mathematics thesis bachelor

Senior Thesis

This page is for Undergraduate Senior Theses.  For Ph.D. Theses, see here .

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: The document ‘ Faculty research areas ’ lists the research interests of current members of the Math Department.

So that Math Department senior theses can more easily benefit other undergraduate, 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 your permission, please send an electronic version of your thesis to cindy@math. The format can be in order of preference: DVI, PS, PDF. In the case of submitting a DVI format, make sure to include all EPS figures. You can also submit Latex or MS word source files.

If you are looking for information and advice from students and faculty about writing a senior thesis, look at this document. It was compiled from comments of students and faculty in preparation for, and during, an information session. Let Wes Cain ([email protected]) know if you have any questions not addressed in the document.

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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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2024 Senior Theses - Graduated with Distinction

Angikar ghosal.

Representation Theoretic Formulation of Quantum Error Correcting Codes Advisor: Robert Calderbank

Benjamin Goldstein

Soap-Film-Like Surfaces of Revolution Advisor: Demetre Kazaras

Noah Harris

Black Hole Thermodynamics, Large N Gauge Theories, and Deriving the AdS/CFT Correspondence Advisor: Paul Aspinwall

Long-Time Behavior of Some ODEs with Partial Damping Advisor: Kyle Liss

Aram Lindroth

Towards a Functional Equation for the $\mathbb{A}^1$-Logarithmic Zeta Function Advisor: Kirsten Wickelgren

Emmanuel Mokel

Monitoring Nonstationary Variance to Assess Convergence of Markov Chain Monte Carlo Advisor: Jonathan Mattingly

Nathan Nguyen

Towards Solving Variational Graphon Problem for Random Hypergraphs Advisor: Nicholas Cook

Nathanael Ong

On the Betti Numbers of Rank 2 Compact Locally Symmetric Spaces Advisor: Mark Stern

Jean-Luc Rabideau

Random Restrictions in the p-Biased Measure Advisor: Henry Pfister

Riki Shimizu

Unveil Sleep Spindles with Concentration of Frequency and Time (ConceFT) Advisor: Hau-Tieng Wu

December 2023

Quantum State Tomography via Tensor Ring Representation Advisor: Jianfeng Lu

Jesse Zhang

Answer Filtration with Filtration: Toward a Theory of Lifetime Filtration for Multiparameter Persistence Modules Advisor: Ezra Miller

Alex Burgin

The Schrodinger Maximal Function and Generalizations Advisor: Lillian Pierce

Nick Chakraborty

Improve Accuracy and Speed of Manifold Reconstruction and De-Noising from Scattered Data in R 2 Advisor: Hongkai Zhao

Jeffrey Cheng

Mixing in Measure Preserving Dynamical Systems Advisor: Tarek Elgindi

Carson Dudley

A Mathematical Model of a Peritoneal Staphylococcus Aureus infection Advisor: Anna Nelson

Riley Fisher

Pattern Formation in Evolving Domains Advisor: Tom Witelski

Multitaper Wave-Shape F-Test For Detecting Non-Sinusoidal Oscillations Advisor: Hau-Tieng Wu

Diffusing on multiple fibers Advisor: Ingrid Daubechies and Shira Faigenbaum

December 2022

Symmetric Formulas for Products of Permutations Advisor: Benjamin Rossman

A homotopic variant of policy gradients for the linear quadratic regulator problem Advisor: Andrea Agazzi

Nathan Geist

Homological algebra of modules over real polyhedral groups Advisor: Ezra Miller

Braden Hoagland

Percolation Processes on Dynamically Grown Graphs Advisor: Rick Durrett

Daniel Hwang

Analyzing the bistability of the minimally bistable ERK network using the discriminant locus Advisor: Maggie Regan

Wallace Peaslee

Dolbeault Cohomology of Non-Compact Metric Graphs Advisor: Joseph Rabinoff

Mathematical Modeling of TIE1 and Endothelial Metabolism Advisor: Michael Reed

December 2021

Some Mathematical Problems in Quantum Computing and Quantum Information Advisor: Robert Calderbank

Anuk Dayaprema

Solitons for the closed G2 Laplacian flow in the cohomogeneity-one setting Advisor: Mark Haskins

Ziyang Ding

At the Intersection of Deep Sequential and State-space Model Framework Advisor: Sayan Mukherjee

Lucas Fagan

Schur Polynomials and Crystal Graphs Advisor: Spencer Leslie

Resolving Simpson’s Paradox in NC Public School Grading System Advisor: Greg Herschlag

Phoebe Klett

Implementing non-canonical Sylvan Resolutions Advisor: Ezra Miller

Jianyou Wang

Deep Reinforcement Adaptive Computational Processor Advisor: Vahid Tarokh

Alex Damian

Theoretical Guarantees for Signal Recovery Advisor: Hau-tieng Wu

Blythe Davis

The Spherical Manifold Realization Problem Advisor: Faramarz Vafaee

Onkar Gujral

Khovanov Homology and Knot Concordance dvisor: Adam Levine

Xiayimei Han

Hodge Representations of Calabi-Yau 3 Folds Advisor:  Colleen Robles

Remy Kassem

Symmetry Detection of Unknown Volumes from Projected Variations Advisor: Xiuyuan Cheng

Joey Li

Algebraic Data Structures for Decomposing Multipersistence  Modules Advisor: Ezra Miller 

Evaluating Bayesian Convolutional Neural Networks in the Clinic Advisor: Paul Bendich

Jonathan Michala

Uniqueness of Ranked Pairs Advisor: Hubert Bray 

Benjamin Nativi

An Analogue of Gauss Composition for Binary Cubic Forms Advisor: Aaron Pollack

Computing Values of Symmetric Square L-Functions using Ichino's Pullback Formula Advisor: Aaron Pollack

Junmo Ryang

Embedding Lagrangian Surfaces Advisor: Robert Bryant

Irina Cristali

Poisson Percolation on the Square Lattice Advisors: Rick Durrett, Matthew Junge

Creating Musical Rubato Using Deep Learning Advisor: Ezra Miller

Zhenhua Liu

Stationary One-Sided Area Minimizing Hypersurfaces with Isolated Singularities Advisors: William Allard, Hubert Bray, Robert Bryant

Xueying Wang

Unfolding High-Dimensional Convex Polyhedra Advisor: Ezra Miller

Claire Wiebe

Analyzing the Effects of Partisan Correlation on Election Outcomes using Order Statistics Advisor: Jonathan Mattingly

Gaitling Zhou

Elliptic Curves over Dedekind Domains Advisor: William Pardon

(you can search for archived versions of these theses here )

• Surabhi Beriwal  Statistical analysis of fruit fly wing vein topology  (2018) [with E. Miller]
• Trung Can  The Heisenberg-Weyl Group, Finite Symplectic Geometry, and their applications   (2018) [with R. Calderbank]
• Feng Gui  On Calibrations for Area Minimizing Cones  (2018) with [H. Bray]
• Neel Kurupassery   Cryptographic Primitives in Artin Groups of Type I k (m)    (2018)  [with M. Abel]
• Eric Peshkin  T he quantification of markers of economic development from time-series satellite imagery using deep learning   (2018) with [with P. Bendich and D. Thomas]
• Weiyao Wang   Understanding Operator Reed-Muller Codes Through the Weyl Transform   (2018) [with R. Calderbank]
• Alexander Pieloch  The Topology of Moduli Spaces of Real Algebraic Curves  (2017) [with R. Hain]
• Samadwara Reddy  The Vietoris–Rips Complexes of Finite Subsets of an Ellipse of Small Eccentricity  (2017) [with H. Adams]
• Lindsey Brown  An Application of Abstract Algebra to the Neural Code for Sound Localization in Barn Owls  (2016) [with M. Reed]
• David Builes  The Large Cardinal Hierarchy  (2016) [with R. Hodel]
• Kyle Casey  Siegel Modular Forms  (2016) [with L. Saper]
• Bryan Runjing Liu  Modeling the Effects of Positive and Negative Feedback in Kidney Blood Flow Control  (2016) [with A. Layton]
• Francois Thelot A Maximum Entropy Based Approach for the Description of the Conformational Ensemble of Calmodulin from Paramagnetic NMR (2016) [with M. Maggioni and B. Donald]
• Will Victor  Efficient algorithms for Traffic Data Analysis  (2016)[computer science with P. Agarwal]
• Paul Ziquan Yang  Morphisms with Only Mild Singular Fibers and Bertini Theorems over Finite Fields  (2016) [with C. Schoen]
• Rex Zhitao Ying  Approximation Algorithms of Dynamic Time Warping and Edit Distance  (2016) [computer science with P. Agarwal]
• Roger Zou  Deformable Graph Model for Trackng Epithelial Cell Sheets in Florescence Microscopy  (2016)[computer science with C. Tomasi]
• Anne Talkington  Modeling the Dynamics of Cancerous Cells in vivo  (2015) [with R. Durrett]
• Rowena Gan  Geometry of Impressionist Music  (2015) [with E. Miller]
• David Hemminger  Augmentation Rank of Satellites with Braid Pattern  (2015) [with L. Ng and C. Cornwell]
• Mandy Jiang  Dynamic random network model for human papilloma virus transmission  (2015) [with M. Ryser]
• Hunter Nisonoff  Efficient Partition Function Estimatation in Computational Protein Design  (2015) [with M. Maggioni]
• Eugene Rabinovich  The Conformal Manifold in N=(2,2) SCFTs    (2015)  [physics  with R. Plesser]
• Marshall Ratliff  Introducing the Cover tree to Music Information Retrieval  (2015) [with P. Bendich]
• Brett Schnobrich  Heisenberg-Weyl Group, Subspace Packings, and Image Processing  (2015) [with R. Calderbank]
• Christy Vaughn  Stochastic Study of Gerrymandering  (2015) [with J. Mattingly]
• Aashiq Dheeraj  A Stochastic Spatial Model for Tumor Growth  (2014) [with R. Durrett]
• Joshua Izzard  Rank p 2  Representations of Semisimple Lie Algebras  (2014) [with J. Getz]
• Kathleen Lan  Coalescing random walks on n-block Markov chains  (2014) [with K. McGoff]
• Leslie Lei Lei  Infinite Swapping Simulated Tempering  (2014) [with J. Lu]
• Julia Ni  A convex approach to tree-based wavelet compression  (2014) [with A. Thompson]
• Jiarou Ivy Shen  Merge times and hitting times of time-inhomogeneous Markov chains  (2014) [with D. Sivakoff]
• Daniel Stern  Low-Order Lagrangians Depending on a Metric and a Matter Field of Arbitrary Rank  (2014) [with H. Bray]
• Daniel Vitek  Knot Contact Homology and the Augmentation Polynomial  (2014) [with C. Cornwell]
• Alexander Wertheim  Complex Multiplication on Elliptic Curves  (2014) [with L. Saper]
• Luxi Wei  Modeling Credit Risk using Rating and Environmental Factors  (2014) [with R. Durrett]
• Timothy Chang  On the existence of a simple winning strategy in the T(4.3) knot game  (2013) [with D. Herzog]
• Conrad de Peuter  Modeling basketball games as alternating renewal-reward processes and predicting match outcomes  (2013) [with R. Durrett]
• Bryan Jacobson  A practical approximation of persistent local homology  (2013) [with P. Bendich]
• Kara Karpman  Simulating mucociliary transport using the method of regularized Stokelets  (2013) [with A. Layton]
• Carmen Lopez  Modeling the folate pathway in Escherichia coli  (2013) [with A. Layton]
• James Mallernee  Strategy and honesty based comparison of preferential ballot voting methods  (2013) [with H. Bray]
• William Zhang  Evolutionary dynamics in host pathogen model  (2013) [with R. Durrett]
• Ben Bellis  Investigation of a Local Computation of the Signature from the Triangulation of a Manifold  (2012) [with M. Stern]
• Adrian Chan  Pricing financial derivatives with multi-task machine learning and mixed effects method  (2012) [with J. Bouvrie]
• Kyu Won Choi  Relative contributions of common jumps in realized correlations  (2012) [with A. Petters]
• Veronica Ciocanel  Analysis of the nonlinear dynamics of the forced planar string pendulum  (2012) [with T. Witelski]
• Kaveh Danesh  A branching process model of ovarian cancer  (2012) [with R. Durrett]
• Theo Frehlinghuysen  Carbon sequestration via forest management techniques  (2012) [with D. Kraines]
• Yingyi Shen  A study of edge toric ideals using associated graphs  (2012) [with S. Mapes]
• Daniel Thielman  Complex-balanced steady state of chemical reaction networks that contain an Eulerian cycle  (2012) [with C. Berkesch]
• Kaitlin Daniels  Noise driven Transitions between stable equilibria in stochastic dynamical systems  (2011) [with A. Athreya]
• Alan Guo  Lattice point methods for combinatorial games  (2011) [with E. Miller]
• Nils Hultgren  Centrality and network analysis: A perturbative approach to dynamical importance  (2011) [with I. Matic]
• Hans Kist  Estimating carbon sequestration potential in the boreal forests  (2011) [with D. Kraines]
• Misha Lavrov  Invariants in Legendrian links in the solid torus  (2011) [with D. Rutherford]
• Philip Pham  Tubuloglomerular feedback signal transduction in the loops of Henle  (2011) [with A. Layton]
• Thames Sae Sue  A simple cardiac model exhibiting stationary discordant alternans  (2011) [with D. Schaeffer]
• Max Tabachnik  An analysis of preferential ballot voting methods  (2011) [with H. Bray]
• Bo Waggoner  A model of the foot and ankle in running  (2011) [with E. Bouzarth]
• Wutichai Chongchitmate  Classification of Legendrian knots and links  (2010) [with L. Ng]
• Jason D. Lee  Multiscale analysis of dynamic graphs  (2010) [with M. Maggioni]
• Jeremy Semko  Statistical analysis simulations of coarsening droplets coating a hydrophobic surface  (2010) [with T. Witelski]
• Amy Wen  Model of feedback-mediated dynamics of coupled nephrons with compliant thick ascending limbs  (2010) [with A. Layton]
• Jason Ferguson  Factorization of Primes in Biquadratic Extensions of Q  (2009) [with C. Schoen]
• Jared Haftel  A Closer Look at ADC multivariate GARCH  (2009) [with M. Huber]
• Mark Hallen  Improving accuracy and scope of quantitative FRAP analysis  (2009) [with A. Layton]
• Andy Ng  Retinoid Transport in the Vision cycle  (2009) [with J. Mercer]
• Aaron Pollack  Relations between special derivations arising from modular forms  (2009) [with R. Hain]
• Jesse Thorner  Simplicial homology and DeRham’s theorem  (2009) [with W. Allard]
• Barry Wright III  Objective measures of preferential ballot voting systems  (2009) [with H. Bray]
• Michael Bauer  Existence and stability of patterns arising from square wave forcing of the damped Mathieu equation  (2008) [with A. Catlla]
• Tirasan Khandhawit  On Legandrean and transverse knots  (2008) [with L. Ng]
• Aalok Shah  An overview of fast marching and optimal control methods for trajectory optimization  (2008) [with W. Allard]
• Charles Staats III  Application of discrete geometry to the construction of Laurent-rational zeros  (2008) [with S. Sharif]
• Elliott Wolf  Computational pathways to Godel’s first incompletness theorem  (2008) [with R. Hodel]
• Lingen Zhang  The motion of sets of vortices  (2008) [with T. Witelski]
• Morgan Brown  An algorithm for tracking persistence pairing of a discrete homotopy of Morse functions on S 2   (2007) [with J.Harer]
• Brandon Levin  Class field theory and the problem of representing primes by binary quadratic forms  (2007) [with L. Saper]
• Stepan Paul  Lines and conics relative to degenerating divisors in CP 2   (2007) [with J. Davis]
• James Zou  3-D reconstruction and topological analysis of root architecture  (2007) [with J. Harer]
• Pradeep Baliga  Dynamic cellular automata model of toll plaza traffic flows  (2006) [with W. G. Mitchener]
• Adam Chandler  Dynamic cellular automata model of toll plaza traffic flows  (2006) [with W. G. Mitchener]
• Matthew Fischer  Mapping model of cardiac-membrane dynamics  (2006) [with D. Schaeffer]
• Qinzheng Tian  Simulation of Newtonian fluid flow between rotating cylinders  (2006) [with T. Witelski]
• Yee Lok Wong  Models of instant runoff voting  (2006) [with J. Mattingly]
• Oaz Nir  Mechanical arms and algebraic topology  (2005) [with J.Harer]
• Mayank Varia  Explicit calculation of the L invariant for Kummer surfaces  (2005) [with J. Hanke]
• David Arthur  On the higher Hasse-Witt matrices and related in variants  (2004) [with W. Pardon]
• Suzy Borgschulte  A mathematical approach to the panting of dogs  (2004) [with M. Reed]
• Lauren M. Childs  Scaling population dynamics from the macroscopic to the microscopic  (2004) [with T. Kepler]
• Ryan Letchworth  Wavelet methods for numerical solutions of differential equations  (2004) [with S. Roudenko]
• David Marks  Coadjoint orbits and geometric quantization  (2004) [with M.R. Plesser]
• Lori Peacock  Distributions of the small eigenvalues of Wishart matrices  (2004) [with B. Rider]
• Lindsay C. Piechnik  Smooth reflexive 4-polytopes have quadratic triangulations  (2004) [with C. Haase]
• Matthew Toups  A solution to the D0-D4 system of equations  (2004) [with M. Stern]
• Jenna VanLiere  Mathematically modelling the growth and diversification of T-cell populations  (2004) [with T. Kepler]
• Matthew J. Atwood  Evaluating singular and nearly singular integrals numerically  (2003) [with J.T. Beale]
• Marie Guerraty  Controlling alternans in a cardiac map model  (2003) [with M. Romeo]
• Meredith C. Houlton  Classification of critical curves and preliminary analysis of caustics  (2003) [with A. Petters]
• Steven R. Nicklas  Envy and satisfaction in the public goods game  (2003) [with D. Kraines]
• Dane R. Voris  A numerical approach to the M t /M t /N t  queue with abandonment  (2003) [with B. Rider]
• Melanie Wood  Invariants and relations of the action of the absolute Galois group on dessins d’enfants and the algebraic fundamental group of the punctured sphere  (2003) [with R. Hain]
• Thomas W. Finley  Efficient Myrinet routing  (2002) [with W. Allard]
• Samuel W. Malone  Alternative Price Processes for Black-Scholes: Empirical Evidence and Theory  (2002) [with A. Petters]
• Carl Miller  Exponential Iterated Integrals and the Solvable Completion of Fundamental Groups  (2001) [with R. Hain]
• Daniel Neill  Optimality under Noise: Higher Memory Strategies for the Alternating Prisoner’s Dilemma  (2001) Computer Science [with D. Kraines]
• Luis Von Ahn  Models of the language of set theory and Zermelo Frankel axioms  (2000) [with R. Hodel]
• Christopher Beasley  Superconformal theories from Branes at Singularities  (1999) Physics [with R. Plesser]
• Alexander Brodie  Measurable Cardinals  (1999) [with R. Hodel]
• Jeffrey DiLisi  The Biology and Mathematics of the Hypothalamic-Pituitary-Testicular Axis  (1999) [with M. Reed]
• Garrett Mitchener  Lattices and Sphere Packing  (1999) [with R. Hain]
• Andrew O. Dittmer  Generalized Formulas for Circular Polygons  (1998) [with R. Hain]
• Richard R. Schneck  Set Theory and Cardinal Arithmetic  (1997) [with R. Hodel]
• Tung T. Tran  Counting Independent Subsets in Nearly Regular Graphs  (1997) [with G. Lawler]
• Paul A. Dreyer  Knot theory and the human pretzel game  (1995) [with J. Harer]
• Paul J. Koss  Effects of noise on the iterated prisoner’s dilemma  (1995) [with D. Kraines]
• Jeff Vanderkam  Eigenfunctions of an acoustic system  (1994) [with T. Beale]
• Linie Chang  Mathematics and immunology: Modeling antigen and antibody interactions  (1993) [with M. Reed]
• Sang H. Chin  Action of the Torelli group on the 3-fold cover of G-hole torus  (1993) [with R. Hain]
• Jennifer Slimowitz  Transitions of gaps between the integers N satisfying N q < j (1993) [with M. Reed]
• David Jones  Primality testing, factoring and continued fractions  (1992) [with C. Schoen]
• Will Schneeberger  The axiom diamond  (1992) [with J. Shoenfield]
• Jeanne Nielsen  Triply periodic minimal surfaces in  R 3  (1991) [with R. Bryant
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• Senior Thesis

A thesis is a more ambitious undertaking than a project. Most thesis writers within Applied Mathematics spend two semesters on their thesis work, beginning in the fall of senior year.  Students typically enroll in Applied Mathematics 91r or 99r (or Economics 985, if appropriate) during each semester of their senior year.  AM 99r is graded on a satisfactory/unsatisfactory basis.  Some concentrators will have completed their programs of study before beginning a thesis; in situations where this is necessary, students may take AM 91r for letter-graded credit, for inclusion in Breadth section (v) of the plan of study.  In the spring semester, the thesis itself may serve as the substantial paper on which the letter grade is based.  Econ 985 is also letter-graded, and may be included in the Breadth section of the plan of study in place of AM 91r.

Another, somewhat uncommon option, is that a project that meets the honors modeling requirement (either through Applied Mathematics 115 or 91r) can be extended to a thesis with about one semester of work.  Obviously the more time that is spent on the thesis, the more substantial the outcome, but students are encouraged to write a thesis in whatever time they have. It is an invaluable academic experience.

The thesis should make substantive use of mathematical, statistical or computational modeling,  though the level of sophistication will vary as appropriate to the particular problem context.  It is expected that conscientious attention will be paid to the explanatory power of mathematical modeling of the phenomena under study, going beyond data analysis to work to elucidate questions of mechanism and causation rather than mere correlation. Models should be designed to yield both understanding and testable predictions. A thesis with a suitable modeling component will automatically satisfy the English honors modeling requirement; however a thesis won't satisfy modeling Breadth section (v) unless the student also takes AM 91r or Econ 985.

Economics 985 thesis seminars are reserved for students who are writing on an economics topic. These seminars are full courses for letter-graded credit which involve additional activities beyond preparation of a thesis. They are open to Applied Mathematics concentrators with suitable background and interests.

Students wishing to enroll in AM 99r or 91r should follow the application instructions on my.harvard.

Thesis Timeline

The timeline below is for students graduating in May. The thesis deadline for May 2025 graduates is Friday, March 28, 2025 at 2:00PM. For off-cycle students, a similar timeline applies, offset by one semester. The thesis due date for March 2025 graduates is Friday, November 22, 2024 at 2:00PM. Late theses are not accepted.

Mid to late August:

Students often find a thesis supervisor by this time, and work with their supervisor to identify a thesis problem. Students may enroll in Econ 985 (strongly recommended when relevant), AM 91r, or AM 99r to block out space in their schedule for the thesis.

Early December:

All fourth year concentrators are contacted by the Office of Academic Programs. Those planning to submit a senior thesis are requested to supply certain information. This is the first formal interaction with the concentration about the thesis.

Mid-January:

A tentative thesis title approved by the thesis supervisor is required by the concentration.

Early February:

The student should provide the name and contact information for a recommended second reader, together with assurance that this individual has agreed to serve. Thesis readers are expected to be teaching faculty members of the Faculty of Arts and Sciences or SEAS. Exceptions to this requirement must be first approved by the Directors, Associate Director, or Assistant Director of Undergraduate Studies. For AM/Economics students writing a thesis on a mathematical economics topic for the March thesis deadline, the second reader will be chosen by the Economics Department. For AM/Economics students writing for the November deadline, the student should recommend the second reader.

On the thesis due date:

Thesis due at 2pm. Late theses are not accepted. Electronic copies in PDF format should be delivered by the student to the two readers and to [email protected] (which will forward to the Directors of Undergraduate Studies, Associate and Assistant Director of Undergraduate Studies) on or before that date and time. An electronic copy should also be submitted via the SEAS  online submission tool  on or before that date. SEAS will keep this electronic copy as a non-circulating backup and will use it to print a physical copy of the thesis to be deposited in the Harvard University Archives. During this online submission process, the student will also have the option to make the electronic copy publicly available via DASH, Harvard’s open-access repository for scholarly work.

Contemporaneously, the two readers will receive a rating sheet to be returned to the Office of Academic Programs before the beginning of the Reading Period, together with their copy of the thesis and any remarks to be transmitted to the student.

The Office of Academic Programs will send readers' comments to the student in late May, after the degree meeting to decide honors recommendations.

Thesis Readers

The thesis is evaluated by two readers, whose roles are further delineated below.  The first reader is the thesis adviser.  The second and reader is recommended by the student and adviser, who should secure the agreement of the individual concerned to serve in this capacity.  The reader must be approved by the Directors, Associate Director, or Assistant Director of Undergraduate Studies.  The second reader is normally are teaching members of the Faculty of Arts and Sciences, but other faculty members or comparable professionals will usually be approved, after being apprised of the responsibilities they are assuming.   For theses in mathematical economics, the choice of the second reader is made in cooperation with the Economics department.  The student and thesis adviser will be notified of the designated second reader by mid-March.

The roles of the thesis adviser and of the outside reader are somewhat different.  Ideally, the adviser is a collaborator and the outside reader is an informed critics.  It is customary for the adviser's report to comment not only on the document itself but also on the background and context of the entire effort, elucidating the overall accomplishments of the student.  The supervisor may choose to comment on a draft of the thesis before the final document is submitted, time permitting.  The outside reader is being asked to evaluate the thesis actually produced, as a prospective scientific contribution — both as to content and presentation.  The reader may choose to discuss their evaluation with the student, after the fact, should that prove to be mutually convenient.

The thesis should contain an informative abstract separate from the body of the thesis.  At the degree meeting, the Committee on Undergraduate Studies in Applied Mathematics will review the thesis, the reports from the two readers and the student’s academic record. The readers (and student) are told to assume that the Committee consists of technical professionals who are not necessarily conversant with the subject matter of the thesis so their reports should reflect this audience.

The length of the thesis should be as long as it needs to be to make the arguments made, but no longer!

Thesis Examples

The most recent thesis examples across all of SEAS can be found on the Harvard DASH (Digital Access to Scholarship at Harvard) repository . Search the FAS Theses and Dissertations collection for "applied mathematics" to find dozens of examples.

Note: Additional samples of old theses can be found in McKay Library. Theses awarded Hoopes' Prizes can be found in Lamont Library.

Recent thesis titles

Theses submitted in 2024.

Theses submitted in 2023

Senior Thesis Submission Information for A.B. Programs

Senior A.B. theses are submitted to SEAS and made accessible via the Harvard University Archives and optionally via  DASH  (Digital Access to Scholarship at Harvard), Harvard's open-access repository for scholarly work.

In addition to submitting to the department and thesis advisors & readers, each SEAS senior thesis writer will use an online submission system to submit an electronic copy of their senior thesis to SEAS; this electronic copy will be kept at SEAS as a non-circulating backup. Please note that the thesis won't be published until close to or after the degree date. During this submission process, the student will also have the option to make the electronic copy publicly available via DASH.  Basic document information (e.g., author name, thesis title, degree date, abstract) will also be collected via the submission system; this document information will be available in  HOLLIS , the Harvard Library catalog, and DASH (though the thesis itself will be available in DASH only if the student opts to allow this). Students can also make code or data for senior thesis work available. They can do this by posting the data to the Harvard  Dataverse  or including the code as a supplementary file in the DASH repository when submitting their thesis in the SEAS online submission system.

Whether or not a student opts to make the thesis available through DASH, SEAS will provide an electronic record copy of the thesis to the Harvard University Archives. The Archives may make this record copy of the thesis accessible to researchers in the Archives reading room via a secure workstation or by providing a paper copy for use only in the reading room.  Per University policy , for a period of five years after the acceptance of a thesis, the Archives will require an author’s written permission before permitting researchers to create or request a copy of any thesis in whole or in part. Students who wish to place additional restrictions on the record copy in the Archives must contact the Archives  directly, independent of the online submission system. 

Students interested in commercializing ideas in their theses may wish to consult Dr. Fawwaz Habbal , Senior Lecturer on Applied Physics, about patent protection. See Harvard's policy for information about ownership of software written as part of academic work.

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Home > College of Natural Sciences > Mathematics > Mathematics Theses, Projects, and Dissertations

Mathematics Theses, Projects, and Dissertations

Theses/projects/dissertations from 2024 2024.

On Cheeger Constants of Knots , Robert Lattimer

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

Theses/Projects/Dissertations from 2023 2023

DNA SELF-ASSEMBLY OF TRAPEZOHEDRAL GRAPHS , Hytham Abdelkarim

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

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

MATHEMATICS BEHIND MACHINE LEARNING , Rim Hammoud

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

Reverse Mathematics of Ramsey's Theorem , Nikolay Maslov

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

Constructing Hyperbolic Polygons in the Poincaré Disk , Akram Zakaria Samweil

KNOT EQUIVALENCE , Jacob Trubey

Theses/Projects/Dissertations from 2022 2022

SYMMETRIC GENERATIONS AND AN ALGORITHM TO PROVE RELATIONS , Diddier Andrade

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

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

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

Symmetric Generation , Ana Gonzalez

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

Simple Groups and Related Topics , Simrandeep Kaur

Homomorphic Images and Related Topics , Alejandro Martinez

LATTICE REDUCTION ALGORITHMS , Juan Ortega

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

Verifying Sudoku Puzzles , Chelsea Schweer

AN EXPOSITION OF ELLIPTIC CURVE CRYPTOGRAPHY , Travis Severns

Theses/Projects/Dissertations from 2021 2021

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

Matroids Determinable by Two Partial Representations , Aurora Calderon Dojaquez

SYMMETRIC REPRESENTATIONS OF FINITE GROUPS AND RELATED TOPICS , Connie Corona

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

MEASURE AND INTEGRATION , JeongHwan Lee

A Study in Applications of Continued Fractions , Karen Lynn Parrish

Partial Representations for Ternary Matroids , Ebony Perez

Theses/Projects/Dissertations from 2020 2020

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

Permutation and Monomial Progenitors , Crystal Diaz

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

Research In Short Term Actuarial Modeling , Elijah Howells

Hyperbolic Triangle Groups , Sergey Katykhin

Exploring Matroid Minors , Jonathan Lara Tejeda

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

Modeling the Spread of Measles , Alexandria Le Beau

Symmetric Presentations and Related Topics , Mayra McGrath

Minimal Surfaces and The Weierstrass-Enneper Representation , Evan Snyder

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

Excluded minors for nearly-paving matroids , Vanessa Natalie Vega

Theses/Projects/Dissertations from 2019 2019

Fuchsian Groups , Bob Anaya

Tribonacci Convolution Triangle , Rosa Davila

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

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

Geodesics on Generalized Plane Wave Manifolds , Moises Pena

Algebraic Methods for Proving Geometric Theorems , Lynn Redman

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

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

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

Theses/Projects/Dissertations from 2018 2018

PROGENITORS, SYMMETRIC PRESENTATIONS AND CONSTRUCTIONS , Diana Aguirre

Monomial Progenitors and Related Topics , Madai Obaid Alnominy

Progenitors Involving Simple Groups , Nicholas R. Andujo

Simple Groups, Progenitors, and Related Topics , Angelica Baccari

Exploring Flag Matroids and Duality , Zachary Garcia

Images of Permutation and Monomial Progenitors , Shirley Marina Juan

MODERN CRYPTOGRAPHY , Samuel Lopez

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

Symmetric Presentations, Representations, and Related Topics , Adam Manriquez

Toroidal Embeddings and Desingularization , LEON NGUYEN

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

Tutte-Equivalent Matroids , Maria Margarita Rocha

Symmetric Presentations and Double Coset Enumeration , Charles Seager

MANUAL SYMMETRIC GENERATION , Joel Webster

Theses/Projects/Dissertations from 2017 2017

Investigation of Finite Groups Through Progenitors , Charles Baccari

CONSTRUCTION OF HOMOMORPHIC IMAGES , Erica Fernandez

Making Models with Bayes , Pilar Olid

An Introduction to Lie Algebra , Amanda Renee Talley

SIMPLE AND SEMI-SIMPLE ARTINIAN RINGS , Ulyses Velasco

CONSTRUCTION OF FINITE GROUP , Michelle SoYeong Yeo

Theses/Projects/Dissertations from 2016 2016

Upset Paths and 2-Majority Tournaments , Rana Ali Alshaikh

Regular Round Matroids , Svetlana Borissova

GEODESICS IN LORENTZIAN MANIFOLDS , Amir A. Botros

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

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

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

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

LIFE EXPECTANCY , Ali R. Hassanzadah

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

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

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

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

Probabilistic Methods In Information Theory , Erik W. Pachas

THINKING POKER THROUGH GAME THEORY , Damian Palafox

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

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

AN INTRODUCTION TO BOOLEAN ALGEBRAS , Amy Schardijn

The Evolution of Cryptology , Gwendolyn Rae Souza

Theses/Projects/Dissertations from 2015 2015

SYMMETRIC PRESENTATIONS AND RELATED TOPICS , Mashael U. Alharbi

Homomorphic Images And Related Topics , Kevin J. Baccari

Geometric Constructions from an Algebraic Perspective , Betzabe Bojorquez

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

Symmetric Presentations and Generation , Dustin J. Grindstaff

HILBERT SPACES AND FOURIER SERIES , Terri Joan Harris Mrs.

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

Simple Groups and Related Topics , Manal Abdulkarim Marouf Ms.

Elliptic Curves , Trinity Mecklenburg

A Fundamental Unit of O_K , Susana L. Munoz

CONSTRUCTIONS AND ISOMORPHISM TYPES OF IMAGES , Jessica Luna Ramirez

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Master's thesis latex template.

"LaTeX is a document preparation system. When writing, the writer uses plain text as opposed to the formatted text found in WYSIWYG ("what  you see is what you get") word processors. The writer uses markup tagging conventions to define the general structure of a document (such as article, book, letter, or thesis), to stylise text throughout a document (such as bold and italics), and to add citations and cross-references. A TeX distribution such as TeX Live or MikTeX is used to produce an output file (such as PDF or DVI) suitable for printing or digital distribution. Within the typesetting system, its name is stylised as L a T e X ." — Adopted from Wikipedia. ( https://en.wikipedia.org/wiki/LaTeX )

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• Note: The generated sample pdf is available because many people asked for it, not because it is a good idea to use it as a reference. The style file and sample LaTeX document contain instructions and comments on why/how certain things were done in a certain way...
• Note: Official Unofficial Guide for Thesis Chairs
• Note: Official LaTeX format approval form; this is an official SDSU form — Do Not Edit .
• Peter Blomgren ( [email protected] , webpage ) reviews LaTeX theses for the Department of Mathematics and Statistics; the Department of Computer Science; and the Computational Sciences program; thus bypassing the review by Montezuma Publishing
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Senior Thesis Guidelines

A senior thesis can form a valuable part of a student's experience in the  Mathematics Major . It is intended to allow students to cover significant areas of mathematics not covered in course work, or not covered there in sufficient depth. The work should be independent and creative. It can involve the solution of a serious mathematics problem, or it can be an expository work, or variants of these. Both the process of doing independent research and mathematics exposition, as well as the finished written product and optional oral presentation, can have a lasting positive impact on a student's educational and professional future.

Supervision

Supervision by a qualified member of the field of mathematics at Cornell is the normal requirement for a senior thesis. Other arrangements are possible, however, provided they are made with the assistance of the student's major advisor, and with the approval of the Mathematics Major Committee.

Finding a supervisor/Encouraging students.  

It should be emphasized that both the writing and the supervising of a senior thesis are optional activities, both for students and faculty. Students interested in doing this will need to find a suitable supervisor — perhaps with the aid of their major advisor or another faculty member whom they know. Advisors and other faculty who encounter students whom they think would benefit from this activity are invited to mention this option to them and assist them in finding a supervisor.

Standard venues for senior theses . 

One obvious way in which a senior thesis can be produced is through an independent research course (MATH 4900); another way is through an REU experience, either at Cornell or elsewhere. (If the REU work was accomplished or initiated elsewhere, a "local expert" will still be needed to supervise or "vouch for" the work as a senior thesis.) In yet a third way, a student may present a faculty member with a solution or partial solution to an interesting problem. In such cases, this could form the core of a senior thesis. Faculty are invited to encourage such work from their students.

Public Lecture

A public lecture in which the results of the senior thesis are presented is welcome but optional. This should be arranged by the thesis supervisor in conjunction with the undergraduate coordinator and adequately advertised. Department faculty and graduate students are encouraged to attend these presentations.

Submission Deadlines

The supervisor must approve the student's thesis. The student will submit a completed first draft of the thesis to the thesis supervisor. If the supervisor asks the student to make changes, the student will have two weeks to do so and submit a PDF copy of the thesis in final form. The thesis will be posted on the department's web site.

For students graduating in December 2024 , the deadline for the first draft is Friday, November 22 and the final submission is due to the thesis supervisor and the undergraduate coordinator on Friday, December 6.

For students graduating in May 2025 , the deadline for the first draft is Friday, April 18 and the final submission is due to the thesis supervisor and the undergraduate coordinator on Friday, May 2.

Format of the Thesis

Ideally, the final document should be TeXed or prepared in some equivalent technical document preparation system. The document must have large left margins (one and one-half inches or slightly larger). The title page should contain:

The student's name and graduating class.

The title of the senior thesis.

The name of the faculty supervisor. (If there is more than one supervisor, list both. If one of the supervisors is not in the Mathematics Department, list the department and institution.)

The date of completion of the thesis.

This information will be used to produce a standard frontispiece page, which will be added to the document in its library copies.

Judgment as to the merit of a senior thesis will be based largely on the recommendation of the faculty member supervising the thesis. The Mathematics Major Committee will use this recommendation both in its determination of honors and in its decision on whether to place the thesis in our permanent library collection.

The senior thesis will automatically be considered by the Mathematics Major Committee as one of the ingredients for deciding on an  honors  designation for the student. Students may receive honors without a thesis and are not guaranteed honors with one. However, an excellent senior thesis combined with an otherwise excellent record can elevate the level of honors awarded.

Library Collection

Meritorious senior theses will be catalogued, bound, and stored in the Mathematics Library.

BYU ScholarsArchive

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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This collection of MIT Theses in DSpace contains selected theses and dissertations from all MIT departments. Please note that this is NOT a complete collection of MIT theses. To search all MIT theses, use MIT Libraries' catalog .

MIT's DSpace contains more than 58,000 theses completed at MIT dating as far back as the mid 1800's. Theses in this collection have been scanned by the MIT Libraries or submitted in electronic format by thesis authors. Since 2004 all new Masters and Ph.D. theses are scanned and added to this collection after degrees are awarded.

MIT Theses are openly available to all readers. Please share how this access affects or benefits you. Your story matters.

If you have questions about MIT theses in DSpace, [email protected] . See also Access & Availability Questions or About MIT Theses in DSpace .

If you are a recent MIT graduate, your thesis will be added to DSpace within 3-6 months after your graduation date. Please email [email protected] with any questions.

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MIT Theses may be protected by copyright. Please refer to the MIT Libraries Permissions Policy for permission information. Note that the copyright holder for most MIT theses is identified on the title page of the thesis.

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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

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An Equivariant Count of Nodal Orbits in an Invariant Pencil of Conics , Candace Bethea

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Rationality Questions and the Derived Category , Alicia Lamarche

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Variable-Order Fractional Partial Differential Equations: Analysis, Approximation and Inverse Problem , Xiangcheng Zheng

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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

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Is it common for an undergraduate thesis in pure mathematics to prove something new?

What do undergraduate students in mathematics do for their thesis, if they have done one, besides expository or applied math?

I was thinking that the kind of research they do is something applied, say using math in social sciences or a problem in one of the less rigorous natural sciences, or discussing such a problem (that's what expository is, right?).

To me it seems something non-expository or non-applied is an original contribution to mathematics, something that PhD students do.

I attended some pure math undergraduate thesis presentations. I was quite surprised: Did they prove anything new? Never bothered to ask due to fear of looking stupid. Would it be out of the ordinary to expect an undergraduate proves something new? If they did not prove anything new, what the heck are they talking about?

It seems like if it's not new, they are giving a lecture. If it's new, that seems like a PhD-level accomplishment.

I mean, do math undergraduates frequently prove new things?

• mathematics
• research-undergraduate

• 6 "Anything new" is rather broad. I myself proved "something new" in by bachelors thesis, in the sense that nobody answered that particular question rigorously before. Was it deep? Probably not. Could I have published it? I don't think so. Still, it was new . –  Raphael Commented Jul 30, 2015 at 8:05
• Depending on the country and the quality of the teaching, yes it is possible. If you have a Professor who gives you an actual problem knowing you have been taught the right modules/topics to investigate it, yes. If you have little teaching and then are told to pick a topic (as it happens in some places) then the chance is significantly lower. –  DetlevCM Commented Jul 30, 2015 at 12:03
• 1 @DetlevCM I'm guessing there may be 1 for every dozens or hundreds. I was actually wondering about the average batch of undergrad math majors whose thesis is in pure math. My guess is in the first place not many math majors will do pure math in their thesis. So what about those who do? They actually try to prove something? What happens if they cannot prove that particular conjecture in a month after they come up with the proposal after a month? 2 months left in the semester. So what happens? –  BCLC Commented Jul 30, 2015 at 16:09
• 1 @JackBauer Yes, that Enigma - I only covered the rotors and left out the switchboard but the switchboard is the trivial part. Heck, I suspect I could write an implementation fairly easily nowadays having gotten better at programming since. (Side note, its not cracking Enigma, its encoding and decoding which is really trivial.) –  DetlevCM Commented Jul 30, 2015 at 17:05
• 1 @JackBauer Something like that. Some researchers claimed a property of the things they worked with; it was crucial for their method to work, but they did not provide a proof. (I don't know if they could have.) I filled that gap. My advisor found it, and I had the luck that it was a reasonably scoped task that took mostly undergrad stuff plus some tinkering. (I think he (and I) hoped I'd happen upon a case where they were wrong, but they weren't.) –  Raphael Commented Jul 30, 2015 at 21:28

5 Answers 5

I'm going to disagree with Oswald. In my experience, undergraduate students do not often prove new things in pure math. I wouldn't even say master's theses often contain new results. There are a few main reasons for this.

Firstly, pure mathematics operates at a level that is not very accessible for most undergraduates, even those doing research. Undergraduates doing research are often well out of their depth and holding on for dear life. This can mostly be attributed to just not having enough time to get up to speed with what is considered modern mathematics. Most courses in mathematics at the undergraduate level are about math from 50-100 years ago (if not older).

Secondly, undergraduates do not often have the mathematical experience to know what the right plan of attack is when faced with an abstract and new problem and they may not know how to check their work thoroughly to make sure there are no major oversights or blunders. A lot of mathematics involves lateral thinking and it takes a lot of time to build those connections. The hardest part of a pure math PhD (in my opinion) is learning how to attack a problem no one has considered before. Standard techniques that others used may not be useful at all to you for one reason or another. An undergraduate won't have the creativity to navigate this kind of issue because the kind of creativity that is needed comes with a lot of experience. Even when an undergraduate student thinks they've proved something, the nuances of their argument likely will not be apparent to them. (This is especially true when it comes to functional analytic/measure theoretic arguments - the devil is in the details.) Thus a proposed proof may not even be close to being right.

Lastly, not many undergraduates in pure math do research because the gap they have to overcome between coursework and modern mathematics is pretty substantial. Those that make contributions in pure math are those that are very, very talented and have very thorough backgrounds (backgrounds that rival master's/PhD students).

Undergraduates in pure math are not expected to make contributions. That is not what research is about for them. Introducing an undergraduate to research serves a couple of different purposes: it introduces them to more advanced topics and it gives them a taste of what research is like so that they can make an informed decision about whether or not graduate school is right for them. As such, the theses are more like surveys of a specialized topic in mathematics. There is a lot of independent learning involved and there may be some unique examples, insights, and connections contained therein. They may not be presenting "original" work, but poster sessions are there to present what they've learned regardless of whether or not it was original. So yes, it is kind of like a lecture. They are undergraduates and far from being experts in their field.

Note that I am not saying that no undergraduate ever produces new results in pure math (there are some high school students that are better than most PhDs), but it is not a common occurrence and is not expected or considered the norm.

• 27 Bingo. Exactly. Further, I think it is bad to promote the mythology that "undergrads can do meaningful research in mathematics" if only because it sets of unrealistic expectations, so that "everyone fails". That is, it does not help anyone to "assure" them that "they can do research while undergraduates", because most likely they will not, and this is not failure. And so on. For that matter, many graduate students misunderstand the degree of "originality/creativity" that will actually play a role in their thesis, since the bulk of the work is assimilation of known techniques... –  paul garrett Commented Jul 29, 2015 at 21:09
• 8 I think a large part of the difference here is subfield. It is very rare for an undergraduate to make a substantial contribution anywhere, or any contribution to a subfield requiring a large amount of background. On the other hand, it's not so unusual for undergraduates to be able to prove new results in many areas of combinatorics, even if these results are unlikely to be interesting to anyone except other undergraduates working on follow-up projects. –  Alexander Woo Commented Jul 29, 2015 at 22:15
• 2 I fully agree with @AlexanderWoo (and, perhaps counter-intuitively, Cameron's Answer): I think undergrads can definitely do bona fide research, in combinatorics if nowhere else. But, it is probably is likely that most undergrads don't do original research. –  pjs36 Commented Jul 29, 2015 at 22:24
• 8 @Alexander Woo - I think it is important to distinguish between undergraduates working alone (who are indeed unlikely to produce much publishable work) versus undergraduates working in collaborations with faculty. For example, the well-known Duluth REU run by Gallian states they have over 200 published papers, in professional journals. These papers seem to be no more likely to be "uninteresting to anyone" than all the other papers in those journals :) See d.umn.edu/~jgallian/progbib.html –  Oswald Veblen Commented Jul 29, 2015 at 22:31
• 3 @JackBauer - see the link that OswaldVeblen provided. All those papers were written by undergrads. Personally I coauthored an REU paper as an undergraduate, and my undergraduate thesis also had original results in graph theory, but I went into computer programming for a couple years and didn't publish before those results ended up (completely independently) as part of someone else's PhD dissertation. If you want details, e-mail me; I'm using my real name and can be easily found by Google. –  Alexander Woo Commented Jul 30, 2015 at 22:49

The answers so far contain a yes and a no, so let me add a yes-and-no.

Undergraduates can - and often do - prove new things, but hardly ever anything of importance. It is up to the advisor to find an interesting question which is simple enough to serve as the topic of a thesis, but not yet dealt with in the literature. Different from a Ph.D., a bachelor or master thesis is heavily constrained in time, so as an advisor you should only give a topic if you are pretty certain that something can be done by an unexperienced researcher in short time. On the other hand just repeating the literature is boring for the student. One way to find good topics is to look at what is often referred to as folklore: Every textbook contains the theorem that X implies Y, and every expert knows that quasi-X already suffices, but noone bothered to write it up. This will most probably not be worth a publication, but proving a theorem not yet contained in the literature is motivating. Another simple method is looking at all the things you excluded from your own papers. If you worked out an example, but did not include it in a publication, you can let the student generalize it.

What you should not do is ask a student a problem you are really interested in. First the student will be frustrated, because the problem is too hard for him, then you will be frustrated, because you will spend much more time explaining things to him then you would need to find the results for yourself, and finally everyone is frustrated, because you find an answer and have to explain it to the student.

• 3 "Every textbook contains the theorem that X implies Y, and every expert knows that quasi-X already suffices, but noone bothered to write it up." Are there a lot of things like that just lying around? For example? –  BCLC Commented Jul 30, 2015 at 16:03
• 1 If someone proves a result, which only serves as a tool, the conditions are quite often too restrictive. For example, Hilbert space is used where reflexive Banach space suffices, or compact can often be replaced by countably compact. In number theory you can look at older paper using exponential sums, and see what improvements for the latter yield in the application. –  Jan-Christoph Schlage-Puchta Commented Jul 31, 2015 at 16:59
• Jan-Christoph Schlage-Puchta, "the conditions are quite often too restrictive", do you mean it wouldn't be of interest to many mathematicians anyway? –  BCLC Commented Aug 5, 2015 at 12:04
• 3 When talking about topics for a Bachelor or Master thesis, I think about problems which are open in the sense that they are not published, but solved in the sense that every expert in the area could immediately write down a proof. So I don't think these questions are interesting to other people. –  Jan-Christoph Schlage-Puchta Commented Aug 10, 2015 at 7:51
• 1 @JackBauer Most of the work is in figuring out what these things are. If I had an example which I knew well enough to cite it here, probably somebody would have proved it. –  Ben Webster Commented Aug 11, 2015 at 17:17

Yes, undergraduates frequently prove new things, in the sense that every year there are new, publishable results proved by undergraduates. So, although a relatively small number of undergraduate math students participate in true "research", there are certainly students who are able to make nontrivial discoveries as undergraduates, and more than one might initially think. I have been at prestigious research schools and at anti-prestigious regional universites in the U.S.A. At every school I have been, there were undergraduates in mathematics with the aptitude for publishable research. The talent needed may not be "common", but it is certainly not "rare". The obstacles are primarily cultural, not intellectual.

The topic of undergraduate research has also been the subject of a question on MathOverflow , which makes for good reading.

For an example from personal experience: I recently published a peer-reviewed paper in what I consider to be a high-quality journal (and which is not in any way a "student" journal), with an undergraduate student co-author, who discovered the proof of one of the main theorems on his own between two of our research meetings.

Another example is the journal Involve , which is devoted to genuine student research. From their self-description :

Involve showcases and encourages high-quality mathematical research involving students from all academic levels. The editorial board consists of mathematical scientists committed to nurturing student participation in research. Submissions in all mathematical areas are encouraged. All manuscripts accepted for publication in Involve are considered publishable in quality journals in their respective fields, and include a minimum of one-third student authorship. Submissions should include substantial faculty input; faculty co-authorship is strongly encouraged. In most cases, the submission (and accompanying cover letter) should come from a faculty member. Involve, bridging the gap between the extremes of purely undergraduate-research journals and mainstream research journals, provides a venue to mathematicians wishing to encourage the creative involvement of students.

One thing that undergraduates are unlikely to have is the breadth of knowledge that is expected for PhD recipients. Particularly in mathematics, PhD students are examined in a range of subjects, and are expected to have mastered large parts of the undergraduate curriculum. Undergraduate research often involves learning enough about one particular area to prove new theorems. The student still needs to spend time learning other areas to have the knowledge expected of a PhD.

The real key for undergraduates who are looking to do publishable research is to find a collaboration with a good faculty mentor. Independent research by undergraduates is indeed quite rare (in fact, the majority of mathematics papers currently published have two or more authors - even experts benefit from collaboration). The MathOverflow thread linked above has more advice from other mathematicians.

• 1 Thanks Oswald. Your example is kind of strange. WOuld your undergraduate co-author even have the opportunity to do such if not for knowing you? –  BCLC Commented Jul 29, 2015 at 18:41
• 1 Perhaps I should have said: I heard a PhD is like an original contribution or something. Doesn't proving something new kind of amount to an original contribution? Again, I understand this may seem stupid. –  BCLC Commented Jul 29, 2015 at 18:42
• 5 I wouldn't say undergraduates frequently prove new things, especially not in pure math. A small number of math undergraduates do serious research and even fewer make major contributions to the work. Most undergraduates hardly have the mathematical chops and insight to make major contributions simply due to lack of enough exposure. –  Cameron Williams Commented Jul 29, 2015 at 19:06
• 2 I respectfully disagree. I'm saying that you're way over-inflating how successful undergraduate students are and my guess is that it's because you've worked with some very successful ones. My point is that on average, so very few that actually do research make contributions. Hell, successful PhD students maybe end up with only one or two papers by the time they're finished. –  Cameron Williams Commented Jul 29, 2015 at 19:47
• 5 So far, I've worked with three (sets of) students at a non-selective school, resulting in three peer-reviewed papers that, in their journals, are indistinguishable from any other research. The students all met the usual standards for co-authorship. (This record is partially because, as a researcher, I know enough to pick math problems where we are likely to find publishable contributions.) When I was at prestigious research schools, I saw even more math majors who would have been able to work on publishable research as undergrads. As I wrote, the issue is much more culture than aptitude. –  Oswald Veblen Commented Jul 29, 2015 at 21:51

I can tell you my experience as I am currently writing an undergraduate thesis (though as a summer project).

I am an undergraduate student in mathematics currently doing a summer « introduction to research » internship. I'm studying probability theory.

As a first year student, about half of my time was spent solidifying my mathematical background in probability, measure theory and analysis. I also spent quite a lot of time studying specialised articles, and finally I applied the general theory I studied to a specific problem, where I did prove something « new », while very closely following other published results. On the way there, I also proved a few lemmas, that, while not of general interest, are « new » and interesting to me.

Clearly, undergraduate students are not expected to find groundbreaking results of general interest. However, they can contribute to mathematics by summarising and gathering related results from multiple articles, applying new theories, finding examples, etc.

A word of advice.

You should not aim for great discoveries, but rather simply try to do your own mathematics. Ask yourself a lot of « stupid » questions and find their answers. That's how you'll end up with a few small new results. Make sure you can grasp the big picture of your field of study, that you look at it from a critical standpoint and that you understand the issues that motivate it.

Do math undergraduates frequently prove new things?

Yes. But not great things, and sometimes things that might already be known to experts (but not widely accessible). I think that it is good enough for an undergrad to prove things that are new to him/her and her classmates/advisor/etc.

Some of the implicit premises of these sorts of questions, or the implicit premises in responses to the question, are really the issue. I would heartily agree that undergrads of all "calibers" should "be in the room" when something resembling "live" mathematics is being discussed. But/and this is most meaningful when we look at the falseness, artificiality, and sterility of the typical undergrad curriculum: it's fake and moribund, with no immediate room for anyone to do anything at all, and no hints about reality, either. Ghastly, yes. But that does not immediately entail a sort of "opposite", that novices need know very little to make meaningful contributions. Raw cleverness has already been exercised, quite systematically, for some hundreds of years (thousands?). People have learned useful things, and to not know these is to not know how to change a tire, or a light bulb, or a furnace filter, or open the door. Not that the usual curriculum helps much, either, I agree! But that does not mean that basic operational skills (involving occasionally subtle mathematics, literally, here) are irrelevant. Getting outside the degenerate "school math" thang is excellent... but thinking that that means "we don't need to know anything!" is obviously silly... even if appealing. "Complicated".

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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

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Theses/Dissertations from 2021 2021

Tukey Morphisms Between Finite Binary Relations , Rhett Barton

A Data Adaptive Model for Retail Sales of Electricity , Johanna Marcelia

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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

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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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Undergraduate Thesis

Math 4999: undergraduate thesis.

Home > Arts and Sciences > Mathematics > MATHEMATICSHONORS

Mathematics Undergraduate Honors Theses

Honors theses from 2024 2024.

Estimating the Payoffs of Variance Swaps using GARCH(1,1) and COGARCH(1,2) , Nicholas Zehnle

Improved Bounds for the Index Conjecture in Zero-Sum Theory , Andrew Pendleton

Honors Theses from 2023 2023

Automorphisms of a Generalized Quadrangle of Order 6 , Ryan Pesak

Demographic Noise and Fragmentation in Stochastic Extinction , Cameron Curtis

Design and Application of Surrogate Models for Hypersonic Inlet Physics , Owen Guch

Examining Factors Using Standard Subspaces and Antiunitary Representations , Paul Anderson

Merging Cross-Platform Gene Expression Data , Jiayi Xu

Minimal Network Structure for Turing Instability , Brendan Millis

Modeling the Effects of Seasonal Births and Predation on Disease Spread , Ally Introne

The Probability Distribution of the Kaplan-Meier Product-Limit Estimator and its Application to Bias and Interval Estimation , Yuxin Qin

Honors Theses from 2022 2022

Approximating Star-Discrepancy with a Genetic Algorithm , Isabel Agostino

Counting Holes in Physical Systems - Applications of Computational Homology to Systems in Physics - , Sage Stanish

Enumerating Switching Isomorphism Classes of Signed Graphs , Nathaniel Healy

Investigating Text Mining Techniques Within the Context of Politicized Social Media Data , Grace Smith

Investigating the Effectiveness of GARCH(1,2) and COGARCH(1,2) Models in Estimating Volatility in the S&P500 Index , Ethan Hackett

Modeling and Analyses of Mechanisms Underlying Network Synaptic Dynamics in Two Neural Circuits , Linda Ma

Modern Theory of Copositive Matrices , Yuqiao Li

Period Doubling Cascades from Data , Alexander Berliner

Schur Class Power Series over the Quaternions , Rongbiao Wang

The Enumeration of Minimum Path Covers of Trees , Merielyn Sher

The Minimum Number of Multiplicity 1 Eigenvalues Among Real Symmetric Matrices Whose Graph is a Tree , Jacob Zimmerman

Voting Rules and Properties , Zhuorong Mao

Honors Theses from 2021 2021

A Survey of Methods to Determine Quantum Symmetry of Graphs , Samantha Phillips

Blockchain in Healthcare: a New Perspective from Social Media Data , Andrew Caietti

Determining Quantum Symmetry in Graphs Using Planar Algebras , Akshata Pisharody

Reality and Strong Reality in Finite Symplectic Groups , Spencer Schrandt

The Minimum Number of Multiplicity 1 Eigenvalues among Real Symmetric Matrices whose Graph is a Tree , Wenxuan Ding

Toward a Holographic Transform for the Quantum Clebsch-Gordan Formula , Ethan Shelburne

Using Machine Learning to Track the Location of the Shock Train in Hypersonic Engines , Alison Reynolds

Honors Theses from 2020 2020

A Mathematical Model for the Trend and Prediction of Movie Revenue , Yuxin Shang

Analysis of Modelling Deficiencies that Contributed to the High Unanticipated Loan Losses Incurred During the Housing Price Collapse of the Great Recession , Jennifer Shulman

Dynamics of Sensory Integration of Olfactory and Mechanical Stimuli Within the Response Patterns of Moth Antennal Lobe Neurons , Harrison Tuckman

Learning & Planning for Self-Driving Ride-Hailing Fleets , Jack Morris

Non-linear Modifications of Black-Scholes Pricing Model with Diminishing Marginal Transaction Cost , Kaidi Wang

Nonnegative Matrix Factorization Problem , Junda An

RMSE-Minimizing Confidence Intervals for the Binomial Parameter , Kexin Feng

Stage-structured Blue Crab Population Model with Fishing, Predation and Cannibalism , Fangming Xu

Honors Theses from 2019 2019

A General Weil-Brezin Map and Some Applications , Benjamin Bechtold

Continuous Opinion Dynamics on an Adaptive Network , Xinyu Zhang

Disentanglement of Whisker Deflection Velocity and Direction , Srijan Bhasin

Eventually Positive Matrices and Tree Sign Patterns , Madellyne Waugh

Minimal Principal Series Representations of SL(3,R) , Jacopo Gliozzi

Partial Difference Sets in Nonabelian Groups and Strongly Regular Cayley Graphs , Gabrielle Tauscheck

Rankin-Cohen Brackets and Fusion Rules for Discrete Series Representations of SL(2,R) , Emilee Cardin

Spectrogram Analysis of Blood Pressure on Neonates with Hypoxic Ischemic Encephalopathy (HIE) , Tianrui Zhu

Totally Positive Completable Matrix Patterns and Expansion , David Allen

Honors Theses from 2018 2018

A Mathematical Study of Competition and Adoption of Two Consumer Products , Chengli Huang

A New Upper Bound for the Diameter of the Cayley Graph of a Symmetric Group , Hangwei Zhuang

Counting Real Conjugacy Classes in Some Finite Classical Groups , Elena Amparo

Implementation and Analysis of the Nonlinear Decomposition Attack on Polycyclic Groups , Yoongbok Lee

Modeling Social Interactions of Yeast Biofilms with a Stochastic Spatial Simulation , Aparajita Sur

Potential Stability of Matrix Sign Patterns , Christopher Hambric

Strongly Real Conjugacy Classes in Unitary Groups over Fields of Even Characteristic , Tanner N. Carawan

The Doubly Stochastic Single Eigenvalue Problem: An Empirical Approach , John Wilkes and Charles Royal Johnson

TP Matrices and TP Completability , Duo Wang

Ultra-High Dimensional Statistical Learning , Yanxin Xu

Honors Theses from 2017 2017

A Mathematical Model of Economic Growth of Two Geographical Regions , Xin Zou

Center Manifold Theory and Computation Using a Forward Backward Approach , Emily E. Schaal

Involutions and Total Orthogonality in Some Finite Classical Groups , Gregory K. Taylor

Saving Babies Using Big Data , Evan Dienstman

Spatial Analysis with Applications on Real Estate Market Price Prediction , Yujing Zheng

TP and TN Completability of Border Patterns , Haoge Chang

Honors Theses from 2016 2016

Computing All Isolated Invariant Sets at a Finite Resolution , Martin Salgado-Flores

Graph packing with constraints on edges , Fangyi Xu

Growing Networks with Positive and Negative Links , Corynne Smith Dech

Normal Matrices Subordinate to a Graph , Morrison Turnansky

Relaxed Coloring of Sparse Graphs , Michael C. Kopreski

Row and Column Distributions of Letter Matrices , Xiaonan Hu

(Un)Stable Manifold Computation via Iterative Forward-Backward Runge-Kutta Type Methods , Dmitriy Zhigunov

Honors Theses from 2015 2015

On the Non-Symmetric Spectra of Certain Graphs , Owen Hill

Relaxation of Planar Graphs With d∆≥2 and No 4-Cycles , Heather A. Hoskins

Honors Theses from 2014 2014

Basins of Attraction for Pulse-Coupled Oscillators , Ryan Gryder

Combinatorially Derived Properties of Young Tableaux , James R. Janopaul-Naylor

Linear and Nonlinear Trees: Multiplicity Lists of Symmetric Matrices , Eric Wityk

Local Zeta Functions over p-Adic Fields , Stephen P. Cameron

Nonlinear Models of Zooplankton Communities , Catherine King

Honors Theses from 2013 2013

A Population Density Model of Domain Calcium-Mediated Inactivation of L-Type Ca Channels , Kiah Hardcastle

Finding Open Locating Dominating Sets on Infinite and Finite Graphs , Allison Oldham

On Almost Normal Matrices , Tyler J. Moran

Statistical Inference Based on Upper Record Values , Daniel J. Luckett

Honors Theses from 2012 2012

A Model for Blue Crab Population in the Chesapeake Bay , Timothy J. Becker

Analysis and Simulation of an Optimal Control Model of an Oyster Population Displaying an Allee Effect , Timothy Raymond McDade

Circadian Oscillations of the Intestinal Stem Cell Lineage , Brian Waldman

Finding the Minimum Randic Index , Sarah Joyce Kunkler

Fixed Points of Pick and Stieltjes functions: A Linear Algebraic Approach , Nicholas Andrew Woods

Global Dynamics of Pulse-Coupled Oscillators , Allison Leslie Corish

Perfect Partitions of Some (0,1)-Matrices , Jeffrey Soosiah

Permutations with Extremal Routings on Cycles , Luis Alejandro Valentin

Strongly Real Conjugacy Classes of the Finite Unitary Group , Zach Gates

Synchronous Oscillatory Solutions in a Two Patch Predator-Prey Model , Matthew H. Becker

The Laplacian on Isotropic Quantum Graphs: Solutions and Applications , Patrick King

Honors Theses from 2011 2011

A New Lower Bound on the Minimum Density of Vertex Identifying Codes for the Infinite Hexagonal Grid , Ariel J. Cukierman

Basins of Attraction in Stage Structured Populations , Georgia Waite Pfeiffer

Critical Exponents: Old and New , Olivia J. Walch

Factoring Banded Permutations and Bounds on the Density of Vertex Identifying Codes on the Infinite Snub Hexagonal Grid , Chase A. Albert

Persistent Activity in Assortative Networks of Integrate and Fire Neurons , Matthew D. Peppe

Poles and Zeros of Generalized Carathéodory Class Functions , Yael Gilboa

Solution Theory for Systems of Bilinear Equations , Dian Yang

Topological Characterization of Extinction in a Coupled Ricker Patch Model , Benjamin Robert Holman

Honors Theses from 2010 2010

Bistability in Differential Equation Model of Oyster Population and Sediment Volume , William Crowell Jordan-Cooley

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Bachelor thesis in mathematics

The department of mathematics supervises bachelor theses in pure and applied mathematics. Information for students can be found in the Swedish version .

Bachelor theses

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Apply for standard admission to Kelley

Students who enroll in IU Bloomington by Spring 2025 or earlier apply for standard admission to the Kelley School based on the following criteria.

For an application to be eligible for review, students must complete:

• Application for admission to Kelley in the second semester (defined as fall/spring) of enrollment on the IU Bloomington campus, applications submitted after 2 semesters will not be considered*. 
• A minimum of 30 credit hours of college coursework by the time the application is reviewed. Credits may include any college-level coursework on the transcript, such as SLST coursework, AP credit, IB credit, test credit, dual enrollment coursework, and ACP coursework. 
• Full-time enrollment at IUB (minimum of 12 credit hours) in the application semester. 
• Integrated Core prerequisite courses (14.5 hours in total, may include coursework transferred in – utilize Credit Transfer Service and IU Intercampus Transfer to learn more on how your coursework may transfer in.): 
• BUS-A100 Basic Accounting (1 credit)  
• BUS-C104/106 Business Presentations (3 credits) 
• BUS-K201/204 The Computer in Business (3 credits)  
• BUS-T175 Compass 1 (1.5 credits) 
• ENG-W131** English Composition (3 credits)  
• ECON-B251 Fundamentals of Economics for Business I (3 credits)

*Students who officially declared a major outside business, took courses in pursuit of that major for a full semester or more and later determined they plan to apply to Kelley may be considered for an application beyond their second semester on the IU Bloomington campus

Is math required for admission to Kelley?

No, completion of a math course is not required to be eligible for Kelley standard admission.

While math is not required as part of the standard admission process, it is required for completion of a Kelley degree.

• Students who entered IU Summer/Fall 2023 or Spring 2024 must complete both MATH-M 118 and MATH-M 119 (or approved equivalents) for the degree.
• Students who entered IU Summer/Fall 2024 or Spring 2025 must complete one   of the following: MATH-B 110: Mathematics of Business and Public Affairs (new course) or MATH-M 118 or MATH-M 119 for the degree.

If a student chooses to complete their required math course during the first year, the course(s) will be considered as a part of the admissions review.

If a student chooses to complete MATH-M 118 and/or MATH-M 119 at another college or university, they should use the  IU Credit Transfer Service  to find a transferable course(s) and view  transfer credit policies  and processes. The course(s) will not be a part of the admissions review.

Students should follow the  ALEKS math placement  guidelines, in consultation with their academic advisor, and take the course(s) as directed by the placement exam. Additionally, in this conversation students can determine when to complete the course knowing it will need to be successfully completed no later than the first semester of the second year, as math modeling is a prerequisite to ECON-E 370/STAT-S 301, which must be successfully completed prior to I-Core.

Approved equivalent courses for both  MATH-M 118 AND MATH-M 119 are acceptable for satisfying degree requirements

• Approved MATH equivalents for students who started during this timeframe can be found on the I-Core prereqs page of the 2023-24 Kelley academic bulletin .
• Approved MATH equivalents for students who started during this timeframe can be found on the I-Core prereqs page of the 2024-25 Kelley academic bulletin .

First Semester Academic Record Review:

Students who have either of the following on their academic record at the end of their first semester at IU Bloomington will be ineligible to pursue standard admission to the Kelley School of Business and will be dropped from all Kelley School of Business admissions courses before the start of the next semester. * Students should work with their AMES advisor to select new courses in their alternative major.

Three (3) or more of the following:

• Any letter grade below a B (B-, C+, C, C-)
• Withdrawal (W)
• Incomplete (I)
• X grade (X)
• Any grade of D+, D, D-, or F

*Students will be dropped from BUS-A 100, BUS-C 104/106, BUS-K 201/204, BUS-T 175, and ECON-B 251. Students will not be dropped from ENG-W 131 or equivalent course.

How are pre-Business students admitted to Kelley?

Automatic admission.

Students whose records indicate grades of Bs or better in every IU Bloomington course on the first attempt will be automatically admitted.

Comprehensive Review

Students whose records indicate any of the following will have their applications comprehensively reviewed by the Kelley Undergraduate Admissions committee. The admissions committee reviews grades in  all IU Bloomington courses, not just business courses. A student with any of the following risk factors is in jeopardy of their standard admission application being denied.

• One or more grades below a B (B-, C+, C, C-, D+, D-, or F) in an IU Bloomington course.
• Withdrawals (W’s), X’s ( X grade replacement policy), or unresolved incompletes (I’s) 

Students whose applications will undergo a comprehensive review should meet with their AMES academic advisor to ensure they are creating a plan and enrolling in courses for their alternative major in case they are not admitted to Kelley.

Students whose records indicate two unsuccessful attempts to complete a single I-Core prerequisite, including grades below a C, withdrawals (W’s), incompletes (I’s), and X grades, will  have their applications automatically denied.

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