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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
- USF Research
- USF Libraries
Digital Commons @ USF > College of Arts and Sciences > Mathematics and Statistics > Theses and Dissertations
Mathematics and Statistics Theses and Dissertations
Theses/dissertations from 2024 2024.
The Effect of Fixed Time Delays on the Synchronization Phase Transition , Shaizat Bakhytzhan
On the Subelliptic and Subparabolic Infinity Laplacian in Grushin-Type Spaces , Zachary Forrest
Utilizing Machine Learning Techniques for Accurate Diagnosis of Breast Cancer and Comprehensive Statistical Analysis of Clinical Data , Myat Ei Ei Phyo
Quandle Rings, Idempotents and Cocycle Invariants of Knots , Dipali Swain
Comparative Analysis of Time Series Models on U.S. Stock and Exchange Rates: Bayesian Estimation of Time Series Error Term Model Versus Machine Learning Approaches , Young Keun Yang
Theses/Dissertations from 2023 2023
Classification of Finite Topological Quandles and Shelves via Posets , Hitakshi Lahrani
Applied Analysis for Learning Architectures , Himanshu Singh
Rational Functions of Degree Five That Permute the Projective Line Over a Finite Field , Christopher Sze
Theses/Dissertations from 2022 2022
New Developments in Statistical Optimal Designs for Physical and Computer Experiments , Damola M. Akinlana
Advances and Applications of Optimal Polynomial Approximants , Raymond Centner
Data-Driven Analytical Predictive Modeling for Pancreatic Cancer, Financial & Social Systems , Aditya Chakraborty
On Simultaneous Similarity of d-tuples of Commuting Square Matrices , Corey Connelly
Symbolic Computation of Lump Solutions to a Combined (2+1)-dimensional Nonlinear Evolution Equation , Jingwei He
Boundary behavior of analytic functions and Approximation Theory , Spyros Pasias
Stability Analysis of Delay-Driven Coupled Cantilevers Using the Lambert W-Function , Daniel Siebel-Cortopassi
A Functional Optimization Approach to Stochastic Process Sampling , Ryan Matthew Thurman
Theses/Dissertations from 2021 2021
Riemann-Hilbert Problems for Nonlocal Reverse-Time Nonlinear Second-order and Fourth-order AKNS Systems of Multiple Components and Exact Soliton Solutions , Alle Adjiri
Zeros of Harmonic Polynomials and Related Applications , Azizah Alrajhi
Combination of Time Series Analysis and Sentiment Analysis for Stock Market Forecasting , Hsiao-Chuan Chou
Uncertainty Quantification in Deep and Statistical Learning with applications in Bio-Medical Image Analysis , K. Ruwani M. Fernando
Data-Driven Analytical Modeling of Multiple Myeloma Cancer, U.S. Crop Production and Monitoring Process , Lohuwa Mamudu
Long-time Asymptotics for mKdV Type Reduced Equations of the AKNS Hierarchy in Weighted L 2 Sobolev Spaces , Fudong Wang
Online and Adjusted Human Activities Recognition with Statistical Learning , Yanjia Zhang
Theses/Dissertations from 2020 2020
Bayesian Reliability Analysis of The Power Law Process and Statistical Modeling of Computer and Network Vulnerabilities with Cybersecurity Application , Freeh N. Alenezi
Discrete Models and Algorithms for Analyzing DNA Rearrangements , Jasper Braun
Bayesian Reliability Analysis for Optical Media Using Accelerated Degradation Test Data , Kun Bu
On the p(x)-Laplace equation in Carnot groups , Robert D. Freeman
Clustering methods for gene expression data of Oxytricha trifallax , Kyle Houfek
Gradient Boosting for Survival Analysis with Applications in Oncology , Nam Phuong Nguyen
Global and Stochastic Dynamics of Diffusive Hindmarsh-Rose Equations in Neurodynamics , Chi Phan
Restricted Isometric Projections for Differentiable Manifolds and Applications , Vasile Pop
On Some Problems on Polynomial Interpolation in Several Variables , Brian Jon Tuesink
Numerical Study of Gap Distributions in Determinantal Point Process on Low Dimensional Spheres: L -Ensemble of O ( n ) Model Type for n = 2 and n = 3 , Xiankui Yang
Non-Associative Algebraic Structures in Knot Theory , Emanuele Zappala
Theses/Dissertations from 2019 2019
Field Quantization for Radiative Decay of Plasmons in Finite and Infinite Geometries , Maryam Bagherian
Probabilistic Modeling of Democracy, Corruption, Hemophilia A and Prediabetes Data , A. K. M. Raquibul Bashar
Generalized Derivations of Ternary Lie Algebras and n-BiHom-Lie Algebras , Amine Ben Abdeljelil
Fractional Random Weighted Bootstrapping for Classification on Imbalanced Data with Ensemble Decision Tree Methods , Sean Charles Carter
Hierarchical Self-Assembly and Substitution Rules , Daniel Alejandro Cruz
Statistical Learning of Biomedical Non-Stationary Signals and Quality of Life Modeling , Mahdi Goudarzi
Probabilistic and Statistical Prediction Models for Alzheimer’s Disease and Statistical Analysis of Global Warming , Maryam Ibrahim Habadi
Essays on Time Series and Machine Learning Techniques for Risk Management , Michael Kotarinos
The Systems of Post and Post Algebras: A Demonstration of an Obvious Fact , Daviel Leyva
Reconstruction of Radar Images by Using Spherical Mean and Regular Radon Transforms , Ozan Pirbudak
Analyses of Unorthodox Overlapping Gene Segments in Oxytricha Trifallax , Shannon Stich
An Optimal Medium-Strength Regularity Algorithm for 3-uniform Hypergraphs , John Theado
Power Graphs of Quasigroups , DayVon L. Walker
Theses/Dissertations from 2018 2018
Groups Generated by Automata Arising from Transformations of the Boundaries of Rooted Trees , Elsayed Ahmed
Non-equilibrium Phase Transitions in Interacting Diffusions , Wael Al-Sawai
A Hybrid Dynamic Modeling of Time-to-event Processes and Applications , Emmanuel A. Appiah
Lump Solutions and Riemann-Hilbert Approach to Soliton Equations , Sumayah A. Batwa
Developing a Model to Predict Prevalence of Compulsive Behavior in Individuals with OCD , Lindsay D. Fields
Generalizations of Quandles and their cohomologies , Matthew J. Green
Hamiltonian structures and Riemann-Hilbert problems of integrable systems , Xiang Gu
Optimal Latin Hypercube Designs for Computer Experiments Based on Multiple Objectives , Ruizhe Hou
Human Activity Recognition Based on Transfer Learning , Jinyong Pang
Signal Detection of Adverse Drug Reaction using the Adverse Event Reporting System: Literature Review and Novel Methods , Minh H. Pham
Statistical Analysis and Modeling of Cyber Security and Health Sciences , Nawa Raj Pokhrel
Machine Learning Methods for Network Intrusion Detection and Intrusion Prevention Systems , Zheni Svetoslavova Stefanova
Orthogonal Polynomials With Respect to the Measure Supported Over the Whole Complex Plane , Meng Yang
Theses/Dissertations from 2017 2017
Modeling in Finance and Insurance With Levy-It'o Driven Dynamic Processes under Semi Markov-type Switching Regimes and Time Domains , Patrick Armand Assonken Tonfack
Prevalence of Typical Images in High School Geometry Textbooks , Megan N. Cannon
On Extending Hansel's Theorem to Hypergraphs , Gregory Sutton Churchill
Contributions to Quandle Theory: A Study of f-Quandles, Extensions, and Cohomology , Indu Rasika U. Churchill
Linear Extremal Problems in the Hardy Space H p for 0 p , Robert Christopher Connelly
Statistical Analysis and Modeling of Ovarian and Breast Cancer , Muditha V. Devamitta Perera
Statistical Analysis and Modeling of Stomach Cancer Data , Chao Gao
Structural Analysis of Poloidal and Toroidal Plasmons and Fields of Multilayer Nanorings , Kumar Vijay Garapati
Dynamics of Multicultural Social Networks , Kristina B. Hilton
Cybersecurity: Stochastic Analysis and Modelling of Vulnerabilities to Determine the Network Security and Attackers Behavior , Pubudu Kalpani Kaluarachchi
Generalized D-Kaup-Newell integrable systems and their integrable couplings and Darboux transformations , Morgan Ashley McAnally
Patterns in Words Related to DNA Rearrangements , Lukas Nabergall
Time Series Online Empirical Bayesian Kernel Density Segmentation: Applications in Real Time Activity Recognition Using Smartphone Accelerometer , Shuang Na
Schreier Graphs of Thompson's Group T , Allen Pennington
Cybersecurity: Probabilistic Behavior of Vulnerability and Life Cycle , Sasith Maduranga Rajasooriya
Bayesian Artificial Neural Networks in Health and Cybersecurity , Hansapani Sarasepa Rodrigo
Real-time Classification of Biomedical Signals, Parkinson’s Analytical Model , Abolfazl Saghafi
Lump, complexiton and algebro-geometric solutions to soliton equations , Yuan Zhou
Theses/Dissertations from 2016 2016
A Statistical Analysis of Hurricanes in the Atlantic Basin and Sinkholes in Florida , Joy Marie D'andrea
Statistical Analysis of a Risk Factor in Finance and Environmental Models for Belize , Sherlene Enriquez-Savery
Putnam's Inequality and Analytic Content in the Bergman Space , Matthew Fleeman
On the Number of Colors in Quandle Knot Colorings , Jeremy William Kerr
Statistical Modeling of Carbon Dioxide and Cluster Analysis of Time Dependent Information: Lag Target Time Series Clustering, Multi-Factor Time Series Clustering, and Multi-Level Time Series Clustering , Doo Young Kim
Some Results Concerning Permutation Polynomials over Finite Fields , Stephen Lappano
Hamiltonian Formulations and Symmetry Constraints of Soliton Hierarchies of (1+1)-Dimensional Nonlinear Evolution Equations , Solomon Manukure
Modeling and Survival Analysis of Breast Cancer: A Statistical, Artificial Neural Network, and Decision Tree Approach , Venkateswara Rao Mudunuru
Generalized Phase Retrieval: Isometries in Vector Spaces , Josiah Park
Leonard Systems and their Friends , Jonathan Spiewak
Resonant Solutions to (3+1)-dimensional Bilinear Differential Equations , Yue Sun
Statistical Analysis and Modeling Health Data: A Longitudinal Study , Bhikhari Prasad Tharu
Global Attractors and Random Attractors of Reaction-Diffusion Systems , Junyi Tu
Time Dependent Kernel Density Estimation: A New Parameter Estimation Algorithm, Applications in Time Series Classification and Clustering , Xing Wang
On Spectral Properties of Single Layer Potentials , Seyed Zoalroshd
Theses/Dissertations from 2015 2015
Analysis of Rheumatoid Arthritis Data using Logistic Regression and Penalized Approach , Wei Chen
Active Tile Self-assembly and Simulations of Computational Systems , Daria Karpenko
Nearest Neighbor Foreign Exchange Rate Forecasting with Mahalanobis Distance , Vindya Kumari Pathirana
Statistical Learning with Artificial Neural Network Applied to Health and Environmental Data , Taysseer Sharaf
Radial Versus Othogonal and Minimal Projections onto Hyperplanes in l_4^3 , Richard Alan Warner
Ensemble Learning Method on Machine Maintenance Data , Xiaochuang Zhao
Theses/Dissertations from 2014 2014
Properties of Graphs Used to Model DNA Recombination , Ryan Arredondo
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Home > Computational, Mathematical, and Physical Sciences > Mathematics Education > Theses and Dissertations
Mathematics Education Theses and Dissertations
Theses/dissertations from 2024 2024.
Rigorous Verification of Stability of Ideal Gas Layers , Damian Anderson
Documentation of Norm Negotiation in a Secondary Mathematics Classroom , Michelle R. Bagley
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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Home > USC Columbia > Arts and Sciences > Mathematics > Mathematics Theses and Dissertations
Mathematics Theses and Dissertations
Theses/dissertations from 2023 2023.
Extreme Covering Systems, Primes Plus Squarefrees, and Lattice Points Close to a Helix , Jack Robert Dalton
On the Algebraic and Geometric Multiplicity of Zero as a Hypergraph Eigenvalue , Grant Ian Fickes
Deep Learning for Studying Materials Stability and Solving Thermodynamically Consistent PDES With Dynamic Boundary Conditions in Arbitrary Domains , Chunyan Li
Widely Digitally Delicate Brier Primes and Irreducibility Results for Some Classes of Polynomials , Thomas David Luckner
Deep Learning Methods for Some Problems in Scientific Computing , Yuankai Teng
Theses/Dissertations from 2022 2022
Covering Systems and the Minimum Modulus Problem , Maria Claire Cummings
The Existence and Quantum Approximation of Optimal Pure State Ensembles , Ryan Thomas McGaha
Structure Preserving Reduced-Order Models of Hamiltonian Systems , Megan Alice McKay
Tangled up in Tanglegrams , Drew Joseph Scalzo
Results on Select Combinatorial Problems With an Extremal Nature , Stephen Smith
Poset Ramsey Numbers for Boolean Lattices , Joshua Cain Thompson
Some Properties and Applications of Spaces of Modular Forms With ETA-Multiplier , Cuyler Daniel Warnock
Theses/Dissertations from 2021 2021
Simulation of Pituitary Organogenesis in Two Dimensions , Chace E. Covington
Polynomials, Primes and the PTE Problem , Joseph C. Foster
Widely Digitally Stable Numbers and Irreducibility Criteria For Polynomials With Prime Values , Jacob Juillerat
A Numerical Investigation of Fractional Models for Viscoelastic Materials With Applications on Concrete Subjected to Extreme Temperatures , Murray Macnamara
Trimming Complexes , Keller VandeBogert
Multiple Frailty Model for Spatially Correlated Interval-Censored , Wanfang Zhang
Theses/Dissertations from 2020 2020
An Equivariant Count of Nodal Orbits in an Invariant Pencil of Conics , Candace Bethea
Finite Axiomatisability in Nilpotent Varieties , Joshua Thomas Grice
Rationality Questions and the Derived Category , Alicia Lamarche
Counting Number Fields by Discriminant , Harsh Mehta
Distance Related Graph Invariants in Triangulations and Quadrangulations of the Sphere , Trevor Vincent Olsen
Diameter of 3-Colorable Graphs and Some Remarks on the Midrange Crossing Constant , Inne Singgih
Two Inquiries Related to the Digits of Prime Numbers , Jeremiah T. Southwick
Windows and Generalized Drinfeld Kernels , Robert R. Vandermolen
Connections Between Extremal Combinatorics, Probabilistic Methods, Ricci Curvature of Graphs, and Linear Algebra , Zhiyu Wang
An Ensemble-Based Projection Method and Its Numerical Investigation , Shuai Yuan
Variable-Order Fractional Partial Differential Equations: Analysis, Approximation and Inverse Problem , Xiangcheng Zheng
Theses/Dissertations from 2019 2019
Classification of Non-Singular Cubic Surfaces up to e-invariants , Mohammed Alabbood
On the Characteristic Polynomial of a Hypergraph , Gregory J. Clark
A Development of Transfer Entropy in Continuous-Time , Christopher David Edgar
Moving Off Collections and Their Applications, in Particular to Function Spaces , Aaron Fowlkes
Finding Resolutions of Mononomial Ideals , Hannah Melissa Kimbrell
Regression for Pooled Testing Data with Biomedical Applications , Juexin Lin
Numerical Methods for a Class of Reaction-Diffusion Equations With Free Boundaries , Shuang Liu
An Implementation of the Kapustin-Li Formula , Jessica Otis
A Nonlinear Parallel Model for Reversible Polymer Solutions in Steady and Oscillating Shear Flow , Erik Tracey Palmer
A Few Problems on the Steiner Distance and Crossing Number of Graphs , Josiah Reiswig
Successful Pressing Sequences in Simple Pseudo-Graphs , Hays Wimsatt Whitlatch
On The Generators of Quantum Dynamical Semigroups , Alexander Wiedemann
An Examination of Kinetic Monte Carlo Methods with Application to a Model of Epitaxial Growth , Dylana Ashton Wilhelm
Dynamical Entropy of Quantum Random Walks , Duncan Wright
Unconditionally Energy Stable Linear Schemes for a Two-Phase Diffuse Interface Model with Peng-Robinson Equation of State , Chenfei Zhang
Theses/Dissertations from 2018 2018
Theory, Computation, and Modeling of Cancerous Systems , Sameed Ahmed
Turán Problems and Spectral Theory on Hypergraphs and Tensors , Shuliang Bai
Quick Trips: On the Oriented Diameter of Graphs , Garner Paul Cochran
Geometry of Derived Categories on Noncommutative Projective Schemes , Blake Alexander Farman
A Quest for Positive Definite Matrices over Finite Fields , Erin Patricia Hanna
Comparison of the Performance of Simple Linear Regression and Quantile Regression with Non-Normal Data: A Simulation Study , Marjorie Howard
Special Fiber Rings of Certain Height Four Gorenstein Ideals , Jaree Hudson
Graph Homomorphisms and Vector Colorings , Michael Robert Levet
Local Rings and Golod Homomorphisms , Thomas Schnibben
States and the Numerical Range in the Regular Algebra , James Patrick Sweeney
Thermodynamically Consistent Hydrodynamic Phase Field Models and Numerical Approximation for Multi-Component Compressible Viscous Fluid Mixtures , Xueping Zhao
Theses/Dissertations from 2017 2017
On the Existence of Non-Free Totally Reflexive Modules , J. Cameron Atkins
Subdivision of Measures of Squares , Dylan Bates
Unconditionally Energy Stable Numerical Schemes for Hydrodynamics Coupled Fluids Systems , Alexander Yuryevich Brylev
Convergence and Rate of Convergence of Approximate Greedy-Type Algorithms , Anton Dereventsov
Covering Subsets of the Integers and a Result on Digits of Fibonacci Numbers , Wilson Andrew Harvey
Nonequispaced Fast Fourier Transform , David Hughey
Deep Learning: An Exposition , Ryan Kingery
A Family of Simple Codimension Two Singularities with Infinite Cohen-Macaulay Representation Type , Tyler Lewis
Polynomials Of Small Mahler Measure With no Newman Multiples , Spencer Victoria Saunders
Theses/Dissertations from 2016 2016
On Crown-free Set Families, Diffusion State Difference, and Non-uniform Hypergraphs , Edward Lawrence Boehnlein
Structure of the Stable Marriage and Stable Roommate Problems and Applications , Joe Hidakatsu
Binary Quartic Forms over Fp , Daniel Thomas Kamenetsky
On a Constant Associated with the Prouhet-Tarry-Escott Problem , Maria E. Markovich
Some Extremal And Structural Problems In Graph Theory , Taylor Mitchell Short
Chebyshev Inversion of the Radon Transform , Jared Cameron Szi
Modeling of Structural Relaxation By A Variable-Order Fractional Differential Equation , Su Yang
Theses/Dissertations from 2015 2015
Modeling, Simulation, and Applications of Fractional Partial Differential Equations , Wilson Cheung
The Packing Chromatic Number of Random d-regular Graphs , Ann Wells Clifton
Commutator Studies in Pursuit of Finite Basis Results , Nathan E. Faulkner
Avoiding Doubled Words in Strings of Symbols , Michael Lane
A Survey of the Kinetic Monte Carlo Algorithm as Applied to a Multicellular System , Michael Richard Laughlin
Toward the Combinatorial Limit Theory of free Words , Danny Rorabaugh
Trees, Partitions, and Other Combinatorial Structures , Heather Christina Smith
Fast Methods for Variable-Coefficient Peridynamic and Non-Local Diffusion Models , Che Wang
Modeling and Computations of Cellular Dynamics Using Complex-fluid Models , Jia Zhao
Theses/Dissertations from 2014 2014
The Non-Existence of a Covering System with all Moduli Distinct, Large and Square-Free , Melissa Kate Bechard
Explorations in Elementary and Analytic Number Theory , Scott Michael Dunn
Independence Polynomials , Gregory Matthew Ferrin
Turán Problems on Non-uniform Hypergraphs , Jeremy Travis Johnston
On the Group of Transvections of ADE-Diagrams , Marvin Jones
Fake Real Quadratic Orders , Richard Michael Oh
Theses/Dissertations from 2013 2013
Shimura Images of A Family of Half-Integral Weight Modular Forms , Kenneth Allan Brown
Sharp Bounds Associated With An Irreducibility Theorem For Polynomials Having Non-Negative Coefficients , Morgan Cole
Deducing Vertex Weights From Empirical Occupation Times , David Collins
Analysis and Processing of Irregularly Distributed Point Clouds , Kamala Hunt Diefenthaler
Generalizations of Sperner's Theorem: Packing Posets, Families Forbidding Posets, and Supersaturation , Andrew Philip Dove
Spectral Analysis of Randomly Generated Networks With Prescribed Degree Sequences , Clifford Davis Gaddy
Selected Research In Covering Systems of the Integers and the Factorization of Polynomials , Joshua Harrington
The Weierstrass Approximation Theorem , LaRita Barnwell Hipp
The Compact Implicit Integration Factor Scheme For the Solution of Allen-Cahn Equations , Meshack K. Kiplagat
Applications of the Lopsided Lovász Local Lemma Regarding Hypergraphs , Austin Tyler Mohr
Study On Covolume-Upwind Finite Volume Approximations For Linear Parabolic Partial Differential Equations , Rosalia Tatano
Coloring Pythagorean Triples and a Problem Concerning Cyclotomic Polynomials , Daniel White
Theses/Dissertations from 2012 2012
A Computational Approach to the Quillen-Suslin Theorem, Buchsbaum-Eisenbud Matrices, and Generic Hilbert-Burch Matrices , Jonathan Brett Barwick
Mathematical Modeling and Computational Studies for Cell Signaling , Kanadpriya Basu
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Home > FACULTIES > Applied Mathematics > APMATHS-ETD
Applied Mathematics Theses and Dissertations
This collection contains theses and dissertations from the Department of Applied Mathematics, collected from the Scholarship@Western Electronic Thesis and Dissertation Repository
Theses/Dissertations from 2023 2023
Visual Cortical Traveling Waves: From Spontaneous Spiking Populations to Stimulus-Evoked Models of Short-Term Prediction , Gabriel B. Benigno
Spike-Time Neural Codes and their Implication for Memory , Alexandra Busch
Study of Behaviour Change and Impact on Infectious Disease Dynamics by Mathematical Models , Tianyu Cheng
Series Expansions of Lambert W and Related Functions , Jacob Imre
Data-Driven Exploration of Coarse-Grained Equations: Harnessing Machine Learning , Elham Kianiharchegani
Pythagorean Vectors and Rational Orthonormal Matrices , Aishat Olagunju
The Magnetic Field of Protostar-Disk-Outflow Systems , Mahmoud Sharkawi
A Highly Charged Topic: Intrinsically Disordered Proteins and Protein pKa Values , Carter J. Wilson
Population Dynamics and Bifurcations in Predator-Prey Systems with Allee Effect , Yanni Zeng
Theses/Dissertations from 2022 2022
A Molecular Dynamics Study Of Polymer Chains In Shear Flows and Nanocomposites , Venkat Bala
On the Spatial Modelling of Biological Invasions , Tedi Ramaj
Complete Hopf and Bogdanov-Takens Bifurcation Analysis on Two Epidemic Models , Yuzhu Ruan
A Theoretical Perspective on Parasite-Host Coevolution with Alternative Modes of Infection , George N. Shillcock
Theses/Dissertations from 2021 2021
Mathematical Modelling & Simulation of Large and Small Scale Structures in Star Formation , Gianfranco Bino
Mathematical Modelling of Ecological Systems in Patchy Environments , Ao Li
Credit Risk Measurement and Application based on BP Neural Networks , Jingshi Luo
Coevolution of Hosts and Pathogens in the Presence of Multiple Types of Hosts , Evan J. Mitchell
SymPhas: A modular API for phase-field modeling using compile-time symbolic algebra , Steven A. Silber
Population and Evolution Dynamics in Predator-prey Systems with Anti-predation Responses , Yang Wang
Theses/Dissertations from 2020 2020
The journey of a single polymer chain to a nanopore , Navid Afrasiabian
Exploration Of Stock Price Predictability In HFT With An Application In Spoofing Detection , Andrew Day
Multi-Scale Evolution of Virulence of HIV-1 , David W. Dick
Contraction Analysis of Functional Competitive Lotka-Volterra Systems: Understanding Competition Between Modified Bacteria and Plasmodium within Mosquitoes. , Nickolas Goncharenko
Phage-Bacteria Interaction and Prophage Sequences in Bacterial Genomes , Amjad Khan
The Effect of the Initial Structure on the System Relaxation Time in Langevin Dynamics , Omid Mozafar
Mathematical modelling of prophage dynamics , Tyler Pattenden
Hybrid Symbolic-Numeric Computing in Linear and Polynomial Algebra , Leili Rafiee Sevyeri
Abelian Integral Method and its Application , Xianbo Sun
Theses/Dissertations from 2019 2019
Algebraic Companions and Linearizations , Eunice Y. S. Chan
Algorithms for Mappings and Symmetries of Differential Equations , Zahra Mohammadi
Algorithms for Bohemian Matrices , Steven E. Thornton
A Survey Of Numerical Quadrature Methods For Highly Oscillatory Integrals , Jeet Trivedi
Theses/Dissertations from 2018 2018
Properties and Computation of the Inverse of the Gamma function , Folitse Komla Amenyou
Optimization Studies and Applications: in Retail Gasoline Market , Daero Kim
Models of conflict and voluntary cooperation between individuals in non-egalitarian social groups , Cody Koykka
Investigation of chaos in biological systems , Navaneeth Mohan
Bifurcation Analysis of Two Biological Systems: A Tritrophic Food Chain Model and An Oscillating Networks Model , Xiangyu Wang
Ecology and Evolution of Dispersal in Metapopulations , Jingjing Xu
Selected Topics in Quantization and Renormalization of Gauge Fields , Chenguang Zhao
Three Essays on Structural Models , Xinghua Zhou
Theses/Dissertations from 2017 2017
On Honey Bee Colony Dynamics and Disease Transmission , Matthew I. Betti
Simulation of driven elastic spheres in a Newtonian fluid , Shikhar M. Dwivedi
Feasible Computation in Symbolic and Numeric Integration , Robert H.C. Moir
Modelling Walleye Population and Its Cannibalism Effect , Quan Zhou
Theses/Dissertations from 2016 2016
Dynamics of Discs in a Nematic Liquid Crystal , Alena Antipova
Modelling the Impact of Climate Change on the Polar Bear Population in Western Hudson Bay , Nicole Bastow
A comparison of solution methods for Mandelbrot-like polynomials , Eunice Y. S. Chan
A model-based test of the efficacy of a simple rule for predicting adaptive sex allocation , Joshua D. Dunn
Universal Scaling Properties After Quantum Quenches , Damian Andres Galante
Modeling the Mass Function of Stellar Clusters Using the Modified Lognormal Power-Law Probability Distribution Function , Deepakshi Madaan
Bacteria-Phage Models with a Focus on Prophage as a Genetic Reservoir , Alina Nadeem
A Sequence of Symmetric Bézout Matrix Polynomials , Leili Rafiee Sevyeri
Study of Infectious Diseases by Mathematical Models: Predictions and Controls , SM Ashrafur Rahman
The survival probability of beneficial de novo mutations in budding viruses, with an emphasis on influenza A viral dynamics , Jennifer NS Reid
Essays in Market Structure and Liquidity , Adrian J. Walton
Computation of Real Radical Ideals by Semidefinite Programming and Iterative Methods , Fei Wang
Studying Both Direct and Indirect Effects in Predator-Prey Interaction , Xiaoying Wang
Theses/Dissertations from 2015 2015
The Effect of Diversification on the Dynamics of Mobile Genetic Elements in Prokaryotes: The Birth-Death-Diversification Model , Nicole E. Drakos
Algorithms to Compute Characteristic Classes , Martin Helmer
Studies of Contingent Capital Bonds , Jingya Li
Determination of Lie superalgebras of supersymmetries of super differential equations , Xuan Liu
Edge states and quantum Hall phases in graphene , Pavlo Piatkovskyi
Evolution of Mobile Promoters in Prokaryotic Genomes. , Mahnaz Rabbani
Extensions of the Cross-Entropy Method with Applications to Diffusion Processes and Portfolio Losses , Alexandre Scott
Theses/Dissertations from 2014 2014
A Molecular Simulation Study on Micelle Fragmentation and Wetting in Nano-Confined Channels , Mona Habibi
Study of Virus Dynamics by Mathematical Models , Xiulan Lai
Applications of Stochastic Control in Energy Real Options and Market Illiquidity , Christian Maxwell
Options Pricing and Hedging in a Regime-Switching Volatility Model , Melissa A. Mielkie
Optimal Contract Design for Co-development of Companion Diagnostics , Rodney T. Tembo
Bifurcation of Limit Cycles in Smooth and Non-smooth Dynamical Systems with Normal Form Computation , Yun Tian
Understanding Recurrent Disease: A Dynamical Systems Approach , Wenjing Zhang
Theses/Dissertations from 2013 2013
Pricing and Hedging Index Options with a Dominant Constituent Stock , Helen Cheyne
On evolution dynamics and strategies in some host-parasite models , Liman Dai
Valuation of the Peterborough Prison Social Impact Bond , Majid Hasan
Sensitivity Analysis of Minimum Variance Portfolios , Xiaohu Ji
Eigenvalue Methods for Interpolation Bases , Piers W. Lawrence
Hybrid Lattice Boltzmann - Molecular Dynamics Simulations With Both Simple and Complex Fluids , Frances E. Mackay
Ecological Constraints and the Evolution of Cooperative Breeding , David McLeod
A single cell based model for cell divisions with spontaneous topology changes , Anna Mkrtchyan
Analysis of Re-advanceable Mortgages , Almas Naseem
Modeling leafhopper populations and their role in transmitting plant diseases. , Ji Ruan
Topological properties of modular networks, with a focus on networks of functional connections in the human brain , Estefania Ruiz Vargas
Computation Sequences for Series and Polynomials , Yiming Zhang
Theses/Dissertations from 2012 2012
A Real Options Valuation of Renewable Energy Projects , Natasha Burke
Approximate methods for dynamic portfolio allocation under transaction costs , Nabeel Butt
Optimal clustering techniques for metagenomic sequencing data , Erik T. Cameron
Phase Field Crystal Approach to the Solidification of Ferromagnetic Materials , Niloufar Faghihi
Molecular Dynamics Simulations of Peptide-Mineral Interactions , Susanna Hug
Molecular Dynamics Studies of Water Flow in Carbon Nanotubes , Alexander D. Marshall
Valuation of Multiple Exercise Options , T. James Marshall
Incomplete Market Models of Carbon Emissions Markets , Walid Mnif
Topics in Field Theory , Alexander Patrushev
Pricing and Trading American Put Options under Sub-Optimal Exercise Policies , William Wei Xing
Further applications of higher-order Markov chains and developments in regime-switching models , Xiaojing Xi
Theses/Dissertations from 2011 2011
Bifurcations and Stability in Models of Infectious Diseases , Bernard S. Chan
Real Options Models in Real Estate , Jin Won Choi
Models, Techniques, and Metrics for Managing Risk in Software Engineering , Andriy Miranskyy
Thermodynamics, Hydrodynamics and Critical Phenomena in Strongly Coupled Gauge Theories , Christopher Pagnutti
Molecular Dynamics Studies of Interactions of Phospholipid Membranes with Dehydroergosterol and Penetrating Peptides , Amir Mohsen Pourmousa Abkenar
Socially Responsible Investment in a Changing World , Desheng Wu
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181 Mathematics Research Topics From PhD Experts
If you are reading this blog post, it means you are looking for some exceptional math research topics. You want them to be original, unique even. If you manage to find topics like this, you can be sure your professor will give you a top grade (if you write a decent paper, that is). The good news is that you have arrived at just the right place – at the right time. We have just finished updating our list of topics, so you will find plenty of original ideas right on this page. All our topics are 100 percent free to use as you see fit. You can reword them and you don’t need to give us any credit.
And remember: if you need assistance from a professional, don’t hesitate to reach out to us. We are not just the best place for math research topics for high school students; we are also the number one choice for students looking for top-notch research paper writing services.
Our Newest Research Topics in Math
We know you probably want the best and most recent research topics in math. You want your paper to stand out from all the rest. After all, this is the best way to get some bonus points from your professor. On top of this, finding some great topics for your next paper makes it easier for you to write the essay. As long as you know at least something about the topic, you’ll find that writing a great paper or buy phd thesis isn’t as difficult as you previously thought.
So, without further ado, here are the 181 brand new topics for your next math research paper:
Cool Math Topics to Research
Are you looking for some cool math topics to research? We have a list of original topics for your right here. Pick the one you like and start writing now:
- Roll two dice and calculate a probability
- Discuss ancient Greek mathematics
- Is math really important in school?
- Discuss the binomial theorem
- The math behind encryption
- Game theory and its real-life applications
- Analyze the Bernoulli scheme
- What are holomorphic functions and how do they work?
- Describe big numbers
- Solving the Tower of Hanoi problem
Undergraduate Math Research Topics
If you are an undergraduate looking for some research topics for your next math paper, you will surely appreciate our list of interesting undergraduate math research topics:
- Methods to count discrete objects
- The origins of Greek symbols in mathematics
- Methods to solve simultaneous equations
- Real-world applications of the theorem of Pythagoras
- Discuss the limits of diffusion
- Use math to analyze the abortion data in the UK over the last 100 years
- Discuss the Knot theory
- Analyze predictive models (take meteorology as an example)
- In-depth analysis of the Monte Carlo methods for inverse problems
- Squares vs. rectangles (compare and contrast)
Number Theory Topics to Research
Interested in writing about number theory? It is not an easy subject to discuss, we know. However, we are sure you will appreciate these number theory topics:
- Discuss the greatest common divisor
- Explain the extended Euclidean algorithm
- What are RSA numbers?
- Discuss Bézout’s lemma
- In-depth analysis of the square-free polynomial
- Discuss the Stern-Brocot tree
- Analyze Fermat’s little theorem
- What is a discrete logarithm?
- Gauss’s lemma in number theory
- Analyze the Pentagonal number theorem
Math Research Topics for High School
High school students shouldn’t be too worried about their math papers because we have some unique, and quite interesting, math research topics for high school right here:
- Discuss Brun’s constant
- An in-depth look at the Brahmagupta–Fibonacci identity
- What is derivative algebra?
- Describe the Symmetric Boolean function
- Discuss orders of approximation in limits
- Solving Regiomontanus’ angle maximization problem
- What is a Quadratic integral?
- Define and describe complementary angles
- Analyze the incircle and excircles of a triangle
- Analyze the Bolyai–Gerwien theorem in geometry
- Math in our everyday life
Complex Math Topics
If you want to give some complex math topics a try, we have the best examples below. Remember, these topics should only be attempted by students who are proficient in mathematics:
- Mathematics and its appliance in Artificial Intelligence
- Try to solve an unsolved problem in math
- Discuss Kolmogorov’s zero-one law
- What is a discrete random variable?
- Analyze the Hewitt–Savage zero-one law
- What is a transferable belief model?
- Discuss 3 major mathematical theorems
- Describe and analyze the Dempster-Shafer theory
- An in-depth analysis of a continuous stochastic process
- Identify and analyze Gauss-Markov processes
Easy Math Research Paper Topics
Perhaps you don’t want to spend too much time working on your next research paper. Who can blame you? Check out these easy math research paper topics:
- Define the hyperbola
- Do we need to use a calculator during math class?
- The binomial theorem and its real-world applications
- What is a parabola in geometry?
- How do you calculate the slope of a curve?
- Define the Jacobian matrix
- Solving matrix problems effectively
- Why do we need differential equations?
- Should math be mandatory in all schools?
- What is a Hessian matrix?
Logic Topics to Research
We have some interesting logical topics for research papers. These are perfect for students interested in writing about math logic. Pick one right now:
- Discuss the reductio ad absurdum approach
- Discuss Boolean algebra
- What is consistency proof?
- Analyze Trakhtenbrot’s theorem (the finite model theory)
- Discuss the Gödel completeness theorem
- An in-depth analysis of Morley’s categoricity theorem
- How does the Back-and-forth method work?
- Discuss the Ehrenfeucht–Fraïssé game technique
- Discuss Aleph numbers (Aleph-null and Aleph-one)
- Solving the Suslin problem
Algebra Topics for a Research Paper
Would you like to write about an algebra topic? No problem, our seasoned writers have compiled a list of the best algebra topics for a research paper:
- Discuss the differential equation
- Analyze the Jacobson density theorem
- The 4 properties of a binary operation in algebra
- Analyze the unary operator in depth
- Analyze the Abel–Ruffini theorem
- Epimorphisms vs. monomorphisms: compare and contrast
- Discuss the Morita duality in algebraic structures
- Idempotent vs. nilpotent in Ring theory
- Discuss the Artin-Wedderburn theorem
- What is a commutative ring in algebra?
- Analyze and describe the Noetherian ring
Math Education Research Topics
There is nothing wrong with writing about math education, especially if your professor did not give you writing prompts. Here are some very nice math education research topics:
- What are the goals a mathematics professor should have?
- What is math anxiety in the classroom?
- Teaching math in UK schools: the difficulties
- Computer programming or math in high school?
- Is math education in Europe at a high enough level?
- Common Core Standards and their effects on math education
- Culture and math education in Africa
- What is dyscalculia and how does it manifest itself?
- When was algebra first thought in schools?
- Math education in the United States versus the United Kingdom
Computability Theory Topics to Research
Writing about computability theory can be a very interesting adventure. Give it a try! Here are some of our most interesting computability theory topics to research:
- What is a multiplication table?
- Analyze the Scholz conjecture
- Explain exponentiating by squaring
- Analyze the Myhill-Nerode theorem
- What is a tree automaton?
- Compare and contrast the Pushdown automaton and the Büchi automaton
- Discuss the Markov algorithm
- What is a Turing machine?
- Analyze the post correspondence problem
- Discuss the linear speedup theorem
- Discuss the Boolean satisfiability problem
Interesting Math Research Topics
We know you want topics that are interesting and relatively easy to write about. This is why we have a separate list of our most interesting math research topics:
- What is two-element Boolean algebra?
- The life of Gauss
- The life of Isaac Newton
- What is an orthodiagonal quadrilateral?
- Tessellation in Euclidean plane geometry
- Describe a hyperboloid in 3D geometry
- What is a sphericon?
- Discuss the peculiarities of Borel’s paradox
- Analyze the De Finetti theorem in statistics
- What are Martingales?
- The basics of stochastic calculus
Applied Math Research Topics
Interested in writing about applied mathematics? Our team managed to create a list of awesome applied math research topics from scratch for you:
- Discuss Newton’s laws of motion
- Analyze the perpendicular axes rule
- How is a Galilean transformation done?
- The conservation of energy and its applications
- Discuss Liouville’s theorem in Hamiltonian mechanics
- Analyze the quantum field theory
- Discuss the main components of the Lorentz symmetry
- An in-depth look at the uncertainty principle
Geometry Topics for a Research Paper
Geometry can be a very captivating subject, especially when you know plenty about it. Check out our list of geometry topics for a research paper and pick the best one today:
- Most useful trigonometry functions in math
- The life of Archimedes and his achievements
- Trigonometry in computer graphics
- Using Vincenty’s formulae in geodesy
- Define and describe the Heronian tetrahedron
- The math behind the parabolic microphone
- Discuss the Japanese theorem for concyclic polygons
- Analyze Euler’s theorem in geometry
Math Research Topics for Middle School
Yes, even middle school children can write about mathematics. We have some original math research topics for middle school right here:
- Finding critical points in a graph
- The basics of calculus
- What makes a graph ultrahomogeneous?
- How do you calculate the area of different shapes?
- What contributions did Euclid have to the field of mathematics?
- What is Diophantine geometry?
- What makes a graph regular?
- Analyze a full binary tree
Math Research Topics for College Students
As you’ve probably already figured out, college students should pick topics that are a bit more complex. We have some of the best math research topics for college students right here:
- What are extremal problems and how do you solve them?
- Discuss an unsolvable math problem
- How can supercomputers solve complex mathematical problems?
- An in-depth analysis of fractals
- Discuss the Boruvka’s algorithm (related to the minimum spanning tree)
- Discuss the Lorentz–FitzGerald contraction hypothesis in relativity
- An in-depth look at Einstein’s field equation
- The math behind computer vision and object recognition
Calculus Topics for a Research Paper
Let’s face it: calculus is not a very difficult field. So, why don’t you pick one of our excellent calculus topics for a research paper and start writing your essay right away:
- When do we need to apply the L’Hôpital rule?
- Discuss the Leibniz integral rule
- Calculus in ancient Egypt
- Discuss and analyze linear approximations
- The applications of calculus in real life
- The many uses of Stokes’ theorem
- Discuss the Borel regular measure
- An in-depth analysis of Lebesgue’s monotone convergence theorem
Simple Math Research Paper Topics for High School
This is the place where you can find some pretty simple topics if you are a high school student. Check out our simple math research paper topics for high school:
- The life and work of the famous Pierre de Fermat
- What are limits and why are they useful in calculus?
- Explain the concept of congruency
- The life and work of the famous Jakob Bernoulli
- Analyze the rhombicosidodecahedron and its applications
- Calculus and the Egyptian pyramids
- The life and work of the famous Jean d’Alembert
- Discuss the hyperplane arrangement in combinatorial computational geometry
- The smallest enclosing sphere method in combinatorics
Business Math Topics
If you want to surprise your professor, why don’t you write about business math? We have some exceptional topics that nobody has thought about right here:
- Is paying a loan with another loan a good approach?
- Discuss the major causes of a stock market crash
- Best debt amortization methods in the US
- How do bank loans work in the UK?
- Calculating interest rates the easy way
- Discuss the pros and cons of annuities
- Basic business math skills everyone should possess
- Business math in United States schools
- Analyze the discount factor
Probability and Statistics Topics for Research
Probability and statistics are not easy fields. However, you can impress your professor with one of our unique probability and statistics topics for research:
- What is the autoregressive conditional duration?
- Applying the ANOVA method to ranks
- Discuss the practical applications of the Bates distribution
- Explain the principle of maximum entropy
- Discuss Skorokhod’s representation theorem in random variables
- What is the Factorial moment in the Theory of Probability?
- Compare and contrast Cochran’s C test and his Q test
- Analyze the De Moivre-Laplace theorem
- What is a negative probability?
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Edinburgh Research Archive
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Mathematics thesis and dissertation collection
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This collection contains a selection of the latest doctoral theses completed at the School of Mathematics. Please note this is not a comprehensive record.
This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.
Recent Submissions
Efficient monte carlo methods for bayesian state-space model inference , well-posedness of nonlinear schrödinger equations from deterministic and probabilistic viewpoints , applications and improvements of the adaptive large neighbourhood search , lᵖ boundary value problems for elliptic and parabolic operators , twistor theory and its applications in asymptotically flat spacetimes , theory and simulation of interacting particle systems and mckean-vlasov processes: the super measure class, ergodicity, and weak error , spencer cohomology, supersymmetry and the structure of killing superalgebras , higher triangulated categories and fourier-mukai transforms on abelian surfaces and threefolds , investigating computer aided assessment of mathematical proof by varying the format of students' answers and the structure of assessment design by stack , estimation and application of bayesian hawkes process models , novel statistical learning approaches for open banking-type data , statistical and machine learning approaches to genomic medicine , using markov chain monte carlo in vector generalized linear mixed models: with an application to integral projection models in ecology , symmetries of riemann surfaces and magnetic monopoles , kan extensions in probability theory , regression analysis for extreme value responses and covariates , categorical torelli theorems for fano threefolds , laplacians for structure recovery on directed and higher-order graphs , efficient interior point algorithms for large scale convex optimization problems , solving sampling and optimization problems via tamed langevin mcmc algorithms in the presence of super-linearities .
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Department of Mathematics
Senior theses.
An undergraduate thesis is a singly-authored mathematics document, usually between 10 and 80 pages, on some topic in mathematics. The thesis is typically a mixture of exposition of known mathematics and an account of your own research.
To write an undergraduate thesis, you need to find a faculty advisor who will sponsor your project. The advisor will almost surely be a faculty member of the pure math department, though on occasion we have accepted theses written by people with applied math advisors. In these rare cases, the theses have been essentially pure math theses.
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2010 | Alex Kruckman | The Ax-Kochen Theorem: An Application of Model Theory to Algebra | Dan Abramovich/Michael Rosen |
2010 | Thomas Lawler | On the Local Structure of Triangulation Graphs | Richard Schwartz |
2011 | Andrew Furnas | Mathematical Modeling of Woven Fabric | Govind Menon |
2011 | Eric Sporkin | Modifying the BLS Signature Scheme Using Isogenies | Reinier Broker |
2011 | Tyler K. Woodruff | Discrepancy Upper Bounds for Certain Families of Rotated Squares | Jill Pipher |
2012 | Nadejda Drenska | Representation of Periodic Data with Fourier Methods and Wavelets | Jill Pipher |
2012 | Zev Chonoles | Hermite's Theorem for Function Fields | Michael Rosen |
2013 | Kevin Casto |
| Richard Schwartz/Govind Menon |
2013 | In-Jee Jeong |
| Richward Schwartz |
2013 | Benjamin LeVeque |
| Jeffrey Hoffstein |
2013 | Lucas Mason-Brown |
| Michael Rosen |
2013 | Yilong Yang |
| Richard Schwartz |
2014 | Nicholas Lourie |
| Richard Schwartz |
2014 | Michael Thaler | Extending Conway's Tiling Groups to a Triangular Lattice with Three Deformations | Richard Schwartz |
2015 | Justin Semonsen | Factorization of Birational Maps | Dan Abramovich |
2015 | Kamron Vachiraprasith | On the Average Order of Arithmetic Functions Over Monic Square-Free Polynomials in Finite Fields | Michael Rosen |
2015 | Francis White |
| Sergei Treil |
2015 | Zijian Yao | Arakelov Theory on Arithmetic Surfaces | Stephen Lichtenbaum |
2016 | Claire Frechette |
| Melody Chan |
2018 | Collin Cademartori |
| Govind Menon |
2018 | Michael Mueller |
| Thomas Goodwillie |
2018 | Lewis Silletto |
| Richard Schwartz |
2020 | Jongyung Lee |
| Dan Abramovich |
2020 | Owen Lynch |
| Yuri Sulyma |
2021 | Alexander Bauman |
| Bena Tshishiku |
2021 | Matei P. Coiculescu |
| Richard Schwartz |
2021 | Henry Talbott |
| Richard Schwartz |
2021 | Nathan Zelesko |
| Melody Chan |
2022 | Griffin Edwards |
| Yuri Sulyma |
2022 | Dichuan David Gao |
| Justin Holmer |
2022 | Jasper Liu |
| Jeffrey Hoffstein |
2024 | Alex Feiner |
| Joseph Silveman |
2024 | Mattie Ji | Some Morse Theoretic Results on Definable Functions | Richard Schwartz |
2024 | Tyler Lane |
| Brendan Hassett |
2024 | Smita Rajan |
| Brendan Hassett |
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Theses and Dissertations
Recent Theses
Melinda Kleczynski Master of Science in Mathematical Sciences Advisor: Allan Struthers Thesis Title: Pseudo-Companion Matrices for Polynomial Systems
Fadhila Yosof Master of Science in Mathematical Sciences Advisor: Qiuying Sha Thesis Title: CUR Matrix Decomposition Method for Joint Analysis of Multiple Phenotypes
Joshua Davies Master of Science in Mathematical Sciences Advisor: William Keith Thesis Title: Distribution of Permutation Statistics Across Pattern Avoidance Classes, and the Search for a Denert-Associated Condition Equivalent to Pattern Avoidance
Qiuchen Hai Master of Science in Mathematical Sciences Advisor: Jianping Dong Thesis Title: On the Equivalence Between Bayesian and Frequentist Nonparametric Hypothesis Testing
Mitchell Tahtinen Master of Science in Mathematical Sciences Advisor: Kui Zhang Thesis Title: Analysis of Data from a Study to Identify Potential Biomarkers to Indicate Renal Injury
Teresa Woods Master of Science in Mathematical Sciences Advisors: Shari Stockero/Yeonwoo Rho Thesis Title: Analysis of Aleks Mathematics Placement Test Data
Anna Pascoe Master of Science in Mathematical Sciences Advisor: Shari Stockero Thesis Title: Learning to Notice and Use Student Thinking in Undergraduate Mathematics Courses
Dilek Erkmen Master of Science in Mathematical Sciences Advisor: Alexander Labovsky Thesis Title: Defect-Deferred Correction Method for the Two-Domain Convection-Dominated Convection-Diffusion Problem
Henriette Groenvik Master of Science in Mathematical Sciences Advisor: Yeonwoo Rho Thesis Title: A Self-Normalizing Approach to the Specification Test of Mixed-Frequency Models
Mustafa Aggul Master of Science in Mathematical Sciences Advisor: Alexander Labovsky Thesis Title: A High Accuracy Minimally Invasive Regularization Technique for Navier-Stokes Equations at High Reynolds Number
Shengnan Li Master of Science in Mathematical Sciences Advisor: Min Wang Thesis Title: Objective Bayesian Analysis of a Generalized Lognormal Distribution
Recent Dissertations
Samuel Judge PhD in Mathematical Sciences Advisor: Fabrizio Zanello Dissertation Title: On the Density of the Odd Values of the Partition Function
Xiaoyu Liang PhD in Mathematical Sciences Advisors: Shuanglin Zhang/Qiuying Sha Dissertation Title: Joint Analysis of Multiple Phenotypes in Association Studies
Zhenchuan Wang PhD in Mathematical Sciences Advisors: Shuanglin Zhang/Qiuying Sha Dissertation Title: Joint Analysis for Multiple Traits
Xinlan Yang PhD in Mathematical Sciences Advisor: Qiuying Sha Dissertation Title: Statistical Methods for Detecting Causal Rare Variants and Analyzing Multiple Phenotypes
Huanhuan Zhu PhD in Mathematical Sciences Advisors: Shuanglin Zhang/Qiuying Sha Dissertation Title: Statistical Methods for Analyzing Multivariate Phenotypes and Detecting Causal Rare Variants
Ala Alzaalig PhD in Mathematical Sciences Advisor: Jiguang Sun Dissertation Title: Direct Sampling Methods for Inverse Scattering Problems
Bryan Freyberg PhD in Mathematical Sciences Advisors: Melissa Keranen/Dalibor Froncek Dissertation Title: Distance Magic/Antimagic Type Labelings
Mustafa Gezek PhD in Mathematical Sciences Advisors: Vladimir Tonchev Dissertation Title: Combinatorial Problems Related to Codes, Designs and Finite Geometries
Olabanji Shonibare PhD in Mathematical Sciences Advisors: Kathleen Feigl/Franz Tanner Dissertation Title: Numerical Simulation of Viscoelastic Multiphase Flows Using an Improved Adaptive Approach
Samer Alokaily PhD in Mathematical Sciences Advisors: Kathleen Feigl/Franz Tanner Dissertation Title: Modeling and Simulation of the Peristaltic Flow of Newtonian and Non-Newtonian Fluids with Application to the Human Body
Adrian Pastine PhD in Mathematical Sciences Advisors: Donald Kreher/Melissa Keranen Dissertation Title: Two Problems of Gerhard Ringel
Chao Liang PhD in Mathematical Sciences Advisors: Franz Tanner/Kathleen Feigl Dissertation Title: Development of Computational Methods for the Investigation of Liquid Drop Phenomena in External Flows
Note: Search the J. R. Van Pelt and Opie Library Catalog for online availability of recent theses.
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Home > A&S > Math > MATH_GRADPROJ
Mathematics Graduate Projects and Theses
Theses/dissertations from 2023 2023.
Association of Lockdown Policies with COVID-19 Early Case Growth Rates in the United States , Anna Barefield
A History of the Hurwitz Problem Concerning Branched Coverings , James Alexander Byars
Theses/Dissertations from 2022 2022
Relationships Between COVID-19 Infection Rates, Healthcare Access, Socioeconomic Status, and Cultural Diversity , MarGhece P. J. Barnes
The Matrix Sortability Problem , Seth Cleaver
Cognitive Demand of Teacher-Created Mathematics Assessments , Megan Marie Schmidt
Waring Rank and Apolarity of Some Symmetric Polynomials , Max Brian Sullivan
Security Analysis of Lightweight Cryptographic Primitives , William Unger
Regression Analysis of Resilience and COVID-19 in Idaho Counties , Ishrat Zaman
Theses/Dissertations from 2021 2021
Tukey Morphisms Between Finite Binary Relations , Rhett Barton
A Data Adaptive Model for Retail Sales of Electricity , Johanna Marcelia
Exploring the Beginnings of Algebraic K-Theory , Sarah Schott
Zariski Geometries and Quantum Mechanics , Milan Zanussi
Theses/Dissertations from 2020 2020
The Directed Forest Complex of Cayley Graphs , Kennedy Courtney
Beliefs About Effective Instructional Practices Among Middle Grades Teachers of Mathematics , Lauren A. Dale
Analytic Solutions for Diffusion on Path Graphs and Its Application to the Modeling of the Evolution of Electrically Indiscernible Conformational States of Lysenin , K. Summer Ware
Theses/Dissertations from 2019 2019
Dynamic Sampling Versions of Popular SPC Charts for Big Data Analysis , Samuel Anyaso-Samuel
Computable Reducibility of Equivalence Relations , Marcello Gianni Krakoff
On the Fundamental Group of Plane Curve Complements , Mitchell Scofield
Radial Basis Function Finite Difference Approximations of the Laplace-Beltrami Operator , Sage Byron Shaw
Formally Verifying Peano Arithmetic , Morgan Sinclaire
Theses/Dissertations from 2018 2018
Selective Strong Screenability , Isaac Joseph Coombs
Mathematics Student Achievement in the Context of Idaho’s Advanced Opportunities Initiative , Nichole K. Hall
Secure MultiParty Protocol for Differentially-Private Data Release , Anthony Harris
Theses/Dissertations from 2017 2017
A Stable Algorithm for Divergence-Free and Curl-Free Radial Basis Functions in the Flat Limit , Kathryn Primrose Drake
The Classification Problem for Models of ZFC , Samuel Dworetzky
Joint Inversion of Compact Operators , James Ford
Trend and Return Level of Extreme Snow Events in New York City , Mintaek Lee
Multi-Rate Runge-Kutta-Chebyshev Time Stepping for Parabolic Equations on Adaptively Refined Meshes , Talin Mirzakhanian
Investigating College Instructors’ Methods of Differentiation and Derivatives in Calculus Classes , Wedad Mubaraki
The Random Graph and Reciprocity Laws , Spencer M. Nelson
Classification of Vertex-Transitive Structures , Stephanie Potter
Theses/Dissertations from 2016 2016
On the Conjugacy Problem for Automorphisms of Trees , Kyle Douglas Beserra
The Density Topology on the Reals with Analogues on Other Spaces , Stuart Nygard
Latin Squares and Their Applications to Cryptography , Nathan O. Schmidt
Solution Techniques and Error Analysis of General Classes of Partial Differential Equations , Wijayasinghe Arachchige Waruni Nisansala Wijayasinghe
Numerical Computing with Functions on the Sphere and Disk , Heather Denise Wilber
Theses/Dissertations from 2015 2015
The Classical Theory of Rearrangements , Monica Josue Agana
Nonlinear Partial Differential Equations, Their Solutions, and Properties , Prasanna Bandara
The Impact of a Quantitative Reasoning Instructional Approach to Linear Equations in Two Variables on Student Achievement and Student Thinking About Linearity , Paul Thomas Belue
Student Understanding of Function and Success in Calculus , Daniel I. Drlik
Monodromy Representation of the Braid Group , Phillip W. Hart
The Frobenius Problem , Anna Marie Megale
Theses/Dissertations from 2014 2014
Pi-1-1-determinacy and Sharps , Shehzad Ahmed
A Radial Basis Function Partition of Unity Method for Transport on the Sphere , Kevin Aiton
Diagrammatically Reducible 2-Complexes , Tyler Allyn
A Stochastic Parameter Regression Model for Long Memory Time Series , Rose Marie Ocker
Theses/Dissertations from 2013 2013
The Assignment Packet Grading System , Sarah Nichole Bruce
Using Learner-Generated Examples to Support Student Understanding of Functions , Martha Ottelia Dinkelman
Computing Curvature and Curvature Normals on Smooth Logically Cartesian Surface Meshes , John Thomas Hutchins
Schur's Theorem and Related Topics in Ramsey Theory , Summer Lynne Kisner
Theses/Dissertations from 2012 2012
On the Geometry of Virtual Knots , Rachel Elizabeth Byrd
A Stochastic Parameter Regression Approach for Time-Varying Relationship between Gold and Silver Prices , Birsen Canan-McGlone
Uncertainty Analysis of RELAP5-3D© , Alexandra E. Gertman and George L. Mesina
A Statistical Method for Regularizing Nonlinear Inverse Problems , Chad Clifton Hammerquist
Perfect Stripes from a General Turing Model in Different Geometries , Jean Tyson Schneider
Stability and Convergence for Nonlinear Partial Differential Equations , Oday Mohammed Waheeb
Regular Homotopy of Closed Curves on Surfaces , Katherine Kylee Zebedeo
Theses/Dissertations from 2011 2011
Coloring Problems , Thomas Antonio Charles Chartier
Modules Over Localized Group Rings for Groups Mapping Onto Free Groups , Nicholas Davidson
How Do We Help Students Interpret Contingency Tables? A Study on the Use of Proportional Reasoning as an Intervention , Kathleen M. Isaacson
A Fictitious Point Method for Handling Boundary Conditions in the RBF-FD Method , Joseph Lohmeier
Theses/Dissertations from 2010 2010
Developmental Understanding of the Equals Sign and Its Effects on Success in Algebra , Ryan W. Brown
The Inquiry Learning Model as an Approach to Mathematics Instruction , Michael C. Brune
Galois Theory for Differential Equations , Soheila Eghbali
Stably Free Modules Over the Klein Bottle , Andrew Misseldine
Combinatorics and Topology of Curves and Knots , Bailey Ann Ross
Theses/Dissertations from 2009 2009
Concept Booklets: Examining the Performance Effects of Journaling of Mathematics Course Concepts , Todd Stephen Fogdall
Effective Sample Size in Order Statistics of Correlated Data , Neill McGrath
Transparency in Formal Proof , Cap Petschulat
Weight Selection by Misfit Surfaces for Least Squares Estimation , Garrett Saunders
The Effects of a Standards-Based Mathematics Curriculum on the Self-Efficacy and Academic Achievement of Previously Unsuccessful Students , Cindy Chesley Shaw
Analytical Upstream Collocation Solution of a Quadratic Forced Steady-State Convection-Diffusion Equation , Eric Paul Smith
Solvability Characterizations of Pell Like Equations , Jason Smith
Theses/Dissertations from 2008 2008
Tube-Equivalence of Spanning Surfaces and Seifert Surfaces , Thomas Glass
Simple Tests for Short Memory in ARFIMA Models , Timothy A. C. Hughes
Incomparable Metrics on the Cantor Space , Trevor Jack
Richards' Equation and Its Constitutive Relations as a System of Differential-Algebraic Equations , Shannon K. Murray
Theses/Dissertations from 2007 2007
Theorem Proving in Elementary Analysis , Joanna Porter Guild
An Investigation of Lucas Sequences , Dustin E. Hinkel
A Canonical Countryman Line , William Russell Hudson
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- The effect of problem-solving teaching approach on learning fractions in Grade 8 Agadagba, Oghenerukewe Emmanuel ( 2024 ) Problem-solving teaching approach is critical in improving learners’ cognition and problem-solving skills in different content areas in mathematics. Therefore, this quantitative study evaluated the effect of the problem-solving ...
- 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 ...
- Grade 9 mathematics teachers’ strategies to address mathematical proficiency in their teaching of linear equations : a case of selected schools in Gauteng North District Mothudi, Teresa Ntsae ( 2022-12-10 ) The purpose of this research was to look into Grade 9 mathematics teachers’ strategies to address mathematical proficiency in their teaching of linear equations. The study was intrigued by the performance of learners in ...
- Grade 6 mathematics teachers’ development of learner mathematical proficiency in addition and subtraction of common fractions, in the Tshwane South District of Gauteng Lendis, Ashley Pearl ( 2022-11-30 ) The study was motivated by the fact that learners are not performing well in the topic of fractions due to the lack of conceptual understanding of the concept. The purpose of this qualitative study based on an interpretive ...
- The performance and learning difficulties of Grade 10 learners in solving euclidean geometry problems in Tshwane West District Olabode, Adedayo Abosede ( 2023-01-31 ) There is a growing trend of declining performance in the final year (Grade 12) mathematics examinations in the South African public school system. The study aimed to evaluate Grade 10 learners in the Tshwane West District ...
- A collaborative model for teaching and learning mathematics in secondary schools Ngwenya, Vusani ( 2021-11 ) Mathematics pass rates in South African schools, as in many developing nations, continue to be a source of concern for educators and policymakers alike. Improving mathematics performance is non-negotiable if Africa is to ...
- 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 ...
- An exploration of learning difficulties experienced by grade 12 learners in euclidean geometry : a case of Ngaka Modiri Molema district Mudhefi, Fungirai ( 2022-08-20 ) The purpose of this study was to investigate the learning difficulties experienced by Grade 12 learners in Euclidean geometry. Despite the efforts exerted in terms of time, material and human resources in the teaching and ...
- The relationship between anxiety, working memory and achievement in mathematics in grade 5 learners : a case study of Tshepisong schools Mnguni, Maria Tebogo ( 2022-01-21 ) This study investigated the relationship between anxiety, working memory and achievement in mathematics in grade 5 learners at Tshepisong schools. A sample of 300 grade 5 learners from Tshepisong schools was selected using ...
- The effects of using a graphic calculator as a cognitive tool in learning grade 10 data handling Rambao, Mpho ( 2022-09 ) The integration of technology in the mathematics classroom is believed to have an influence on how the learners learn and change their perception of mathematics. Therefore, technology tools are developed to enhance the ...
- Integration of ethnomathematics in the teaching of probability in secondary school mathematics in Zimbabwe Turugari, Munamato ( 2022-06 ) Underpinned by the social constructivism theory and the praxis of integrating ethnomathematics in the teaching of probability, this PAR developed a policy framework for facilitating the integration of ethno-mathematics in ...
- Evaluating Grade 10 learners’ change in understanding of similar triangles following a classroom intervention Maweya, Amokelo Given ( 2022 ) Geometry, in particular Euclidean geometry, has been highlighted as a subject in mathematics that presents a variety of challenges to many secondary school learners. Many students struggle to gain appropriate knowledge of ...
- 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 ...
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Dissertations for Mathematics Education
Abel, brian b., the impact of a computer based math instruction program on fifth grade student academic performance on the texas assessment of knowledge and skills in one school district, abramowitz, sarah knapp, a computer-enhanced course in descriptive statistics at the college level: an analysis of student achievement and attitudes, abrego, patricia c., perceptions of campus administrators, teachers, and students on use of interactive videoconferencing for the delivery of high school algebra in selected rural public high schools in south texas, adams, marietta smith, gender differences in the complexity of virtual lego block designs of kindergarten students, adamy, peter hilton, an analysis of factors that influence technology integration by math teacher educators, adleman, kathleen a., problem-solving strategies of young children working on a combinatorics task in a computer environment, adolphson, keith victor, mathematical embodiment through robotics activities, aguilar, darla jean, calculator use in developmental mathematics in a community college, ahn, doehee, an exploratory study into the development of cognitive and metacognitive processes in mathematics problem-solving via computer, aldred, keith gregson, the effects of contextualized technical courses, where mathematics is embedded, situated, and generative, on the mathematics achievement of high school students, alexander, melina, evaluation of mathematics methods online: planning knowledge, classroom applications, and pupil outcomes, alghazo, iman mohammad, a study of the technology competencies of preservice secondary mathematics teachers, al-harthi, hamood k., student-faculty power/knowledge relations: the implications of the internet in mathematics education and social studies education programs at sultan qaboos university, allanson, patricia elizabeth, social mathworking: the effects of online reflection on algebra i students' sense of community and perceived learning, allen, roseann p., algebraic functions in a graphing technology environment: student performance after small group work using teacher-generated versus student-generated examples, allison, tracy michelle hunter, the impact of classroom performance system-based instruction with peer instruction upon student achievement and motivation in eighth grade math students, almekbel, abdullah s. m., the impact of a teacher enhancement program on 7th through 12th grade mathematics instruction with regard to curriculum, technology, and assessment, alshehri, khaled abdullah, the influence of mathematics teachers' knowledge in technology, pedagogy and content (tpack) on their teaching effectiveness in saudi public schools, alzahrani, khalid s., the attitudes of high school mathematics teachers in jeddah, saudi arabia, toward using calculators in teaching mathematics, the effect of incorporating geometer's sketchpad in a high school geometry course to improve conceptual understanding, inductive reasoning, and motivation, sign in or register, sign in using email & password.
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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.
“Exploring the Dynamics of Chaos: A Study of Fractal Patterns and Nonlinear Systems” |
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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Mathematics & Statistics Department
As a capstone project, every graduate of Reed College completes a thesis in their senior year. Here seniors can find instructions and resources for completing a mathematical thesis. Anyone can also find a list of thesis projects from Math & Stats from the last couple of decades. Jump to past thesis projects.
Current Thesis Instructions and Resources
Math-Stats Thesis Schedule A list of department-specific assignments, due dates, and submission links for the thesis year.
Senior Handbook College-wide schedules, degree requirements, resources for your thesis year, and resources for life beyond Reed—an important read as you start your year!
Thesis Proposal Form
Help with writing and research Library’s guide to thesis and resources
LaTeX at Reed Typesetting help, including the thesis template.
MathSciNet ( on campus only ) An important resource for mathematical literature searches
Past Thesis Projects
Marlo Albers (Mathematics) The h-Vector Conjecture for Matroids with Cycle Systems
Apollo Albright (Mathematics-Physics) Transmission of an Electron through a Saddle Potential
Kush Arya (Computer Science-Mathematics) Verifying Arithmetic Incompleteness
He Bai (Mathematics with a concentration in Statistics) Extending Targeted Function Balancing to Models without Linear Representations
Conor Bekaert (Mathematics with a concentration in Statistics) Towards a Weighted Joint Statistical Model for Rankings and Ratings
Lena Bloom (Mathematics) Maximum Overdrive: a Frequency Response Analysis of Distortion Due to Clipping
Mollie Boor (Mathematics) Towards Constructing the Affine Partition Algebra
Kenai Burton-Heckman (Mathematics with a concentration in Statistics) tfb: a Package for Targeted Function Balancing
David Carlip (Mathematics) Some Approaches to Hilbert-Kunz Multiplicity
Adam Cohen (Mathematics-Physics) Calculus on Twisty Stuff: The Local Index Theory of Dirac Operators
Asa Ferguson (Mathematics with a concentration in Statistics) Comparing Classic Parametric and Novel Machine-Learning Techniques to Analyze Survival Data: an Application to Historical Population-Based HIV Surveys in Sub-Saharan Africa
Quinn Hargrove (Mathematics with a concentration in Statistics) Visualizations to Improve Ranked Data Analyses, with Applications to Board Game Data
April Kopec (Computer Science-Mathematics) Scaling Explainable Artificial Intelligence Filtering and Approximations for Influence Functions for Large Language Models
Astrid Lilly (Mathematics) An Invitation to Tate's Thesis
Xinran Liu (Mathematics with a concentration in Statistics) Classical Simulation for Quantum Random Circuit Sampling in the Regime of Anti-concentration
Yancheng Liu (Computer Science-Mathematics) Suboptimal Multi-Heuristic Approaches for Solving the Rubik’s Cube Incorporating Deep Learning and Group Theory
Ethan MacBrough (Mathematics) Sparse Theorems are Full of Triangles
Solis McClain (Mathematics) Matroids and Their Cycle Systems: The h-Vector Conjecture for a New Class of Matroids
Ethan McDonald (Computer Science-Mathematics) Exploring Memory Tiering Policies for Composable Memory Systems
Olly Milshtein (Mathematics) The Cobordism Hypothesis and Topological Quantum Field Theories
Tina Qin (Mathematics) Autoregressive Time Series Modeling: A Comparative Analysis of Parameter Estimation and State Prediction Methods
Calliope Reimann (Mathematics) Extending Galois Connections between Posets to their Representations
Olive Ross (Mathematics-Physics) An Examination of Hinterleitner Doubly Special Relativity
Riley Shahar (Computer Science-Mathematics) Categories for Cryptographic Composability
Ava Sorgman (Mathematics) A Spectral Graph Theoretic Analysis of the Sign Flipping Sequence
Peihua Su (Mathematics-Physics) Benjamin-Ono Periodic Traveling Waves: Pole Dynamics and Dispersion Relations
Thomas Ulmer (Computer Science-Mathematics) Symbolic Analysis on C Binaries
Yuheng Wen (Computer Science-Mathematics) An Efficient Privacy-Preserving Satellites Collision Detection Method: Applying Private Set Intersection Using Garbled Circuit
Valerie Wu (Mathematics-Physics) The Tenfold Way and Beyond: Classification of Topological Insulators and Superconductors
Louise Xu (Computer Science-Mathematics) Privacy Paradox: Regularized Neural Networks and Distributional Differential Privacy
Guangyi Zhang (Mathematics-Physics) A Geodesic Journey into the Wormholes
Zach Barbanell (Computer Science-Mathematics) Optimizing Gadgets for Fully Homomorphic Encryption
Scott Blair (Mathematics) A Taste of Differential Field Theory
Wolfgang Brightenburg (Mathematics with a concentration in Statistics) On Estimating the Number of Clusters: Mind the Gap!
Kellen Brosnahan (Mathematics) Representation Theory, Schur-Weyl Duality, and the Partition Algebra
Jesse Cao (Mathematics-Physics) Classical Jackiw-Teitelboim Gravity: Towards Quantization
Victor Chen (Mathematics) The Impact of Schools on Traffic Congestion: A Case Study in California K-12 Public Schools
Malen Cuteric (Mathematics with a concentration in Statistics) MAUPing Up: An Empirical Analysis of Error Rates in Dasymetric Mapping
Zack Dooley (Mathematics) A Survey of Categorification: Towards Categorical Algebra and Higher Categories
Jacob Finkelstein (Mathematics) An Accessible Proof of the Prime Number Theorem
Ilana Frey-Kim (Computer Science-Mathematics) Simplicial Homology Computation Using Discrete Morse Theory
Roscoe Haynie (Computer Science-Mathematics) A Zero-Knowledge Proof for Norinori
Bhavjot Khurana (Mathematics with a concentration in Statistics) Supervised Machine Learning to Predict Student Proficiency in Oregon Public Schools
Hannah Kuder (Mathematics-Physics) The Beesis
Anna Luce (Mathematics) The CW Decomposition of the Grassmannian Manifold
Oliver Mansbach (Mathematics) Persisting Through The Convexity: Convex Modules for the Commutative
Olivia McGough (Mathematics) Persistent Homology and Applications to Graph Data
Keith Ng (Computer Science-Mathematics) Building To The Third Story: An AI To Play Santorini
Sean O'Donnell (Mathematics) Primes in Extensions and Expressions via Binary Quadratic Forms
Blaze Okonogi-Neth (Mathematics) An Introduction to Elliptic Curves, Modular Forms, and the Modularity Theorem
Rayn Samson (Mathematics-Physics) Relativistic Ehrenfest Relations for Klein-Gordon Fields
Sol Skinner (Mathematics with a concentration in Statistics) Making Sense of Making Sense of Sensitivity
Monroe Stephenson (Mathematics) Kazhdan-Lusztig Polynomials of Matroids
Josh Yamamoto (Mathematics with a concentration in Statistics) A Bayesian Approach to Zero-Inflation Modeling
Larry Zeng (Computer Science-Mathematics) Exploring Noninterference in Programming Languages: A Study of Simple Dependency Core Calculus and Logical Relations
Daniel Zou (Computer Science-Mathematics) Differentially Private Weighted Linear Regression
Emmanuel Arthur (Computer Science-Mathematics) The Stable Roommates Problem With Globally-Ranked Pairs
Alice Barker (Mathematics) Representations of sl2(C) and Connection to Temperley-Lieb Diagrams
Cruz Barnum (Computer Science-Mathematics) Indistinguishability Obfuscation From the Ground Up
Erik Beserra (Mathematics) Khovanov Homology: Putting Pants on Knots
Ian Cates-Doglio (Mathematics with a concentration in Statistics) Snow Avalanche Predictions by Ensemble Modeling
Harry Chen (Mathematics) Metric Balls and Infinitely Degenerate Elliptic PDEs
Peter Chen (Mathematics) Mask, Vaccine and Covid
Tyler Dunaisky (Mathematics) Dynamics of Quadratic Rational Maps with Maximal Automorphism Group
Rylie Foster (Computer Science-Mathematics) An Introduction to Data-Driven Modal Analysis
Catherine Gong (Mathematics) Group Actions in Music Theory
Evan Griggs (Mathematics) Cyclic Cones & Non-singular Refinements of Cyclic Fans
Alex Hsu (Mathematics) A Gentle Introduction to Homotopy Type Theory
Thomas Kelleher (Mathematics) An Operad-Theoretic Exploration of the Coherence Theorem for Monoidal Categories
Josh Klein Valente (Computer Science-Mathematics) An Introduction to Elliptic Curves and Applications in Cryptography
Tunç Başar Köse (Computer Science-Mathematics) Approximate Message Passing for Principal Component Analysis: Theory and Practice
Jay Kruer (Computer Science-Mathematics) The Way of Glue: An Invitation to the Categorical Semantics of Lambda Calculi
Sarah Kumar (Mathematics) Understanding Lie Algebras : An Alternate Perspective on Weyl's Theorem
Harpeth Lee (Mathematics with a concentration in Statistics) A Comparison of Data-Driven Partial Least Squares to Existing Partial Least Squares Models
Henry Lindeman (Computer Science-Mathematics) Normal Attention : A Novel Self-Attention Linearization Strategy for Abstractive Summarization of Long Documents
Daniel McFadden (Mathematics-Physics) Star Formation Quenching in Centaurus A
Paul Nguyen (Mathematics with a concentration in Statistics) Inference for Random Forests
Jasmine Peng (Mathematics-Economics) Foreign Direct Investment and Earnings in China
Elizabeth Prestegaard (Mathematics) The Lattice of Alexandrov Topologies
Evan Pugh (Mathematics with a concentration in Statistics) Analyzing the Impact of Vaccinations, Government Policy and Other Factors on the COVID-19 Pandemic
Holden Saberhagen (Mathematics-Physics) Modeling the Integer Quantum Hall Effect
Daksh Shami (Computer Science-Mathematics) Exploration of the Hidden Subgroup Problem
Jakob Shimer (Computer Science-Mathematics) CNF Reduction in Weighted Model Counting
Sharon Wang (Mathematics) Kasteleyn's Tiling Theorem Using Complex Weights
George Zhao (Mathematics) A Construction of the Derived Category and Derived Functors
Shisham Adhikari (Mathematics-Economics) Inequality in Ramsey Growth Model with Heterogeneous Rates of Return: Are rich getting higher returns on investment than poor?
Francis Baer (Mathematics) Adams Spectral Sequence Computations of BP<1> cooperations at Odd Primes
Ryen Burris (Mathematics-Physics) Modelling Vibration of Membranes Under Non-Uniform Tension
Reilly Cannon (Computer Science-Mathematics) Differential Privacy: the Gap Statistic and the Mapper Algorithm
Nicholas Cecil (Mathematics) Nets, Filters, and Convergence
Simon Couch (Mathematics with a concentration in Statistics) Tidy Model Stacking with R
Luke Doms (Mathematics) A Geometric Interpretation of the Coefficients of the Standard Simplex's Ehrhart Polynomial
Evan Franchere (Mathematics) Trust the Cones: Computing Diagonal Cartier Algebras of Affine Toric Varieties
Zhengyao Gu (Computer Science-Mathematics) Selective Prediction: Training and Evaluation Methods
Usman Hafeez (Mathematics) A^1 Milnor Numbers
Brenham Hooper (Mathematics with a concentration in Statistics) Classifying Types of Young Stars Using Supervised Machine Learning
Albert Ji (Computer Science-Mathematics) Universal Approximation and Interpolation in Neural Networks
Théo Lavier (Mathematics-Physics) A First Look at Rate Induced Tipping
Jiarong Li (Computer Science-Mathematics) Complex Network Comparison using Graphlets
Jonathan Li (Mathematics-Economics) Simulating Repeated Coalition Formation under Uncertainty
Yilin Li (Computer Science-Mathematics) What If English Had No Spaces? Investigating the Challenges of NLP for Character-Based Languages
Sarah Maebius (Mathematics with a concentration in Statistics) Statistical Learning Methods for Tree Classification using Remote Sensing Imagery
Peter Marcus (Mathematics) Computing the Henselization of a Valued Field
Kiki McBride (Mathematics) Klein Has Me in Stitches! (An Exploration of Mathematical Constructions of the Klein Quartic and Creation of Analogous Crochet Models)
Alan Moore (Mathematics with a concentration in Statistics) Inference on Latent Structure Random Graphs: Context, Theory and Applications
Weihang Qin (Computer Science-Mathematics) Raymarching Hyperbolic Geometry
Bijay Rai (Mathematics-Economics) On Track: Access to Improved Road Network and Poverty Alleviation in Mid and Far Western Nepal
William Ren (Mathematics-Economics) Casino Revenue and Life Quality in Macau
Cleo Schaumann (Mathematics) Young Tableaux, Schur Polynomials, and Crystals
Taylor Sedoo (Mathematics) Exposing Chaos: Attracting Differences
Hrishee Shastri (Computer Science-Mathematics) Cutting the Chord: Interleaved and Demand Aware Skip Graphs
Timothy Shinners (Mathematics with a concentration in Statistics) Modelling Mount Rainier’s Volcanic Event Sequence
Aryeh Stahl (Computer Science-Mathematics) A Generalized Approach to Graph De-anonymization
Ali Taqi (Mathematics with a concentration in Statistics) Spectral Statistics of Random Matrices
Ian Wahbe (Computer Science-Mathematics) Improvements to the Heuristic Rural Postman Problem
Daniel Wang (Mathematics) Diagrammatic Algebras to Describe the Endomorphism Algebra of $\mathfrak{gl}_n$-Modules
Riley Waugh (Mathematics) Regularity Theory of Degenerate Elliptic Partial Differential Equations
Grayson White (Mathematics with a concentration in Statistics) A Hierarchical Bayesian Approach to Small Area Estimation of Forest Attributes
Olek Wojcik (Mathematics-Economics) Higher Education Responses to COVID-19
Lucas Yong (Computer Science-Mathematics) An Exploration of Topological Quantum Computation
Kayleigh Bangs (Mathematics-Philosophy) This Thesis is Indeducible: Approaches for Justifying the Consistency of Peano Arithmetic After Gödel
Henry Blanchette (Computer Science-Mathematics) Purity and effect
Naomi Boss (Mathematics with a concentration in Statistics) Hindsight is 2020: Evaluating a Presidential Election Forecasting Model During a Global Pandemic
Maxine Calle (Mathematics) Morse theory and flow categories
Nick Chaiyachakorn (Mathematics) THREE EASY PIECES IN HARMONIC ANALYSIS Singular integrals, the Hardy space H1, and boundedness results
Lixuan Chen (Mathematics-Economics) Is education finally paying-off in urban China? : evidence from 1989-2015
William Daniel (Mathematics-Economics) Machine learning application in credit card fraud
Wenxin Du (Mathematics with a concentration in Statistics) A close look at specification curve analysis and existing applications
Canyon Foot (Mathematics with a concentration in Statistics) Graphical approaches to recovering distributions under selection bias and missing data
Iris Griffith (Mathematics with a concentration in Statistics) Do androids dream of electric trees? : classifying and predicting forest attributes using deep neural network models
Collin Guo (Mathematics with a concentration in Statistics) Linearizing quadratic stochastic processes for metagame mixing time analysis
Kaitlyn Hepp (Mathematics) Rowmotion on Doppelgänger Pairs
Robert Irvin (Mathematics-Economics) Simulating the price of anarchy in auctions
Claire Jellison (Mathematics-Economics) Giving by the numbers : a study of peer effects with online crowdfunding
Zekican Kazan (Mathematics with a concentration in Statistics) The longest increasing subsequence as a test statistic
Young Kim (Mathematics) Resolutions of Rees algebras
Ryan Kobler (Mathematics-Economics) Spatial effects and environmental hedonic valuation in Portland, Oregon
Mason Koch (Computer Science-Mathematics) Reinforcement learning for Pokemon AI
Noah Koster (Computer Science-Mathematics) Neuronal Dynamics of the Action Potential: Spiking Behavior in the FitzHugh-Nagumo Model and others
Ryan Neumann (Computer Science-Mathematics) An exploration of reinforcement learning through video games
Shulav Neupane (Mathematics-Economics) Citation and collaboration behavior at the university level in agricultural sciences
Jiajing Peng (Mathematics-Economics) Nonprofits as infrastructure for regional economic resilience : evidence from US metropolitan area during the great recession
Huaying Qiu (Mathematics with a concentration in Statistics) Forest type classification in interior Alaska using G-LiHT data
Kaiyan Shi (Computer Science-Mathematics) Investigation on 1D area law and XXZ model
David Tamas-Parris (Computer Science-Mathematics) Elliptic Curves Aren't Secure? SIKE!
Lucas Williams (Mathematics) How to do proof by picture and get away with it :the representation theory of quantum groups and connections to knot theory
Livia Xu (Mathematics) Toppling ideals of M-matrices
Matthew Yancheff (Mathematics with a concentration in Statistics) Statistical Inference on Brownian Motion with Drift
Anton Zavorotny (Mathematics) Vassiliev knot invariants and the graph bialgebra of lando
Aiman Absar (Mathematics-Economics) Revealing Anomalies in Behavior of Rational Agents: Applying Game Theory to Behavioral Economics
Sean Allen (Mathematics-Physics) Reservoir Computing: Observing the Baker's Map
Edwin Alvarado (Mathematics-Economics) Impact of Fast Fashion on Welfare in Developing Countries
Edsel Arce (Mathematics with a concentration in Statistics) Klaytheism, Competition, Free Throws
Matthew Atteberry (Computer Science) Reinforcement Learning: An Overview
Miles Baker (Computer Science) Don't Point Yourself Into a Corner: Using Static Analysis to Prevent Memory Leaks in C
Kyu Cho (Mathematics) Integer programming methods and the fleet assignment problem
J.R. Cruise (Mathematics-Physics) An Exploration in Perturbation: Asymptotic Ailments to Quantum Consternation
Zichen Cui An Introduction to Topological Complexity
Theodore Dounias (Political Science-Mathematics) Turnout and Mail Voting in Colorado or: How I Learned to Stop Worrying and Love Voter Registration Files
Tanmay Dubey (Computer Science-Mathematics) Latent Dirichlet Allocation: an Application to Computer Systems Conference Papers
Ira Globus-Harris (Computer Science-Mathematics) Differentially Private One-Way Analysis of Variance
Ethan Gordon (Mathematics-Economics) Tragedy of the Common (Application)s: A Mechanism-Design Approach to College Admissions in the United States
Dylan Huff (Computer Science) PowerPoint Natively on the Web, a Java PPTX Extension
Emmett Kahn (Computer Science) DNA Compression Using Machine Learning
Michael Kalange (Computer Science-Mathematics) Embed With the Entropy: Applying Word2Vec to Lossless Text Compression
Rhody Kaner (Computer Science) Gender Representation in Computer Science
Jay Lee (Mathematics with a concentration in Statistics) From Interpolation to Imputation: Ballot Completion in a Ranked Choice Election
Alexander Lloyd-Damnjanovic (Mathematics with a concentration in Statistics) Kronecker Sequences and Persistent Homology
Nathaniel McFadden (Mathematics-Physics) Exact Solutions of Spin Chains
Joseph Meyer (Mathematics) Generating free verse poetry with transformer networks
Alexander Moore (Mathematics with a concentration in Statistics) Mean Estimation via Neural Network Methods in Complex Survey Imputation
Ananthan Nambiar (Computer Science) Computing the Language of Life
Nicole Niesen Quadratic and Biquadratic Reciprocity
Caroline Padula Surprising Facts About the Thue-Morse Sequence
Asher Payton (Mathematics-Physics) A simple bound state
Richard Pham (Computer Science-Mathematics) Graph reconfiguration in the context of permutation routing
Pallavi Prakash Rational Periodic Points of Quadratic Maps: An Exploration Through Rational Parameterizations of the Dynatomic Polynomials
Jeremy Rachels (Mathematics) Moduli spaces of polarized abelian varieties and the paramodular group
Angelica Richardson (Computer Science-Mathematics) Composing Cellular Automata for Modeling n-Component Reaction Diffusion Systems
Miranda Rintoul (Mathematics with a concentration in Statistics) Multinomial Logistic Regression for Natural Language Processing
Alec Stashevsky (Mathematics-Economics) Domestic Remittance in China: Rural - Urban Migration's Train of Inequality
Marika Swanberg (Computer Science-Mathematics) Noisy Quantum Oracles: A Study of Algorithmic Robustness
Lana Tollas (Mathematics-Economics) Airport Capacity and Airline Delays: A Quantitative Analysis
Torin Woods-Eliot The Type A Cluster Algebra and Catalan Combinatorics
Hayden Veytia (Mathematics) An encyclopedia of infinitely nested square roots
Yifan Wu (Mathematics-Economics) Can I Remain a Unicorn: An Analysis of the IPO Decision in Tech Industry
Tristan Wylde-Larue On the Quantum Base Size of a Group
Caroline Yearwood The Dual Steenrod Algebra and Graph Theory
Jialun Zhao (Mathematics-Physics) The AdS3
Ziyuan Zhong (Mathematics with a concentration in Computer Science) Combined Program, Columbia University
Yevgeniya Zhukova Cobordism Hypothesis: Macaroni as Mathematics
Jalan Ziyad (Computer Science-Physics) Quantum Search in the Face of Decoherence: Insights From Histories Approach
Nathan Duncan Heart of Zero-Knowledge
Jean Munyo Frey-Edwards M-matrices and Chip-Firing
Joshua Gancher Fully Homomorphic Encryption
Gregory Alex Ledger Implementing Component-Based Garbled Circuits
Simran Mahtani Network Analysis with Focus on Centrality
Emma Miller A Quantum Walk on the Heisenberg Group
Alexandra Salem Explanation and Simulation of the HHL Algorithm
Riley Thornton Some Problems are Hard: Borel Complexity and C*-algebras
Reilly Villanueva Analyzing Radiocarbon Data with Temporal Order Constraints
Qiaoyu Yang Split Reactive Brownian Dynamics
Barney Potter (Mathematics-Biology) Modeling Cell Signaling Networks with Prize-Collecting Subhypernetworks
Sarah Brauner (Mathematics-Economics) A New Order of Things: The Structure of Partial Orders in the Face of Lower Bounds
Alexis Saul Chasin (Mathematics-Economics) Auctions Speak Louder than Words: Application of Alternate Auction Criteria to Dynamic Tax Investment
Julia Welling Hofmann (Mathematics-Economics) H2 Uh-Oh: A game-theoretic analysis of water quality trading
Taylor Holdaway (Mathematics-Economics) The Effects of Drought on Non-Agricultural Output in the United States
Vladislav Mankov (Mathematics-Economics) Distributional Implications of a Vehicle Miles Traveled Tax
Ahyan Panjwani (Mathematics-Economics) Estimating the Impact of Commodity Market Shocks on Real Business Cycles Using Bayesian Methods
Dean K. Young (Mathematics-Economics) Myopic Loss Aversion in Investment Behavior
Timoteo Delgado-Esbenshade (Mathematics-Physics) Bound Orbits in Classical Electrodynamics
William Holdhusen (Mathematics-Physics) First Quantization of the Radiation Reaction Force
Joseph Joe (Mathematics-Physics) 256 Shades of Grey: Topological Analysis of the Gray-Scott Model Using Persistence Landscapes
Charles McIntyre (Mathematics-Physics) Computing the Band Structure of InSb and CdTe Quantum Dots
Jeremy Cosel (Mathematics with a concentration in Computer Science) Clean Up After Yourself: Implementing Garbage Collection
Joshua Hepworth (Mathematics with a concentration in Computer Science) The States of Splendor: Searching Game Trees with Partial Information
Isabella Jorissen (Mathematics with a concentration in Computer Science) Tiling the Heavens In special cases where 'the Heavens' is ℝ2
Liam Bowcock (Mathematics with a concentration in Statistics) Aggregating Over Ordinal Scales Using the Sugeno Integral
Will Jones (Mathematics with a concentration in Statistics) Multilevel Models and Missing Data Models for Crowdsourced Bicycle Route Ratings
Philip Stallworth (Mathematics with a concentration in Statistics) A Cluster Model for K-Tree Samplings of a Spatial Point Process
Andrew Blount Sequential Model-Based Optimization of Expensive Blackbox Functions –or- How to Do Well When You Don’t Know What You’re Doing
Madeline Brandt Intersecting Hypergraphs and Decompositions of Complete Uniform Hypergraphs
Amah Orphelia Ellogne (Mathematics-Economics) The effect of rainfall shocks on intimate partner violence against women
Susannah Glickman The Character of an Optimal Query: An examination of queries in the dihedral hidden subgroup Problem
Galen Harrison Differentially Private Statistics: Implementation and performance of PTR and objective perturbation methods.
Justin Katz Eigenfunction decompositions of function spaces on various physical domains
Damon Melton Jordan Canonical Forms of Commuting Nilpotent Matrices
Jacob Menick The Discrete Wavelet Transform and Applications to Data Compression
Carl Proepper (Mathematics-Physics) Generalized Statistical Techniques for Differentiating Dark Matter Models at the Large Hadron Collider
Robert Rennie Toward a Minimal Finite for the Real Projective Plane
Zachary Stout Lobachevsky, Poincaré, and Hyperbolic Geometry
Brett T. Beutell To Bayes or not to Bayes : Markov chain Monte Carlo for approximation of the posterior distribution of Bayesian networks
Max L. Carpenter Quasicrystalline combs in De Bruijn's generalized function space
Max F. Del Giudice A simple case of the Siegel-Weil formula
Emma J. Furth Hamiltonian cycle algorithms for square and triangular grid graphs
Jedediah B. Grabman Two player zero-sum games
Blake David Hall Classifying the hundred acre wood
Tessa Hoppenfeld The structure of the Jacobian group of a graph
Austin W. Humphrey Volume of SLn(Z)\SLn(R)
Mason Kennedy Representation theory and the spherical Laplacian
Thomas J. LaMarre Massively parallel computation with graphics processing units
Laura Lyman Principal series of GL(2) over a finite field
Galen O'Sullivan Counting on simplicial complexes
Yotam Reshef Formalization and mathematical rigour
Andrew J. Roetker The state of process calculi and concurrency
Elijah Van Wing Present value under non-constant models of interest
Christopher Vittal Non-unique factorization in rings of integer-valued polynomials
Mark Walth Manifolds and maps : an introduction to cobordism
Andrew Warren Nonstandard analysis is sometimes useful : several applications
Sofia D. Wright Generating the superstable configurations of a graph via its acyclic orientations
Wyatt K. Alt Enumeration of domino tilings on the projective grid graph
Jess Delaney Markov chain monte carlo and the black-scholes formula
Michael J. George-Hallgren Toward a category-theoretic construction of the adeles
Alden Jones Time-varying risk premia and the euro : a state-space model
Michael Scott Kincaid Is the euro optimal? : an examination of trade and cycles in Europe
Jacob S. Kopczynski Pushy computing : complexity theory and the game abalone
Atsuya Kumano Seeking unpredictability in deterministic systems : definitions of chaos in topological dynamics
Mikhail Lepilov Quantum state discrimination of symmetric mixed states
Luis Edmund Maldonado Generalizing the curry-howard isomorphism to classical logic
Andrew P. Malkin A combinatorial game theoretic analysis of the impartial game of dots and boxes
Alex Perusse The applications of the theory of representations in the natural sciences
Clara M. Redwood Curving paper : a folding algorithm for origami ellipsoid patterns using curved crease couplets
Marcus P. Robinson Critical groups of simplicial complexes
Darko Trifunovski Computing the extreme core of siegel modular forms
Austin D. Young The finite sums theorem : a topological approach
Skye Aaron Exact solutions and L² differentiability
Gabriel Barello Quantum field theory and general relativistic scattering from a massive central body
Michael Bedford Set theory, the continuum hypothesis, and the axiom of choice
Matthew M. Carlson Euclidian embedding of network location data : design and use
Ethan K Edwards A (slightly) more general quantum algorithm for the multiplication of group elements
Nadir Hajouji The semihull theorem for Siegel modular forms
Jay Harman Two algorithms and a miracle
Samuel F. Hopkins The quantum hidden subgroup problem for semidirect products of cyclic groups
Seth Just Functions on the line
Ivan A. Malison Graph algorithms on graphical processing units : the shortest path problem
Sara Natale The multiple spherical pendulum
Noah C. C. Pfister Vermont rainfall data and extreme value statistics
Justin T. Stewart Randomness as fairness
Ryan Wall A safari through algebraic geometry
Louis E. Webb Poincaré's theorem and tessellations of the hyperbolic plane
Gavin Bell Associated Primes Of A Modified Mayr-Meyer Ideal With N=1
Daniel R. Copeland Quantum State Discrimination And Concept Learning
Reneé G. Dosick Infinite Tessellations : A Proof And Applications Of The Extension Theorem
Laura Florescu New Connections Between The Abelian Sandpile Model And Domino Tilings
Michael Samuel Gottesman A Category Theoretic Introduction To Differential Geometry
Sei Mei Aastra Howe A Derivation Of The Inhomogeneous Lorentz Group From Invariant Null Intervals
Robert J. Kahn War, oil, and railroads : industrialization and the building blocks of city growth in the former U.S.S.R.
David Krueger Extending The Critical Group To Oriented Matroids And Simplicial Complexes
Isaac Lawrence Techniques For Space-Efficient Text-Indexing
Daniel C. Lidral-Porter On Parallel Sorting And An Implementation Of Difference Cover Suffix Array Construction
Sarah MacQueen Origami : A Mathematical System Of Paperfolding
David Lynn Nielsen A Problem Zarankiewicz
Julia Porcino An Analysis Of Permanental Ideals Over Hypermatrices
Siddharth S. Raval Quantum Algorithms For A Few Problems
Nicholas K. Salter A Fourier-Analytic Approach To Polytope Euler-Maclaurin Summation
Trey Sands On simulating a new Keynesian dynamic stochastic general equilibrium model : replicating smets and wouters
Caleb Tillman An Application Of Representation Theory To The Study Of Random Walks On Groups
Gaurav Gokaran Venkataraman Volterra Integral Equation Methods For Theoretical Neuroscience
Wally Jay Wissner Characterizing doubly-special relativistic models with energy- independent metrics
Tianyuan Xu Graph Partitions And Free Resolutions Of Toppling Ideals
Noah Davidson Musical Sequences And Dominating Empires : A Study In Aperiodic Tilings
Raphael Deem Algebraic Error Correction
Hannah Fouasnon A Colorful Clustering : A Structural Analysis Of Hartigan's Modal Method For Block Clustering
Laurel E. Stephenson Haskins Perturbation theory for projected states
Nicholas Insalata A Mosaic Approach To Virtual Reality
Tian Jiang Stability In Chip-Firing Games
Russell Alex Mayhew Found on road dead : a macroeconomic study of the efficacy of vehicle scrappage subsidies and sales incentives
M. Rose Peterman Balanced Incomplete Block Designs
Swaroop Poudel Financial systemic risk : classification and measurement
Erica Hilary Shannon The Connection Between Dimer Covers And Sandpile Groups
Homer Strong Uniform Connected Subgraph Sampling
Justin J. Sumner Functional determinants in the path integral formalism
R. Seth Terashima Message Routing In Random Graphs : Lattice And Ring Models For Peer-To-Peer And Social Networks
Bryson Leigh Uhrig-Fox One system does not fit all : a country-level study of variation in tax systems and the number of the headquarters of multinational corporations
Yannik Van Huele Mathematical Quasicrystals As Generalized Classical Crystals
Laura White-Avian Falling Out Of Attraction Through An Infinite Cascade Of Period Doubling Bifurcations
John Wilmes Algebraic Invariants Of Sandpile Graphs
Andrew S Winterman Statistical Tests Of Equivalence
Godwin Yung An Algorithm For The Calibration Of FTMS Signals To Improve Peptide Identification
Nii Amartey Amarteifio The role of foreign direct investment : a sub-Saharan perspective
Nicholas Chandler-Klein Predictive validity of the new SAT reasoning test
Thomas M. Chartrand Trajectories in the hydrodynamic formulation of quantum mechanics : a computational and theoretical investigation
Regina Collecchia The Entropy Of Musical Classification
Christopher Cotter Permanental Ideals
Benjamin Fischer Funny Ways To Count Dots : Relating The Discrete And Continuous Volumes Of Rational Polyhedra
Cooper Francis Model-Checking Concurrent Systems
Maxwell Hallock The Tutte Polynomial And The Critical Configuration Polynomial On Acyclic Digraphs
Joseph A. Hand Creative destruction in a dynamic stochastic general equilibrium framework : evaluation through calibration and simulation
Bryan Head An Abstraction Of Evolution Through Algebra
Joshua Hoak Mathematical Games
David Jackson Production effects of U.S. agricultural program payments : an empirical examination
Mallory J. Keeler Estimating the effects of the federal estate tax on charitable behavior : evidence since EGTRRA 2001
Upasana Khadka The effects of relief mechanisms from double taxation on foreign direct investment
Tinashe Mashungu Structural adjustment and debt
Daniela Morar Power laws in the stock market
Joshua O'Rourke Frobenius Numbers Of Consecutive Squares
Jacob Perlman Sandpiles : A Bridge Between Graphs And Toric Ideals
William Rosenbaum Analysis On Circles : A Modern View Of Fourier Series
Andrew C. Shapiro Music industry business models in the digital millenium : an empirical analysis of streaming music and multi-product profits
Clara Siegel Radiocarbon Dating Of Mount Baker Lahars : Implications For Volcanic Hazard Assessment
Nayram Tay-Agbozo An Investigation Into Image Segmentation Using Graph Cuts
Cordelia Wylde-LaRue Trigonometry In The Hyperbolic Plane
Michael C. Allard Anomalous diffusion, fractional calculus, and random walks
Eric Brattain-Morrin Entropy, computation, and demons
Devin Chalmers The computable world
Jeffrey Samuel Sebastian Weinmann Cruse Riemann Roch on directed graphs
Jessica Gill Monomial ideals
Jeremy J. Harper Projection-valued measures and the need for quantum observables to be self-adjoint
William Henderson Distributed and mobile systems in the ?-calculus
William R. Henner Ukkonen's linear time suffix trees
Juliet Hougland Separability of the Kerr geodesic Hamilton-Jacobi equation
Andreea Jurculet Fedspeak : the response of interest rates to FOMC communication
Karim Lakhani An introduction to multiresolution analysis and the discrete wavelet transform
Julia F. Lazenby Circulant graphs and their spectra
Joshua Michael Lingerfelt Retail electrical deregulation in Texas
Steven M. McClellan Jr. A computational investigation of Kubota conductors
Peter McCulloch The Ito calculus and option pricing
Tracy L. Mehoke The book of shadows : enumeration of cubick curves
James E. Nye Braid group cryptography
Sara Caitlin O'Connor A new derivation for the formulae for counting elliptic points
Rebecca Schoenberg-Jones Constructing a sandpile machine
Erica C. Strachan Determinants of microcredit success : a case study of Mercy Corps Northwest
Griffen R. Thoma A survey of results related to the study of magic squares
Michael T. Turner Moving ahead, looking behind : social learning in Mexico-U.S. migration
Verónica G. Vergara Larrea Laplacian growth : how mistaken are we by calling it DLA?
Timothy B. Armstrong Federal research funding and patenting in U.S. universities
Samuel J. Billheimer Perihelic motion in orbits about axis-symmetric ellipsoids
Matthew Strom Borman The ranks of a tropical matrix
Heidi Elise Brooks Orbit determination of binary stars from radial velocity measurements
Diego I. Calderón Representation theory of finite groups with applications
Ranganai Gwati Prediction and parameter estimation in the presence of missing data
Vanessa Elaine Holfeltz A lie theoretic approach to robot kinematics
An-Seok Joo Categorical ideas as expressed in the programming language charit
Julia M. Keller Quantifying entanglement
David Kling Valuing views form single-family homes in Portland, OR
Anaiah E. Krueger A brief history of distribution theory
Alice Emily Neels Quantum learning and Reed-Muller codes
Keon H. Parandvash Arbitrage in Hilbert space
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bio-mathematics: introduction to the mathematical model of the hepatitis c virus, lucille j. durfee. pdf. analysis and synthesis of the literature regarding active and direct instruction and their promotion of flexible thinking in mathematics, genelle elizabeth gonzalez. pdf. life expectancy, ali r. hassanzadah. pdf
A selection of Mathematics PhD thesis titles is listed below, some of which are available online: 2023 2022 2021 2020 2019 2018 2017 2016 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000 1999 1998 1997 1996 1995 1994 1993 1992 1991. 2024. Reham Alahmadi - Asymptotic Study of Toeplitz Determinants with Fisher-Hartwig Symbols and Their Double-Scaling Limits
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 ...
Zeros of Harmonic Polynomials and Related Applications, Azizah Alrajhi. PDF. Combination of Time Series Analysis and Sentiment Analysis for Stock Market Forecasting, Hsiao-Chuan Chou. PDF. Uncertainty Quantification in Deep and Statistical Learning with applications in Bio-Medical Image Analysis, K. Ruwani M. Fernando. PDF
Theses/Dissertations from 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 ...
Groups defined by language theoretic classes . Al Kohli, Raad Sameer Al Sheikh (2024-06-11) - Thesis. In this thesis we shall study classes of groups defined by formal languages. Our first main topic is the class of groups defined by having an ET0L co-word problem; i.e., the class of co-ET0L groups.
A senior thesis is required by the Mathematics concentration to be a candidate for graduation with the distinction of High or Highest honors in Mathematics. See the document ' Honors in Mathematics ' for more information about honors recommendations and about finding a topic and advisor for your thesis. With regards to topics and advisors ...
Department of Mathematics. Science Center Room 325. 1 Oxford Street. Cambridge, MA 02138 USA. Tel: (617) 495-2171 Fax: (617) 495-5132. Department Main Office Contact. Web Site Contact. Digital Accessibility. Legacy Department of Mathematics Website.
Theses/Dissertations from 2021. PDF. Simulation of Pituitary Organogenesis in Two Dimensions, Chace E. Covington. PDF. Polynomials, Primes and the PTE Problem, Joseph C. Foster. PDF. Widely Digitally Stable Numbers and Irreducibility Criteria For Polynomials With Prime Values, Jacob Juillerat. PDF.
Theses/Dissertations from 2021. PDF. Mathematical Modelling & Simulation of Large and Small Scale Structures in Star Formation, Gianfranco Bino. PDF. Mathematical Modelling of Ecological Systems in Patchy Environments, Ao Li. PDF. Credit Risk Measurement and Application based on BP Neural Networks, Jingshi Luo. PDF.
The Senior Thesis in Mathematical Sciences course allows students to engage in independent mathematical work in an active and modern subject area of the mathematical sciences, guided by an official research faculty member in the department of mathematics and culminating in a written thesis presented in an appropriate public forum.
If you are an undergraduate looking for some research topics for your next math paper, you will surely appreciate our list of interesting undergraduate math research topics: Methods to count discrete objects. The origins of Greek symbols in mathematics. Methods to solve simultaneous equations. Real-world applications of the theorem of Pythagoras.
Mathematics thesis and dissertation collection. Browse By. By Issue Date Authors Titles Subjects Publication Type Sponsor Supervisors. Search within this Collection: ... the problem of sampling from distributions with super-linearly growing log-gradient and the applications to the related optimization problems. This challenge is tackled in ...
Senior Theses. An undergraduate thesis is a singly-authored mathematics document, usually between 10 and 80 pages, on some topic in mathematics. The thesis is typically a mixture of exposition of known mathematics and an account of your own research. To write an undergraduate thesis, you need to find a faculty advisor who will sponsor your project.
PhD in Mathematical Sciences. Advisors: Franz Tanner/Kathleen Feigl. Dissertation Title: Development of Computational Methods for the Investigation of Liquid Drop Phenomena in External Flows. Note: Search the J. R. Van Pelt and Opie Library Catalog for online availability of recent theses. Listing of recent theses and dissertations, with links ...
To date, the department has awarded over 800 PhD degrees. An average of approximately 15 dissertations per year have been added in recent times. Find below a list of PhD theses completed in our program since 1952. (Additionally, search Ohio State at Math Genealogy, which also includes some theses from other OSU departments.)
The Department of Mathematics offers Bachelor's degrees in Mathematics and Mathematics with Secondary Education option. A student's course of study can be tailored to suit a particular interest in pure mathematics, applied mathematics, mathematics teaching, or statistics. We also offer Master's degrees in Mathematics and Mathematics Education.
Tanveer, Saleh. 2020. Marrero Garcia, Hilary. A Geometric Analysis Approach to Distinguish Basal Serotonin Levels in Control and Depressed Mice. Best, Janet. 2020. Wood, Emily. Analysis of SIS Patch Model and Development of a Modified SEIR Model Applied to the Current Opiate Crisis. Lou, Yuan.
The effect of problem-solving teaching approach on learning fractions in Grade 8. Agadagba, Oghenerukewe Emmanuel (2024) Problem-solving teaching approach is critical in improving learners' cognition and problem-solving skills in different content areas in mathematics. Therefore, this quantitative study evaluated the effect of the problem ...
The impact of a teacher enhancement program on 7th through 12th grade mathematics instruction with regard to curriculum, technology, and assessment. Ph.D. thesis, Ohio University. View Abstract. Add to Collection.
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.
Author, Title, or Publisher . Related Fields . Status . Apply Filters. Author/Title Research Type Related Fields ; Tripathi, R. (2019) Determinantal processes and Stochastic domination ... Math Student Services C-36 Padelford Phone: (206) 543-6830 Fax: (206) 616-6974 [email protected].
Honors in Mathematics Writing a Senior Thesis (2021-2022) 1. Candidacy for Honors. A senior thesis is required for high or highest honors in Mathematics, where-as for straight honors (neither high nor highest), a senior thesis can be submit or four extra courses in Mathematics or approved related fields can be taken (above the required twelve ...
Thesis. As a capstone project, every graduate of Reed College completes a thesis in their senior year. Here seniors can find instructions and resources for completing a mathematical thesis. Anyone can also find a list of thesis projects from Math & Stats from the last couple of decades. Jump to past thesis projects.