further researchable questions (Cai et al., 2019b ).

Of course, researchable questions can also arise from established scholars in a given field—those who are most familiar with the scope of the research that has been done. For example, in 2005, in celebrating the 125th anniversary of the publication of Science ’s first issue, the journal invited researchers from around the world to propose the 125 most important research questions in the scientific enterprise (Kennedy, 2005 ). A list of unanswered questions like this is a great source for researchable questions in science, just as the 23 great questions in mathematics by Hilbert ( 1901 -1902) spurred the field for decades. In mathematics and science education, one can look to research handbooks and compendiums. These volumes often include lists of unanswered research questions in the hopes of prompting further research in various areas (e.g. Cai, 2017 ; Clements, Bishop, Keitel, Kilpatrick, & Leung, 2013 ; Talbot-Smith, 2013 ).

Alignment of Researchable Questions with the Conceptual Framework and Appropriate Research Methods

Cai et al. ( 2020 ) and King et al. ( 2020 ) explicitly discuss the alignment of researchable questions with the conceptual framework and appropriate research methods. In writing journal publications or grant proposals, it is extremely important to justify the significance of the researchable questions based on the chosen theoretical framework and then determine robust methods to answer the research questions. According to Cai et al. ( 2019a ), justification for the significance of the research questions depends on a theoretical framework: “The theoretical framework shapes the researcher’s conception of the phenomenon of interest, provides insight into it, and defines the kinds of questions that can be asked about it” (p. 119). It is true that the notion of a theoretical framework can remain somewhat mysterious and confusing for researchers. However, it is clear that the theoretical framework links research questions to existing knowledge, thus helping to establish their significance; provides guidance and justification for methodological choices; and provides support for the coherence that is needed between research questions, methods, results, and interpretations of findings (Cai & Hwang, 2019 ; Cai et al., 2019c ).

Analyzing reviews for a research journal in mathematics education, Cai et al. ( 2020 ) found that the reviewers wanted manuscripts to be explicit about how the research questions, the theoretical framework, the methods, and the findings were connected. Even for manuscripts that were accepted (pending revisions), making explicit connections across all parts of the manuscript was a challenging proposition. Thus, in preparing manuscripts for publication, it is essential to communicate the significance of a study by developing a coherent chain of justification connecting researchable questions, the theoretical framework, and the research methods chosen to address the research questions.

The Long Journey Has Just Begun with a First Step

As the field of mathematics and science education matures, there is a need to take a step back and reflect on what has been done so that the field can continue to grow. This special issue represents a first step by reflecting on the posing of significant researchable questions to advance research in mathematics and science education. Such reflection is useful and necessary not only for the design of studies but also for the writing of research reports for publication. Most importantly, working on significant researchable questions cannot only contribute to theory generation about the teaching and learning of mathematics and science but also contribute to improving the impact of research on practice in mathematics and science classrooms.

To conclude, we want to draw readers’ attention to a parallel between this reflection on research in our field and a line of research that investigates the development of school students’ problem-posing and questioning skills in mathematics and science (Blonder, Rapp, Mamlok-Naaman, & Hofstein, 2015 ; Cai, Hwang, Jiang, & Silber, 2015 ; Cuccio-Schirripa & Steiner, 2000 ; Hofstein, Navon, Kipnis, & Mamlok-Naaman, 2005 ; Silver, 1994 ; Singer, Ellerton, & Cai, 2015 ). Posing researchable questions is critical for advancing research in mathematics and science education. Similarly, providing students opportunities to pose problems is critical for the development of their thinking and learning. With the first step in this journey made, perhaps we can dream of something bigger further on down the road.

Change history

15 may 2020.

The original version of this article unfortunately contains correction.

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Cai, J., Mamlok-Naaman, R. Posing Researchable Questions in Mathematics and Science Education: Purposefully Questioning the Questions for Investigation. Int J of Sci and Math Educ 18 (Suppl 1), 1–7 (2020). https://doi.org/10.1007/s10763-020-10079-5

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Megamenu featured, megamenu social, math/stats thesis and colloquium topics.

Updated: April 2024

Math/Stats Thesis and Colloquium Topics 2024- 2025

The degree with honors in Mathematics or Statistics is awarded to the student who has demonstrated outstanding intellectual achievement in a program of study which extends beyond the requirements of the major. The principal considerations for recommending a student for the degree with honors will be: Mastery of core material and skills, breadth and, particularly, depth of knowledge beyond the core material, ability to pursue independent study of mathematics or statistics, originality in methods of investigation, and, where appropriate, creativity in research.

An honors program normally consists of two semesters (MATH/STAT 493 and 494) and a winter study (WSP 031) of independent research, culminating in a thesis and a presentation. Under certain circumstances, the honors work can consist of coordinated study involving a one semester (MATH/STAT 493 or 494) and a winter study (WSP 030) of independent research, culminating in a “minithesis” and a presentation. At least one semester should be in addition to the major requirements, and thesis courses do not count as 400-level senior seminars.

An honors program in actuarial studies requires significant achievement on four appropriate examinations of the Society of Actuaries.

Highest honors will be reserved for the rare student who has displayed exceptional ability, achievement or originality. Such a student usually will have written a thesis, or pursued actuarial honors and written a mini-thesis. An outstanding student who writes a mini-thesis, or pursues actuarial honors and writes a paper, might also be considered. In all cases, the award of honors and highest honors is the decision of the Department.

Here is a list of possible colloquium topics that different faculty are willing and eager to advise. You can talk to several faculty about any colloquium topic, the sooner the better, at least a month or two before your talk. For various reasons faculty may or may not be willing or able to advise your colloquium, which is another reason to start early.

RESEARCH INTERESTS OF MATHEMATICS AND STATISTICS FACULTY

Here is a list of faculty interests and possible thesis topics.  You may use this list to select a thesis topic or you can use the list below to get a general idea of the mathematical interests of our faculty.

Colin Adams (On Leave 2024 – 2025)

Research interests:   Topology and tiling theory.  I work in low-dimensional topology.  Specifically, I work in the two fields of knot theory and hyperbolic 3-manifold theory and develop the connections between the two. Knot theory is the study of knotted circles in 3-space, and it has applications to chemistry, biology and physics.  I am also interested in tiling theory and have been working with students in this area as well.

Hyperbolic 3-manifold theory utilizes hyperbolic geometry to understand 3-manifolds, which can be thought of as possible models of the spatial universe.

Possible thesis topics:

• Investigate various aspects of virtual knots, a generalization of knots.
• Consider hyperbolicity of virtual knots, building on previous SMALL work. For which virtual knots can you prove hyperbolicity?
• Investigate why certain virtual knots have the same hyperbolic volume.
• Consider the minimal Turaev volume of virtual knots, building on previous SMALL work.
• Investigate which knots have totally geodesic Seifert surfaces. In particular, figure out how to interpret this question for virtual knots.
• Investigate n-crossing number of knots. An n-crossing is a crossing with n strands of the knot passing through it. Every knot can be drawn in a picture with only n-crossings in it. The least number of n-crossings is called the n-crossing number. Determine the n-crossing number for various n and various families of knots.
• An übercrossing projection of a knot is a projection with just one n-crossing. The übercrossing number of a knot is the least n for which there is such an übercrossing projection. Determine the übercrossing number for various knots, and see how it relates to other traditional knot invariants.
• A petal projection of a knot is a projection with just one n-crossing such that none of the loops coming out of the crossing are nested. In other words, the projection looks like a daisy. The petal number of a knot is the least n for such a projection. Determine petal number for various knots, and see how it relates to other traditional knot invariants.
• In a recent paper, we extended petal number to virtual knots. Show that the virtual petal number of a classical knot is equal to the classical petal number of the knot (This is a GOOD question!)
• Similarly, show that the virtual n-crossing number of a classical knot is equal to the classical n-crossing number. (This is known for n = 2.)
• Find tilings of the branched sphere by regular polygons. This would extend work of previous research students. There are lots of interesting open problems about something as simple as tilings of the sphere.
• Other related topics.

Possible colloquium topics : Particularly interested in topology, knot theory, graph theory, tiling theory and geometry but will consider other topics.

Christina Athanasouli

Research Interests:   Differential equations, dynamical systems (both smooth and non-smooth), mathematical modeling with applications in biological and mechanical systems

My research focuses on analyzing mathematical models that describe various phenomena in Mathematical Neuroscience and Engineering. In particular, I work on understanding 1) the underlying mechanisms of human sleep (e.g. how sleep patterns change with development or due to perturbations), and 2) potential design or physical factors that may influence the dynamics in vibro-impact mechanical systems for the purpose of harvesting energy. Mathematically, I use various techniques from dynamical systems and incorporate both numerical and analytical tools in my work. 

Possible colloquium topics:   Topics in applied mathematics, such as:

• Mathematical modeling of sleep-wake regulation
• Mathematical modeling vibro-impact systems
• Bifurcations/dynamics of mathematical models in Mathematical Neuroscience and Engineering
• Bifurcations in piecewise-smooth dynamical systems

Julie Blackwood

Research Interests:   Mathematical modeling, theoretical ecology, population biology, differential equations, dynamical systems.

My research uses mathematical models to uncover the complex mechanisms generating ecological dynamics, and when applicable emphasis is placed on evaluating intervention programs. My research is in various ecological areas including ( I ) invasive species management by using mathematical and economic models to evaluate the costs and benefits of control strategies, and ( II ) disease ecology by evaluating competing mathematical models of the transmission dynamics for both human and wildlife diseases.

• Mathematical modeling of invasive species
• Mathematical modeling of vector-borne or directly transmitted diseases
• Developing mathematical models to manage vector-borne diseases through vector control
• Other relevant topics of interest in mathematical biology

Each topic (1-3) can focus on a case study of a particular invasive species or disease, and/or can investigate the effects of ecological properties (spatial structure, resource availability, contact structure, etc.) of the system.

Possible colloquium topics:   Any topics in applied mathematics, such as:

Research Interest :  Statistical methodology and applications.  One of my research topics is variable selection for high-dimensional data.  I am interested in traditional and modern approaches for selecting variables from a large candidate set in different settings and studying the corresponding theoretical properties. The settings include linear model, partial linear model, survival analysis, dynamic networks, etc.  Another part of my research studies the mediation model, which examines the underlying mechanism of how variables relate to each other.  My research also involves applying existing methods and developing new procedures to model the correlated observations and capture the time-varying effect.  I am also interested in applications of data mining and statistical learning methods, e.g., their applications in analyzing the rhetorical styles in English text data.

• Variable selection uses modern techniques such as penalization and screening methods for several different parametric and semi-parametric models.
• Extension of the classic mediation models to settings with correlated, longitudinal, or high-dimensional mediators. We could also explore ways to reduce the dimensionality and simplify the structure of mediators to have a stable model that is also easier to interpret.
• We shall analyze the English text dataset processed by the Docuscope environment with tools for corpus-based rhetorical analysis. The data have a hierarchical structure and contain rich information about the rhetorical styles used. We could apply statistical models and statistical learning algorithms to reduce dimensions and gain a more insightful understanding of the text.

Possible colloquium topics:  I am open to any problems in statistical methodology and applications, not limited to my research interests and the possible thesis topics above.

Richard De Veaux 

Research interests: Statistics.

My research interests are in both statistical methodology and in statistical applications.  For the first, I look at different methods and try to understand why some methods work well in particular settings, or more creatively, to try to come up with new methods.  For the second, I work in collaboration with an investigator (e.g. scientist, doctor, marketing analyst) on a particular statistical application.  I have been especially interested in problems dealing with large data sets and the associated modeling tools that work for these problems.

• Human Performance and Aging.I have been working on models for assessing the effect of age on performance in running and swimming events. There is still much work to do. So far I’ve looked at masters’ freestyle swimming and running data and a handicapped race in California, but there are world records for each age group and other events in running and swimming that I’ve not incorporated. There are also many other types of events.
• Variable Selection.  How do we choose variables when we have dozens, hundreds or even thousands of potential predictors? Various model selection strategies exist, but there is still a lot of work to be done to find out which ones work under what assumptions and conditions.
• Problems at the interface.In this era of Big Data, not all methods of classical statistics can be applied in practice. What methods scale up well, and what advances in computer science give insights into the statistical methods that are best suited to large data sets?
• Applying statistical methods to problems in science or social science.In collaboration with a scientist or social scientist, find a problem for which statistical analysis plays a key role.

Possible colloquium topics:

• Almost any topic in statistics that extends things you’ve learned in courses —  specifically topics in Experimental design, regression techniques or machine learning
• Model selection problems

Thomas Garrity (On Leave 2024 – 2025)

Research interest:   Number Theory and Dynamics.

My area of research is officially called “multi-dimensional continued fraction algorithms,” an area that touches many different branches of mathematics (which is one reason it is both interesting and rich).  In recent years, students writing theses with me have used serious tools from geometry, dynamics, ergodic theory, functional analysis, linear algebra, differentiability conditions, and combinatorics.  (No single person has used all of these tools.)  It is an area to see how mathematics is truly interrelated, forming one coherent whole.

While my original interest in this area stemmed from trying to find interesting methods for expressing real numbers as sequences of integers (the Hermite problem), over the years this has led to me interacting with many different mathematicians, and to me learning a whole lot of math.  My theses students have had much the same experiences, including the emotional rush of discovery and the occasional despair of frustration.  The whole experience of writing a thesis should be intense, and ultimately rewarding.   Also, since this area of math has so many facets and has so many entrance points, I have had thesis students from wildly different mathematical backgrounds do wonderful work; hence all welcome.

• Generalizations of continued fractions.
• Using algebraic geometry to study real submanifolds of complex spaces.

Possible colloquium topics:   Any interesting topic in mathematics.

Leo Goldmakher

Research interests:   Number theory and arithmetic combinatorics.

I’m interested in quantifying structure and randomness within naturally occurring sets or sequences, such as the prime numbers, or the sequence of coefficients of a continued fraction, or a subset of a vector space. Doing so typically involves using ideas from analysis, probability, algebra, and combinatorics.

Possible thesis topics:  

Anything in number theory or arithmetic combinatorics.

Possible colloquium topics:   I’m happy to advise a colloquium in any area of math.

Susan Loepp

Research interests: Commutative Algebra.  I study algebraic structures called commutative rings.  Specifically, I have been investigating the relationship between local rings and their completion.  One defines the completion of a ring by first defining a metric on the ring and then completing the ring with respect to that metric.  I am interested in what kinds of algebraic properties a ring and its completion share.  This relationship has proven to be intricate and quite surprising.  I am also interested in the theory of tight closure, and Homological Algebra.

Topics in Commutative Algebra including:

• Using completions to construct Noetherian rings with unusual prime ideal structures.
• What prime ideals of C[[ x 1 ,…, x n ]] can be maximal in the generic formal fiber of a ring? More generally, characterize what sets of prime ideals of a complete local ring can occur in the generic formal fiber.
• Characterize what sets of prime ideals of a complete local ring can occur in formal fibers of ideals with height n where n ≥1.
• Characterize which complete local rings are the completion of an excellent unique factorization domain.
• Explore the relationship between the formal fibers of R and S where S is a flat extension of R .
• Determine which complete local rings are the completion of a catenary integral domain.
• Determine which complete local rings are the completion of a catenary unique factorization domain.

Possible colloquium topics:   Any topics in mathematics and especially commutative algebra/ring theory.

Steven Miller

For more information and references, see http://www.williams.edu/Mathematics/sjmiller/public_html/index.htm

Research interests :  Analytic number theory, random matrix theory, probability and statistics, graph theory.

My main research interest is in the distribution of zeros of L-functions.  The most studied of these is the Riemann zeta function, Sum_{n=1 to oo} 1/n^s.  The importance of this function becomes apparent when we notice that it can also be written as Prod_{p prime} 1 / (1 – 1/p^s); this function relates properties of the primes to those of the integers (and we know where the integers are!).  It turns out that the properties of zeros of L-functions are extremely useful in attacking questions in number theory.  Interestingly, a terrific model for these zeros is given by random matrix theory: choose a large matrix at random and study its eigenvalues.  This model also does a terrific job describing behavior ranging from heavy nuclei like Uranium to bus routes in Mexico!  I’m studying several problems in random matrix theory, which also have applications to graph theory (building efficient networks).  I am also working on several problems in probability and statistics, especially (but not limited to) sabermetrics (applying mathematical statistics to baseball) and Benford’s law of digit bias (which is often connected to fascinating questions about equidistribution).  Many data sets have a preponderance of first digits equal to 1 (look at the first million Fibonacci numbers, and you’ll see a leading digit of 1 about 30% of the time).  In addition to being of theoretical interest, applications range from the IRS (which uses it to detect tax fraud) to computer science (building more efficient computers).  I’m exploring the subject with several colleagues in fields ranging from accounting to engineering to the social sciences.

Possible thesis topics: 

• Theoretical models for zeros of elliptic curve L-functions (in the number field and function field cases).
• Studying lower order term behavior in zeros of L-functions.
• Studying the distribution of eigenvalues of sets of random matrices.
• Exploring Benford’s law of digit bias (both its theory and applications, such as image, voter and tax fraud).
• Propagation of viruses in networks (a graph theory / dynamical systems problem). Sabermetrics.
• Additive number theory (questions on sum and difference sets).

Possible colloquium topics: 

Plus anything you find interesting.  I’m also interested in applications, and have worked on subjects ranging from accounting to computer science to geology to marketing….

Ralph Morrison

Research interests:   I work in algebraic geometry, tropical geometry, graph theory (especially chip-firing games on graphs), and discrete geometry, as well as computer implementations that study these topics. Algebraic geometry is the study of solution sets to polynomial equations.  Such a solution set is called a variety.  Tropical geometry is a “skeletonized” version of algebraic geometry. We can take a classical variety and “tropicalize” it, giving us a tropical variety, which is a piecewise-linear subset of Euclidean space.  Tropical geometry combines combinatorics, discrete geometry, and graph theory with classical algebraic geometry, and allows for developing theory and computations that tell us about the classical varieties.  One flavor of this area of math is to study chip-firing games on graphs, which are motivated by (and applied to) questions about algebraic curves.

Possible thesis topics : Anything related to tropical geometry, algebraic geometry, chip-firing games (or other graph theory topics), and discrete geometry.  Here are a few specific topics/questions:

• Study the geometry of tropical plane curves, perhaps motivated by results from algebraic geometry.  For instance:  given 5 (algebraic) conics, there are 3264 conics that are tangent to all 5 of them.  What if we look at tropical conics–is there still a fixed number of tropical conics tangent to all of them?  If so, what is that number?  How does this tropical count relate to the algebraic count?
• What can tropical plane curves “look like”?  There are a few ways to make this question precise.  One common way is to look at the “skeleton” of a tropical curve, a graph that lives inside of the curve and contains most of the interesting data.  Which graphs can appear, and what can the lengths of its edges be?  I’ve done lots of work with students on these sorts of questions, but there are many open questions!
• What can tropical surfaces in three-dimensional space look like?  What is the version of a skeleton here?  (For instance, a tropical surface of degree 4 contains a distinguished polyhedron with at most 63 facets. Which polyhedra are possible?)
• Study the geometry of tropical curves obtained by intersecting two tropical surfaces.  For instance, if we intersect a tropical plane with a tropical surface of degree 4, we obtain a tropical curve whose skeleton has three loops.  How can those loops be arranged?  Or we could intersect degree 2 and degree 3 tropical surfaces, to get a tropical curve with 4 loops; which skeletons are possible there?
• One way to study tropical geometry is to replace the usual rules of arithmetic (plus and times) with new rules (min and plus).  How do topics like linear algebra work in these fields?  (It turns out they’re related to optimization, scheduling, and job assignment problems.)
• Chip-firing games on graphs model questions from algebraic geometry.  One of the most important comes in the “gonality” of a graph, which is the smallest number of chips on a graph that could eliminate (via a series of “chip-firing moves”) an added debt of -1 anywhere on the graph.  There are lots of open questions for studying the gonality of graphs; this include general questions, like “What are good lower bounds on gonality?” and specific ones, like “What’s the gonality of the n-dimensional hypercube graph?”
• We can also study versions of gonality where we place -r chips instead of just -1; this gives us the r^th gonality of a graph.  Together, the first, second, third, etc. gonalities form the “gonality sequence” of a graph.  What sequences of integers can be the gonality sequence of some graph?  Is there a graph whose gonality sequence starts 3, 5, 8?
• There are many computational and algorithmic questions to ask about chip-firing games.  It’s known that computing the gonality of a general graph is NP-hard; what if we restrict to planar graphs?  Or graphs that are 3-regular? And can we implement relatively efficient ways of computing these numbers, at least for small graphs?
• What if we changed our rules for chip-firing games, for instance by working with chips modulo N?  How can we “win” a chip-firing game in that context, since there’s no more notion of debt?
• Study a “graph throttling” version of gonality.  For instance, instead of minimizing the number of chips we place on the graph, maybe we can also try to decrease the number of chip-firing moves we need to eliminate debt.
• Chip-firing games lead to interesting questions on other topics in graph theory.  For instance, there’s a conjectured upper bound of (|E|-|V|+4)/2 on the gonality of a graph; and any graph is known to have gonality at least its tree-width.  Can we prove the (weaker) result that (|E|-|V|+4)/2 is an upper bound on tree-width?  (Such a result would be of interest to graph theorists, even the idea behind it comes from algebraic geometry!)
• Topics coming from discrete geometry.  For example:  suppose you want to make “string art”, where you have one shape inside of another with string weaving between the inside and the outside shapes.  For which pairs of shapes is this possible?

Possible Colloquium topics:   I’m happy to advise a talk in any area of math, but would be especially excited about talks related to algebra, geometry, graph theory, or discrete mathematics.

Shaoyang Ning (On Leave 2024 – 2025)

Research Interest :  Statistical methodologies and applications. My research focuses on the study and design of statistical methods for integrative data analysis, in particular, to address the challenges of increasing complexity and connectivity arising from “Big Data”. I’m interested in innovating statistical methods that efficiently integrate multi-source, multi-resolution information to solve real-life problems. Instances include tracking localized influenza with Google search data and predicting cancer-targeting drugs with high-throughput genetic profiling data. Other interests include Bayesian methods, copula modeling, and nonparametric methods.

• Digital (disease) tracking: Using Internet search data to track and predict influenza activities at different resolutions (nation, region, state, city); Integrating other sources of digital data (e.g. Twitter, Facebook) and/or extending to track other epidemics and social/economic events, such as dengue, presidential approval rates, employment rates, and etc.
• Predicting cancer drugs with multi-source profiling data: Developing new methods to aggregate genetic profiling data of different sources (e.g., mutations, expression levels, CRISPR knockouts, drug experiments) in cancer cell lines to identify potential cancer-targeting drugs, their modes of actions and genetic targets.
• Social media text mining: Developing new methods to analyze and extract information from social media data (e.g. Reddit, Twitter). What are the challenges in analyzing the large-volume but short-length social media data? Can classic methods still apply? How should we innovate to address these difficulties?
• Copula modeling: How do we model and estimate associations between different variables when they are beyond multivariate Normal? What if the data are heavily dependent in the tails of their distributions (commonly observed in stock prices)? What if dependence between data are non-symmetric and complex? When the size of data is limited but the dimension is large, can we still recover their correlation structures? Copula model enables to “link” the marginals of a multivariate random variable to its joint distribution with great flexibility and can just be the key to the questions above.
• Other cross-disciplinary, data-driven projects: Applying/developing statistical methodology to answer an interesting scientific question in collaboration with a scientist or social scientist.

Possible colloquium topics:   Any topics in statistical methodology and application, including but not limited to: topics in applied statistics, Bayesian methods, computational biology, statistical learning, “Big Data” mining, and other cross-disciplinary projects.

Anna Neufeld

Research interests:  My research is motivated by the gap between classical statistical tools and practical data analysis. Classic statistical tools are designed for testing a single hypothesis about a single, pre-specified model. However, modern data analysis is an adaptive process that involves exploring the data, fitting several models, evaluating these models, and then testing a potentially large number of hypotheses about one or more selected models. With this in mind, I am interested in topics such as (1) methods for model validation and selection, (2) methods for testing data-driven hypotheses (post-selection inference), and (3) methods for testing a large number of hypotheses. I am also interested in any applied project where I can help a scientist rigorously answer an important question using data. 

• Cross-validation for unsupervised learning. Cross-validation is one of the most widely-used tools for model validation, but, in its typical form, it cannot be used for unsupervised learning problems. Numerous ad-hoc proposals exist for validating unsupervised learning models, but there is a need to compare and contrast these proposals and work towards a unified approach.
• Identifying the number of cell types in single-cell genomics datasets. This is an application of the topic above, since the cell types are typically estimated via unsupervised learning.
• There is growing interest in “post-prediction inference”, which is the task of doing valid statistical inference when some inputs to your statistical model are the outputs of other statistical models (i.e. predictions). Frameworks have recently been proposed for post-prediction inference in the setting where you have access to a gold-standard dataset where the true inputs, rather than the predicted inputs, have been observed. A thesis could explore the possibility of post-prediction inference in the absence of this gold-standard dataset.
• Any other topic of student interest related to selective inference, multiple testing, or post-prediction inference.
• Any collaborative project in which we work with a scientist to identify an interesting question in need of non-standard statistics.
• I am open to advising colloquia in almost any area of statistical methodology or applications, including but not limited to: multiple testing, post-selection inference, post-prediction inference, model selection, model validation, statistical machine learning, unsupervised learning, or genomics.

Allison Pacelli

Research interests:   Math Education, Math & Politics, and Algebraic Number Theory.

Math Education.  Math education is the study of the practice of teaching and learning mathematics, at all levels. For example, do high school calculus students learn best from lecture or inquiry-based learning? What mathematical content knowledge is critical for elementary school math teachers? Is a flipped classroom more effective than a traditional learning format? Many fascinating questions remain, at all levels of education. We can talk further to narrow down project ideas.

Math & Politics.  The mathematics of voting and the mathematics of fair division are two fascinating topics in the field of mathematics and politics. Research questions look at types of voting systems, and the properties that we would want a voting system to satisfy, as well as the idea of fairness when splitting up a single object, like cake, or a collection of objects, such as after a divorce or a death.

Algebraic Number Theory.  The Fundamental Theorem of Arithmetic states that the ring of integers is a unique factorization domain, that is, every integer can be uniquely factored into a product of primes. In other rings, there are analogues of prime numbers, but factorization into primes is not necessarily unique!

In order to determine whether factorization into primes is unique in the ring of integers of a number field or function field, it is useful to study the associated class group – the group of equivalence classes of ideals. The class group is trivial if and only if the ring is a unique factorization domain. Although the study of class groups dates back to Gauss and played a key role in the history of Fermat’s Last Theorem, many basic questions remain open.

  Possible thesis topics:

• Topics in math education, including projects at the elementary school level all the way through college level.
• Topics in voting and fair division.
• Investigating the divisibility of class numbers or the structure of the class group of quadratic fields and higher degree extensions.
• Exploring polynomial analogues of theorems from number theory concerning sums of powers, primes, divisibility, and arithmetic functions.

Possible colloquium topics:   Anything in number theory, algebra, or math & politics.

Anna Plantinga

Research interests:   I am interested in both applied and methodological statistics. My research primarily involves problems related to statistical analysis within genetics, genomics, and in particular the human microbiome (the set of bacteria that live in and on a person).  Current areas of interest include longitudinal data, distance-based analysis methods such as kernel machine regression, high-dimensional data, and structured data.

• Impacts of microbiome volatility. Sometimes the variability of a microbial community is more indicative of an unhealthy community than the actual bacteria present. We have developed an approach to quantifying microbiome variability (“volatility”). This project will use extensive simulations to explore the impact of between-group differences in volatility on a variety of standard tests for association between the microbiome and a health outcome.
• Accounting for excess zeros (sparse feature matrices). Often in a data matrix with many zeros, some of the zeros are “true” or “structural” zeros, whereas others are simply there because we have fewer observations for some subjects. How we account for these zeros affects analysis results. Which methods to account for excess zeros perform best for different analyses?
• Longitudinal methods for compositional data. When we have longitudinal data, we assume the same variables are measured at every time point. For high-dimensional compositions, this may not be the case. We would generally assume that the missing component was absent at any time points for which it was not measured. This project will explore alternatives to making that assumption.
• Applied statistics research. In collaboration with a scientist or social scientist, use appropriate statistical methodology (or variations on existing methods) to answer an interesting scientific question.

Any topics in statistical application, education, or methodology, including but not restricted to:

• Topics in applied statistics.
• Methods for microbiome data analysis.
• Statistical genetics.
• Electronic health records.
• Variable selection and statistical learning.
• Longitudinal methods.

Cesar Silva

Research interests :  Ergodic theory and measurable dynamics; in particular mixing properties and rank one examples, and infinite measure-preserving and nonsingular transformations and group actions.  Measurable dynamics of transformations defined on the p-adic field.  Measurable sensitivity.  Fractals.  Fractal Geometry.

Possible thesis topics:    Ergodic Theory.   Ergodic theory studies the probabilistic behavior of abstract dynamical systems.  Dynamical systems are systems that change with time, such as the motion of the planets or of a pendulum.  Abstract dynamical systems represent the state of a dynamical system by a point in a mathematical space (phase space).  In many cases this space is assumed to be the unit interval [0,1) with Lebesgue measure.  One usually assumes that time is measured at discrete intervals and so the law of motion of the system is represented by a single map (or transformation) of the phase space [0,1).  In this case one studies various dynamical behaviors of these maps, such as ergodicity, weak mixing, and mixing.  I am also interested in studying the measurable dynamics of systems defined on the p-adics numbers.  The prerequisite is a first course in real analysis.  Topological Dynamics.  Dynamics on compact or locally compact spaces.

Topics in mathematics and in particular:

• Any topic in measure theory.  See for example any of the first few chapters in “Measure and Category” by J. Oxtoby. Possible topics include the Banach-Tarski paradox, the Banach-Mazur game, Liouville numbers and s-Hausdorff measure zero.
• Topics in applied linear algebra and functional analysis.
• Fractal sets, fractal generation, image compression, and fractal dimension.
• Dynamics on the p-adic numbers.
• Banach-Tarski paradox, space filling curves.

Mihai Stoiciu

Research interests: Mathematical Physics and Functional Analysis. I am interested in the study of the spectral properties of various operators arising from mathematical physics – especially the Schrodinger operator. In particular, I am investigating the distribution of the eigenvalues for special classes of self-adjoint and unitary random matrices.

Topics in mathematical physics, functional analysis and probability including:

• Investigate the spectrum of the Schrodinger operator. Possible research topics: Find good estimates for the number of bound states; Analyze the asymptotic growth of the number of bound states of the discrete Schrodinger operator at large coupling constants.
• Study particular classes of orthogonal polynomials on the unit circle.
• Investigate numerically the statistical distribution of the eigenvalues for various classes of random CMV matrices.
• Study the general theory of point processes and its applications to problems in mathematical physics.

Possible colloquium topics:  

Any topics in mathematics, mathematical physics, functional analysis, or probability, such as:

• The Schrodinger operator.
• Orthogonal polynomials on the unit circle.
• Statistical distribution of the eigenvalues of random matrices.
• The general theory of point processes and its applications to problems in mathematical physics.

Elizabeth Upton

Research Interests: My research interests center around network science, with a focus on regression methods for network-indexed data. Networks are used to capture the relationships between elements within a system. Examples include social networks, transportation networks, and biological networks. I also enjoy tackling problems with pragmatic applications and am therefore interested in applied interdisciplinary research.

• Regression models for network data: how can we incorporate network structure (and dependence) in our regression framework when modeling a vertex-indexed response?
• Identify effects shaping network structure. For example, in social networks, the phrase “birds of a feather flock together” is often used to describe homophily. That is, those who have similar interests are more likely to become friends. How can we capture or test this effect, and others, in a regression framework when modeling edge-indexed responses?
• Extending models for multilayer networks. Current methodologies combine edges from multiple networks in some sort of weighted averaging scheme. Could a penalized multivariate approach yield a more informative model?
• Developing algorithms to make inference on large networks more efficient.
• Any topic in linear or generalized linear modeling (including mixed-effects regression models, zero-inflated regressions, etc.).
• Applied statistics research. In collaboration with a scientist or social scientist, use appropriate statistical methodology to answer an interesting scientific question.
• Any applied statistics research project/paper
• Topics in linear or generalized linear modeling
• Network visualizations and statistics