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Home > A&S > Math > Math Undergraduate Theses
Theses from 2019 2019.
The Name Tag Problem , Christian Carley
The Hyperreals: Do You Prefer Non-Standard Analysis Over Standard Analysis? , Chloe Munroe
A Convolutional Neural Network Model for Species Classification of Camera Trap Images , Annie Casey
Pythagorean Theorem Area Proofs , Rachel Morley
Euclidian Geometry: Proposed Lesson Plans to Teach Throughout a One Semester Course , Joseph Willert
An Exploration of the Chromatic Polynomial , Amanda Aydelotte
Complementary Coffee Cups , Brandon Sams
Nonlinear Integral Equations and Their Solutions , Caleb Richards
Principles and Analysis of Approximation Techniques , Evan Smith
An Introductory Look at Deterministic Chaos , Kenneth Coiteux
A Brief Encounter with Linear Codes , Brent El-Bakri
Axioms of Set Theory and Equivalents of Axiom of Choice , Farighon Abdul Rahim
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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:
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:
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.
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.
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.
Possible colloquium topics:
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.
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:
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:
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:
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.
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.
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:
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.
Any topics in statistical application, education, or methodology, including but not restricted to:
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:
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:
Possible colloquium topics:
Any topics in mathematics, mathematical physics, functional analysis, or probability, such as:
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.
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Wednesday, August 21, 2024 | By jsteepe
Doctoral thesis defence in Physics
Mahdieh Gol Bashmani Moghadam, a Doctor of Philosophy candidate in the Department of Physics, will defend her thesis titled “Hidden Laplace-Runge-Lenz symmetry groups of transformation in Classical Mechanics and General Relativity” on Thursday, August 29 at 10 AM., in RFP 214/215.
The examination committee includes Brian Roy, Chair; Stephen Anco, Supervisor; Cristina Stoica, External Examiner (Wilfrid Laurier University); Henryk Fuks, Internal External Examiner, and Kirill Samokhin and Barak Shoshany, Committee Members.
Tags: FMS , Physics , Thesis defence Categories: Events
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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
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 ...
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
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.
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.
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 ...
2023 Qingci An (F. Lu)Identifiability and data-adaptive RKHS Tikhonov regularization in nonparametric learning problems Letian Chen (J. Bernstein)On Mean Curvature Flows coming out of Cones Ben Dees (C. Mese)On the Singular Sets of Harmonic Maps into F-Connected Complexes Lili He (H. Lindblad)The linear stability of weakly charged and slowly rotating Kerr Newman family of charged black holes ...
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.
Estimation and application of Bayesian Hawkes process models . Deutsch, Isabella (The University of Edinburgh, 2024-03-13) In this thesis, we examine various facets of Bayesian approaches to Hawkes Processes. Hawkes Processes are a flexible class of point processes that are used to model events that occur in clusters or bursts, as classic ...
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.)
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.
Essays on Time Series and Machine Learning Techniques for Risk Management, Michael Kotarinos. PDF. The Systems of Post and Post Algebras: A Demonstration of an Obvious Fact, Daviel Leyva. PDF. Reconstruction of Radar Images by Using Spherical Mean and Regular Radon Transforms, Ozan Pirbudak. PDF
For PhD Thesis, see here.This page is about Senior thesis. In order that senior thesis produced by Harvard math students are easier for other undergrads to benefit from, we would like to exhibit more senior theses online (while all theses are available through Harvard university archives, it would be more convenient to have them online).It is absolutely voluntary, but if you decide to give us ...
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 ...
Modeling and simulation of uni- and multi-flagellar bacterial locomotion in a viscous fluid. PhD Theses 2022. Author. Title. James Petrie. Decentralized contact tracing protocols and a risk analysis approach to pandemic control. Yiming Meng. Bifurcation and Robust Control of Instabilities in the Presence of Uncertainties.
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.
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.
math attitude scores made a significantly predict achievement in mathematics. Richardson and Suinn (1972) created a 98-item Mathematics Anxiety Rating Scale (MARS), which is the most used instrument to measure math anxiety. Suinn, Edie, Nicoletti, and Spinelli (1972) used the . Student achievement . students
ranked 27th in math achievement; and although performance in reading and science were ranked average, mathematics performance was below average (OECD, 2014). The highest performing students (Shanghai-China) outperformed students from the United States by the equivalent of over two years of formal schooling, and students from the
A Thesis Submitted to the Department of Psychology in partial fulfillment of the requirement for the degree of ... Math anxiety, the negative emotional response to math, is a common educational issue observed globally and across many grade levels. Additionally, it negatively impacts math performance and ...
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 ...
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 ...
Mathematics, as we know, " Mathematics is the Queen and servant of Sciences. Confluent learning, as reemphasized by Loon and Nichol (2015), is holistic, it aims to activate and engage. all of ...
Theorem 1.2.1. A homogenous system of linear equations with more unknowns than equations always has infinitely many solutions. The definition of matrix multiplication requires that the number of columns of the first factor A be the same as the number of rows of the second factor B in order to form the product AB.
Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics. ISSN 1088-6826 (online) ISSN 0002-9939 (print)
Mathematics MPhil Thesis. 2025. Change year. 2024; 2023; 2022; 2021; 2020; 2019; 2018; This paper is not offered for 2025. For previous occurrences, try the 2024 version of this year. 120. 600. Jump to. Additional information. Subject regulations Indicative fees current as ...
Doctoral thesis defence in Physics Mahdieh Gol Bashmani Moghadam, a Doctor of Philosophy candidate in the Department of Physics, will defend her thesis titled "Hidden Laplace-Runge-Lenz symmetry groups of transformation in Classical Mechanics and General Relativity" on Thursday, August 29 at 10 AM., in RFP 214/215.