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Main areas of research activity are algebra, including group theory, semigroup theory, lattice theory, and computational group theory, and analysis, including fractal geometry, multifractal analysis, complex dynamical systems, Kleinian groups, and diophantine approximations.

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Groups defined by language theoretic classes , rearrangement groups of connected spaces , modern computational methods for finitely presented monoids , finiteness conditions on semigroups relating to their actions and one-sided congruences , on constructing topology from algebra .

Senior Thesis

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

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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• Senior Theses

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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Home > USC Columbia > Arts and Sciences > Mathematics > Mathematics Theses and Dissertations

Mathematics Theses and Dissertations

Theses/dissertations from 2023 2023.

Extreme Covering Systems, Primes Plus Squarefrees, and Lattice Points Close to a Helix , Jack Robert Dalton

On the Algebraic and Geometric Multiplicity of Zero as a Hypergraph Eigenvalue , Grant Ian Fickes

Deep Learning for Studying Materials Stability and Solving Thermodynamically Consistent PDES With Dynamic Boundary Conditions in Arbitrary Domains , Chunyan Li

Widely Digitally Delicate Brier Primes and Irreducibility Results for Some Classes of Polynomials , Thomas David Luckner

Deep Learning Methods for Some Problems in Scientific Computing , Yuankai Teng

Theses/Dissertations from 2022 2022

Covering Systems and the Minimum Modulus Problem , Maria Claire Cummings

The Existence and Quantum Approximation of Optimal Pure State Ensembles , Ryan Thomas McGaha

Structure Preserving Reduced-Order Models of Hamiltonian Systems , Megan Alice McKay

Tangled up in Tanglegrams , Drew Joseph Scalzo

Results on Select Combinatorial Problems With an Extremal Nature , Stephen Smith

Poset Ramsey Numbers for Boolean Lattices , Joshua Cain Thompson

Some Properties and Applications of Spaces of Modular Forms With ETA-Multiplier , Cuyler Daniel Warnock

Theses/Dissertations from 2021 2021

Simulation of Pituitary Organogenesis in Two Dimensions , Chace E. Covington

Polynomials, Primes and the PTE Problem , Joseph C. Foster

Widely Digitally Stable Numbers and Irreducibility Criteria For Polynomials With Prime Values , Jacob Juillerat

A Numerical Investigation of Fractional Models for Viscoelastic Materials With Applications on Concrete Subjected to Extreme Temperatures , Murray Macnamara

Trimming Complexes , Keller VandeBogert

Multiple Frailty Model for Spatially Correlated Interval-Censored , Wanfang Zhang

Theses/Dissertations from 2020 2020

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

Finite Axiomatisability in Nilpotent Varieties , Joshua Thomas Grice

Rationality Questions and the Derived Category , Alicia Lamarche

Counting Number Fields by Discriminant , Harsh Mehta

Distance Related Graph Invariants in Triangulations and Quadrangulations of the Sphere , Trevor Vincent Olsen

Diameter of 3-Colorable Graphs and Some Remarks on the Midrange Crossing Constant , Inne Singgih

Two Inquiries Related to the Digits of Prime Numbers , Jeremiah T. Southwick

Windows and Generalized Drinfeld Kernels , Robert R. Vandermolen

Connections Between Extremal Combinatorics, Probabilistic Methods, Ricci Curvature of Graphs, and Linear Algebra , Zhiyu Wang

An Ensemble-Based Projection Method and Its Numerical Investigation , Shuai Yuan

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

Theses/Dissertations from 2019 2019

Classification of Non-Singular Cubic Surfaces up to e-invariants , Mohammed Alabbood

On the Characteristic Polynomial of a Hypergraph , Gregory J. Clark

A Development of Transfer Entropy in Continuous-Time , Christopher David Edgar

Moving Off Collections and Their Applications, in Particular to Function Spaces , Aaron Fowlkes

Finding Resolutions of Mononomial Ideals , Hannah Melissa Kimbrell

Regression for Pooled Testing Data with Biomedical Applications , Juexin Lin

Numerical Methods for a Class of Reaction-Diffusion Equations With Free Boundaries , Shuang Liu

An Implementation of the Kapustin-Li Formula , Jessica Otis

A Nonlinear Parallel Model for Reversible Polymer Solutions in Steady and Oscillating Shear Flow , Erik Tracey Palmer

A Few Problems on the Steiner Distance and Crossing Number of Graphs , Josiah Reiswig

Successful Pressing Sequences in Simple Pseudo-Graphs , Hays Wimsatt Whitlatch

On The Generators of Quantum Dynamical Semigroups , Alexander Wiedemann

An Examination of Kinetic Monte Carlo Methods with Application to a Model of Epitaxial Growth , Dylana Ashton Wilhelm

Dynamical Entropy of Quantum Random Walks , Duncan Wright

Unconditionally Energy Stable Linear Schemes for a Two-Phase Diffuse Interface Model with Peng-Robinson Equation of State , Chenfei Zhang

Theses/Dissertations from 2018 2018

Theory, Computation, and Modeling of Cancerous Systems , Sameed Ahmed

Turán Problems and Spectral Theory on Hypergraphs and Tensors , Shuliang Bai

Quick Trips: On the Oriented Diameter of Graphs , Garner Paul Cochran

Geometry of Derived Categories on Noncommutative Projective Schemes , Blake Alexander Farman

A Quest for Positive Definite Matrices over Finite Fields , Erin Patricia Hanna

Comparison of the Performance of Simple Linear Regression and Quantile Regression with Non-Normal Data: A Simulation Study , Marjorie Howard

Special Fiber Rings of Certain Height Four Gorenstein Ideals , Jaree Hudson

Graph Homomorphisms and Vector Colorings , Michael Robert Levet

Local Rings and Golod Homomorphisms , Thomas Schnibben

States and the Numerical Range in the Regular Algebra , James Patrick Sweeney

Thermodynamically Consistent Hydrodynamic Phase Field Models and Numerical Approximation for Multi-Component Compressible Viscous Fluid Mixtures , Xueping Zhao

Theses/Dissertations from 2017 2017

On the Existence of Non-Free Totally Reflexive Modules , J. Cameron Atkins

Subdivision of Measures of Squares , Dylan Bates

Unconditionally Energy Stable Numerical Schemes for Hydrodynamics Coupled Fluids Systems , Alexander Yuryevich Brylev

Convergence and Rate of Convergence of Approximate Greedy-Type Algorithms , Anton Dereventsov

Covering Subsets of the Integers and a Result on Digits of Fibonacci Numbers , Wilson Andrew Harvey

Nonequispaced Fast Fourier Transform , David Hughey

Deep Learning: An Exposition , Ryan Kingery

A Family of Simple Codimension Two Singularities with Infinite Cohen-Macaulay Representation Type , Tyler Lewis

Polynomials Of Small Mahler Measure With no Newman Multiples , Spencer Victoria Saunders

Theses/Dissertations from 2016 2016

On Crown-free Set Families, Diffusion State Difference, and Non-uniform Hypergraphs , Edward Lawrence Boehnlein

Structure of the Stable Marriage and Stable Roommate Problems and Applications , Joe Hidakatsu

Binary Quartic Forms over Fp , Daniel Thomas Kamenetsky

On a Constant Associated with the Prouhet-Tarry-Escott Problem , Maria E. Markovich

Some Extremal And Structural Problems In Graph Theory , Taylor Mitchell Short

Chebyshev Inversion of the Radon Transform , Jared Cameron Szi

Modeling of Structural Relaxation By A Variable-Order Fractional Differential Equation , Su Yang

Theses/Dissertations from 2015 2015

Modeling, Simulation, and Applications of Fractional Partial Differential Equations , Wilson Cheung

The Packing Chromatic Number of Random d-regular Graphs , Ann Wells Clifton

Commutator Studies in Pursuit of Finite Basis Results , Nathan E. Faulkner

Avoiding Doubled Words in Strings of Symbols , Michael Lane

A Survey of the Kinetic Monte Carlo Algorithm as Applied to a Multicellular System , Michael Richard Laughlin

Toward the Combinatorial Limit Theory of free Words , Danny Rorabaugh

Trees, Partitions, and Other Combinatorial Structures , Heather Christina Smith

Fast Methods for Variable-Coefficient Peridynamic and Non-Local Diffusion Models , Che Wang

Modeling and Computations of Cellular Dynamics Using Complex-fluid Models , Jia Zhao

Theses/Dissertations from 2014 2014

The Non-Existence of a Covering System with all Moduli Distinct, Large and Square-Free , Melissa Kate Bechard

Explorations in Elementary and Analytic Number Theory , Scott Michael Dunn

Independence Polynomials , Gregory Matthew Ferrin

Turán Problems on Non-uniform Hypergraphs , Jeremy Travis Johnston

On the Group of Transvections of ADE-Diagrams , Marvin Jones

Fake Real Quadratic Orders , Richard Michael Oh

Theses/Dissertations from 2013 2013

Shimura Images of A Family of Half-Integral Weight Modular Forms , Kenneth Allan Brown

Sharp Bounds Associated With An Irreducibility Theorem For Polynomials Having Non-Negative Coefficients , Morgan Cole

Deducing Vertex Weights From Empirical Occupation Times , David Collins

Analysis and Processing of Irregularly Distributed Point Clouds , Kamala Hunt Diefenthaler

Generalizations of Sperner's Theorem: Packing Posets, Families Forbidding Posets, and Supersaturation , Andrew Philip Dove

Spectral Analysis of Randomly Generated Networks With Prescribed Degree Sequences , Clifford Davis Gaddy

Selected Research In Covering Systems of the Integers and the Factorization of Polynomials , Joshua Harrington

The Weierstrass Approximation Theorem , LaRita Barnwell Hipp

The Compact Implicit Integration Factor Scheme For the Solution of Allen-Cahn Equations , Meshack K. Kiplagat

Applications of the Lopsided Lovász Local Lemma Regarding Hypergraphs , Austin Tyler Mohr

Study On Covolume-Upwind Finite Volume Approximations For Linear Parabolic Partial Differential Equations , Rosalia Tatano

Coloring Pythagorean Triples and a Problem Concerning Cyclotomic Polynomials , Daniel White

Theses/Dissertations from 2012 2012

A Computational Approach to the Quillen-Suslin Theorem, Buchsbaum-Eisenbud Matrices, and Generic Hilbert-Burch Matrices , Jonathan Brett Barwick

Mathematical Modeling and Computational Studies for Cell Signaling , Kanadpriya Basu

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Department of Mathematics

The honors program is a two-semester sequence (Math 99a, "Senior Research" in fall, followed by Math 99b, "Senior Research" in spring) during which senior mathematics majors carry out independent research and the  writing and oral presentation of a senior thesis. Only students who major in the BS in Mathematics or BS in Applied Math may choose the option of writing a thesis in order to be considered for Honors, High Honors or Highest Honors in mathematics. View university resources for undergraduate research support here .

Rules for Senior Honors Thesis

•  A committee of two faculty members, one of whom will be the official instructor, will supervise the work.
• A written thesis proposal must be prepared at the beginning of the first semester, and be approved and signed by both the committee and the Undergraduate Advising Head (UAH), prior to registration for the course. In order to register for the course, the student must requests to take the course in Work Day (see "Request Prerequisite or Permission to Enroll" section under Planning and Registration) .
• A mid-year evaluation must be done by the committee by the end of the first semester, and a written report submitted to the UAH. Students judged to have made insufficient progress will not be permitted to continue in the second semester.
• A thesis in a department-approved format must be submitted to the committee by the last day of classes in the second semester or by a deadline set by the committee members. At a minimum, the thesis must have a title page , a signature page , and an abstract, description of the work performed and the conclusions reached, and references. Students are encouraged to learn the Latex typesetting system ( this repository holds a LaTeX file that serves as a template for senior honors theses in the Brandeis University Department of Mathematics, developed by Chami Lamelas, '22).  We also encourage you to submit your thesis electronically to the library using the following link: Submitting your Thesis to the Library
• The student must defend their thesis in a public oral examination of at least 30 minutes duration by the end of the second semester exam period. The talk should take place in the Math Department and should be accessible to junior math majors. A list of thesis defense talks will be published on the website.
• Written evaluations of the thesis and of the defense must be submitted by the committee to the UAH by the Friday preceding the department degree meeting.
• The level of distinction will be determined by the UAH from evaluation of both the thesis and the student’s academic record.
• Students wishing to graduate in seven semesters must start their thesis research in the spring semester of their junior year, and follow the same rules moved forward one semester.
• The required forms for items (2), (3), and (6) are available on the department website.
• Supervisors outside of the Math Department are acceptable, either in other Brandeis departments or outside of the university. All the rules above apply, including the deadlines. The defense must take place in the Brandeis Math Department. The outside advisor may be an ex officio member of the supervising committee, and advise the committee on the evaluation of the work performed. The grade for Math 99a/b will be determined by the Brandeis instructor of the course. 

Student and Committee Forms for Senior Honors Research

• Student Proposal for Honors Thesis . This form is to be prepared by the student at the beginning of the first semester, and approved and signed by the committee and UAH, prior to registration for the course. You will also need your Instructor to sign an additional form, the  Course Change Form  (see #2) so that you can register.
• In order to register for the course--Course Change Form : This form is to be prepared by the student and signed by both the student and the Instructor. The student then sends the signed form to "[email protected]".

Mid-term Assessment Form . This form is to be prepared by the committee by the end of the first semester, and then submitted by the committee to the UAH.

• Committee Report on Senior Honors Thesis . This form is to be prepared by the committee after the thesis defense and is due to the UAH the Friday before Degree Meetings.

Resources and LATEX Template

View university resources for undergraduate research support.

View funding resources and deadlines for undergraduate research support.

View  how to submit your thesis electronically to Scholar Works. View a template   LaTeX  file that students can choose to use to fill in their information (name, thesis title, advisor etc.),  created by Chami Lamelas '22.

Completed Senior Honors Theses

• Ryan Xie '21: " Mathematically Modeling the Neuron Network Involved in Sleep Regulation " Thesis Advisor: Prof. Jonathan Touboul
• Chami Lamelas, '22  “ Vorticity-Stream Solver for Microfluidic Devices and Applications to Blood Cell Sorters ”   Thesis Advisor: Profs. Thomas Fai and An Huang
• Mathematics Placement

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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Home > A&S > Math > MATH_GRADPROJ

Mathematics Graduate Projects and Theses

Theses/dissertations from 2022 2022.

Relationships Between COVID-19 Infection Rates, Healthcare Access, Socioeconomic Status, and Cultural Diversity , MarGhece P.J. Barnes

The Matrix Sortability Problem , Seth Cleaver

Cognitive Demand of Teacher-Created Mathematics Assessments , Megan Marie Schmidt

Waring Rank and Apolarity of Some Symmetric Polynomials , Max Brian Sullivan

Security Analysis of Lightweight Cryptographic Primitives , William Unger

Regression Analysis of Resilience and COVID-19 in Idaho Counties , Ishrat Zaman

Theses/Dissertations from 2021 2021

Tukey Morphisms Between Finite Binary Relations , Rhett Barton

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

Exploring the Beginnings of Algebraic K-Theory , Sarah Schott

Zariski Geometries and Quantum Mechanics , Milan Zanussi

Theses/Dissertations from 2020 2020

The Directed Forest Complex of Cayley Graphs , Kennedy Courtney

Beliefs About Effective Instructional Practices Among Middle Grades Teachers of Mathematics , Lauren A. Dale

Analytic Solutions for Diffusion on Path Graphs and Its Application to the Modeling of the Evolution of Electrically Indiscernible Conformational States of Lysenin , K. Summer Ware

Theses/Dissertations from 2019 2019

Dynamic Sampling Versions of Popular SPC Charts for Big Data Analysis , Samuel Anyaso-Samuel

Computable Reducibility of Equivalence Relations , Marcello Gianni Krakoff

On the Fundamental Group of Plane Curve Complements , Mitchell Scofield

Radial Basis Function Finite Difference Approximations of the Laplace-Beltrami Operator , Sage Byron Shaw

Formally Verifying Peano Arithmetic , Morgan Sinclaire

Theses/Dissertations from 2018 2018

Selective Strong Screenability , Isaac Joseph Coombs

Mathematics Student Achievement in the Context of Idaho’s Advanced Opportunities Initiative , Nichole K. Hall

Secure MultiParty Protocol for Differentially-Private Data Release , Anthony Harris

Theses/Dissertations from 2017 2017

A Stable Algorithm for Divergence-Free and Curl-Free Radial Basis Functions in the Flat Limit , Kathryn Primrose Drake

The Classification Problem for Models of ZFC , Samuel Dworetzky

Joint Inversion of Compact Operators , James Ford

Trend and Return Level of Extreme Snow Events in New York City , Mintaek Lee

Multi-Rate Runge-Kutta-Chebyshev Time Stepping for Parabolic Equations on Adaptively Refined Meshes , Talin Mirzakhanian

Investigating College Instructors’ Methods of Differentiation and Derivatives in Calculus Classes , Wedad Mubaraki

The Random Graph and Reciprocity Laws , Spencer M. Nelson

Classification of Vertex-Transitive Structures , Stephanie Potter

Theses/Dissertations from 2016 2016

On the Conjugacy Problem for Automorphisms of Trees , Kyle Douglas Beserra

The Density Topology on the Reals with Analogues on Other Spaces , Stuart Nygard

Latin Squares and Their Applications to Cryptography , Nathan O. Schmidt

Solution Techniques and Error Analysis of General Classes of Partial Differential Equations , Wijayasinghe Arachchige Waruni Nisansala Wijayasinghe

Numerical Computing with Functions on the Sphere and Disk , Heather Denise Wilber

Theses/Dissertations from 2015 2015

The Classical Theory of Rearrangements , Monica Josue Agana

Nonlinear Partial Differential Equations, Their Solutions, and Properties , Prasanna Bandara

The Impact of a Quantitative Reasoning Instructional Approach to Linear Equations in Two Variables on Student Achievement and Student Thinking About Linearity , Paul Thomas Belue

Student Understanding of Function and Success in Calculus , Daniel I. Drlik

Monodromy Representation of the Braid Group , Phillip W. Hart

The Frobenius Problem , Anna Marie Megale

Theses/Dissertations from 2014 2014

Pi-1-1-determinacy and Sharps , Shehzad Ahmed

A Radial Basis Function Partition of Unity Method for Transport on the Sphere , Kevin Aiton

Diagrammatically Reducible 2-Complexes , Tyler Allyn

A Stochastic Parameter Regression Model for Long Memory Time Series , Rose Marie Ocker

Theses/Dissertations from 2013 2013

The Assignment Packet Grading System , Sarah Nichole Bruce

Using Learner-Generated Examples to Support Student Understanding of Functions , Martha Ottelia Dinkelman

Computing Curvature and Curvature Normals on Smooth Logically Cartesian Surface Meshes , John Thomas Hutchins

Schur's Theorem and Related Topics in Ramsey Theory , Summer Lynne Kisner

Theses/Dissertations from 2012 2012

On the Geometry of Virtual Knots , Rachel Elizabeth Byrd

A Stochastic Parameter Regression Approach for Time-Varying Relationship between Gold and Silver Prices , Birsen Canan-McGlone

Uncertainty Analysis of RELAP5-3D© , Alexandra E. Gertman and George L. Mesina

A Statistical Method for Regularizing Nonlinear Inverse Problems , Chad Clifton Hammerquist

Perfect Stripes from a General Turing Model in Different Geometries , Jean Tyson Schneider

Stability and Convergence for Nonlinear Partial Differential Equations , Oday Mohammed Waheeb

Regular Homotopy of Closed Curves on Surfaces , Katherine Kylee Zebedeo

Theses/Dissertations from 2011 2011

Coloring Problems , Thomas Antonio Charles Chartier

Modules Over Localized Group Rings for Groups Mapping Onto Free Groups , Nicholas Davidson

How Do We Help Students Interpret Contingency Tables? A Study on the Use of Proportional Reasoning as an Intervention , Kathleen M. Isaacson

A Fictitious Point Method for Handling Boundary Conditions in the RBF-FD Method , Joseph Lohmeier

Theses/Dissertations from 2010 2010

Developmental Understanding of the Equals Sign and Its Effects on Success in Algebra , Ryan W. Brown

The Inquiry Learning Model as an Approach to Mathematics Instruction , Michael C. Brune

Galois Theory for Differential Equations , Soheila Eghbali

Stably Free Modules Over the Klein Bottle , Andrew Misseldine

Combinatorics and Topology of Curves and Knots , Bailey Ann Ross

Theses/Dissertations from 2009 2009

Concept Booklets: Examining the Performance Effects of Journaling of Mathematics Course Concepts , Todd Stephen Fogdall

Effective Sample Size in Order Statistics of Correlated Data , Neill McGrath

Transparency in Formal Proof , Cap Petschulat

Weight Selection by Misfit Surfaces for Least Squares Estimation , Garrett Saunders

The Effects of a Standards-Based Mathematics Curriculum on the Self-Efficacy and Academic Achievement of Previously Unsuccessful Students , Cindy Chesley Shaw

Analytical Upstream Collocation Solution of a Quadratic Forced Steady-State Convection-Diffusion Equation , Eric Paul Smith

Solvability Characterizations of Pell Like Equations , Jason Smith

Theses/Dissertations from 2008 2008

Tube-Equivalence of Spanning Surfaces and Seifert Surfaces , Thomas Glass

Simple Tests for Short Memory in ARFIMA Models , Timothy A. C. Hughes

Incomparable Metrics on the Cantor Space , Trevor Jack

Richards' Equation and Its Constitutive Relations as a System of Differential-Algebraic Equations , Shannon K. Murray

Theses/Dissertations from 2007 2007

Theorem Proving in Elementary Analysis , Joanna Porter Guild

An Investigation of Lucas Sequences , Dustin E. Hinkel

A Canonical Countryman Line , William Russell Hudson

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Home > ETD > Mathematics and Statistics > ETDB_MATH

Mathematics and Statistics Bachelor's Theses

Theses/dissertations from 2023 2023.

Spatiotemporal analysis of actual monthly prices for milkfish, round scad, and tilapia in Philippine provinces from May 2020 to December 2022 , Aeram Clester Aguilar Albo, Lance Ramos Fernando, and Catherine Joy Añabeza Villaflor

Feature selection of the determining factors of family income class using FIES results 2018: A random forest approach with recursive feature elimination, cross-validated , Krizzia Mae M. Angue, Keziah Lois M. Cruz, and Jeremy C. Hilomen

Attributes influencing real-estate property prices: A nonparametric bootstrap regression utilizing web-scraped spatial data , Mhico Mhark Saribong Asuncion, Edgard Ivan Capinig Gonzaga, and Julienne Eunice Sy Yu

Using integer linear programming for university class scheduling in the College of Science in De La Salle University , Renier Joshua L. Cruz and Ma. Teresa Angelica M. DeLos Reyes

Econometric modeling of the effect of COVID-19 on ASEAN utility companies’ stock performance and risk profile , Frederico Miguel T. David and Miguel Q. Tabuzo

Poverty classification: A comparative analysis of classification algorithms on poverty in households in the top three richest and poorest regions in the Philippines using the family income and expenditure survey 2021 , Jonathan Arthur L. Dy, Chrisha Mae Tan Butardo, and Aaron Anthony Munoz Hernandez

Prediction of daily minimum and maximum temperature measurements in the Greater Manila Area using gaussian process modeling for bias correction and artificial neural network methods , Alyanna Marrielle Cabang Gammad and Jo-Anne April Penullar Mejia

Grade repetition in the Philippines: A multilevel approach , Albert Thimothy Maceren Go, Sergio Miguel Emnur Alcala, and Ma. Gabrielle Villafuerte Plastina

An analysis of crop-livestock systems using strongly connected components and multi-objective optimization , Jose Paolo Olano Guarisma and Ma. Clarisa Ruizo Hilario

On Laplacian centrality of a graph: An exposition , Margaret C. Inguillo

On the sum of k-th powers of the first n positive integers , Jancheska Chyles Malilay Malapascua and Arch Raphael Payang Alix

Modeling the clinical and economic burden of non-alcoholic steatohepatitis in the Philippines , Kiah Khyle Suan Medallo, Lyka Janine Asuncion Bocato, and Carlo Angelo Mabini Angeles

Discriminating the harvesting regions of Philippine coffee and cacao beans using principal component analysis (PCA) and Partial Least Squares - Discriminant Analysis (PLS-DA) , Ryan Gabriel T. Tan, Sharlene Cano, and Jack Calvin C. Chua

Theses/Dissertations from 2022 2022

A cointegration analysis on the effect of exchange rate on energy consumption and economic growth in the Philippines , Alyssa Raine Rose Angulo and Kate Louie Aranzaso Javaluyas

Forecasting the Philippines’ GDP growth using long short-term memory neural network regression and mixed-data sampling regression models , Andre Millard M. Arsua and Raphael Matthew D. Azucena

Prophet forecasting and temporal modeling of Covid-19 cases in the Philippines , Mary Colleen A. Bautista and Adrian Joshua B. Nunez

Analyzing spatiotemporal patterns of COVID-19 in the Philippines , Luke Matthews Baetiong Bernardo, Angelo Lowell Buenavista Lim, and Mark Christian Doctora Ramos

Testing the predictive ability of machine learning models for long term investments in cryptocurrency , Enrique V. Calceta and Jefferson R. Datinginoo

Application of the Vector Autoregressive with Exogenous Variable (VARX) framework in modeling and forecasting the growth rate of regular-milled rice price in the Philippines , Grayvqiel Sirach M. Campos, Aimee Jeziel B. Nuñez, and Sophia Loren A. Villanueva

A multivariate time series analysis using vector error correction models in explaining the relationship of financial inclusion and economic growth in the Philippines , Regine Alyana G. Capili and Claribel Jane Mendoza

The relationship between public sentiment and the media on the 2022 national elections in the Philippines using granger causality , Fong-Xiang Gracia Chen and Alyssa Erin Quetingco Gutierrez

Calculating age-specific death rates by sex in the Philippines from life expectancy at birth using the linear link model , Janelle Ong Chua and Kyla Camille Vesagas Ng

On the impact of health protocols in reducing the spread of COVID-19 virus: Analytical approaches through game, reaction network and SEIR models , Sophia Alexandria T. De Leon and Marielle Macaya Salud

Optimal locations of emergency medical tents for pandemic preparedness in Quezon City using facility location models , Lei Di Baroness Tuminez Garganza and Joaquin Miguel Lilam Fuentebella

Designing a regional railway network using an improved gravity model and graph theory approach , Joana Feliz Magtibay Gayeta and John Patrick Diño Jamisola

On the nonexistence of non-convergent Nash equilibria in disapproval voting , Justin Ervin D. Go and Jonathan O. Pinto

Effects of survey weights on the ordinal logistic regression modeling of perceived difficulty in reading comprehension from PISA 2018 , Ronald Gerbaud Evangelista Gucyam, Flynt Bernardino Razal, and Mark Lenard Cunanan Tan

Strategic planning using combinatorial game theory on chess endgames , Carlo Miguel Co Jimenez and Antonio Joaquin Idea Palaca

Spatial analysis on the regional and provincial rice prices in the Philippines , Celine Daphne T. Ko, Diorella Mareena F. Ngo, and Jasmine Kate L. Tan

Spatiotemporal modelling of typhoon severity using backfitting cochrane-orcutt estimation , Alexis Margaret Esperanza Magtibay, Aonee Jorvina Reyes, and Mikaela Angela Cariaga Santos

Establishing natural gas sustainability indicators for ASEAN producers through factor analysis on multivariate time series , Aliyah Margaret Villacorta Manito and Melodie Dy Ngo

Determinants of Telecommunication Infrastructure Index (TII) through Geographically Weighted Regression (GWR) in the Philippines , Renz Marquee Calazan Manuel, Jilian Vergara Menor, and Romeo Clarence Carranza Ramos Jr.

A livability evaluation framework using a multi-source data and network science approach – applied to the cities of Bacoor and Makati, Philippines , Deanne Jaimelyn Ang Ong and Richard Lawrence Lance Trinidad Jao

Effectiveness of the Philippine Stock Exchange Index (PSEi) as training dataset in forecasting Philippine stock prices using neural networks , Noriel Kristine Luzanta Sumayo and Nico Rafael Ayo Ting

Laplacian and signless-laplacian energies of closed shadow graphs , Inseok Sung

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181 Mathematics Research Topics From PhD Experts

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

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

Our Newest Research Topics in Math

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

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

Cool Math Topics to Research

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

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

Undergraduate Math Research Topics

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

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

Number Theory Topics to Research

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

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

Math Research Topics for High School

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

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

Complex Math Topics

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

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

Easy Math Research Paper Topics

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

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

Logic Topics to Research

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

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

Algebra Topics for a Research Paper

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

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

Math Education Research Topics

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

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

Computability Theory Topics to Research

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

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

Interesting Math Research Topics

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

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

Applied Math Research Topics

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

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

Geometry Topics for a Research Paper

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

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

Math Research Topics for Middle School

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

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

Math Research Topics for College Students

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

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

Calculus Topics for a Research Paper

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

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

Simple Math Research Paper Topics for High School

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

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

Business Math Topics

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

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

Probability and Statistics Topics for Research

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

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

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Georgia Institute of Technology College of Sciences

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BS/MS in Mathematics

The Georgia Tech College of Sciences BS/MS degree program enables highly motivated students with strong academic credentials to earn a Bachelor of Science in Mathematics and a Master of Science in Mathematics. The BS/MS program prepares students for competitive career placements with higher earning potentials as well as competitive admission to Ph.D. and professional programs (including medical/law/pharmacy/dental/pharmacy schools). Thesis and non-thesis options are offered for the BS/MS program. Undergraduates with a significant amount of AP/IB/dual enrollment credits are highly encouraged to apply to the BS/MS program.

Program Requirements:

• Students who are currently working toward a BS in Mathematics should apply to the combined BS/MS program once they have earned at least 30 credit hours, but no more than 90 (including transfer credit).
• A minimum undergraduate GPA of 3.3 is required for admission to the program. Students must graduate with their BS with a GPA of at least 3.0 to continue to the MS portion of their studies, and must earn a minimum GPA of 2.7 to graduate with their MS as well as earning a C or better in each math course in the program.
• Students should complete 6 credit hours of coursework that can be counted toward both the BS and MS degrees. This coursework must consist of non-research, non-seminar MATH courses at the 4000-level, and must be completed with a minimum grade of B.
• All students may choose to complete an additional 6 credit hours of approved graduate coursework in Mathematics (at least 6000-level, not research or seminar credit, not Math 6701 or 6702) before completing their BS. These credits will be applied to the MS degree, so long as they were NOT applied to the BS degree.
• For the MS thesis option, students must identify a MS thesis advisor before completing their BS degree. Students pursuing this option are encouraged to begin undergraduate research early, however any research described in an undergraduate thesis may not be used in the MS thesis.

Important:  In order to apply any coursework completed during the BS to the MS degree (the 6 shared credit hours or the further 6 hours of graduate coursework that would count only towards the MS), the student must complete the bachelor's degree with a cumulative GPA of 3.5 or higher and complete the master’s degree within a two-year period from the award date of the bachelor’s degree.

Applications:

The BS/MS Mathematics program application is now available.  Please apply through  Graduate Admission Application (gatech.edu)  and select the BS/MS Math degree.  There is no application fee.

For the Fall 2025 admission cycle, the application deadline will be  December 15, 2024. The upper credit limit listed in the Program Requirements will be in place.

Students who had taken over 90 credits at Georgia Tech prior to the Fall 2022 semester are eligible to apply to the program.  Students who anticipate taking 90 credits before their year of graduation should contact Hunter Lehmann or Chris Jankowski before reaching 90 credits to discuss applying to the program.

Program of Study:

BS in Mathematics: Students must complete all normal requirements for a BS in Mathematics as detailed in the academic catalog ( https://catalog.gatech.edu/programs/mathematics-bs/ ). For more details on this program, please visit the GaTech Mathematics web site.

Note that the 6 credits double counted between the BS and MS degrees will come from the upper level math electives or core requirements. Courses double counted for the BS/MS in math may not also be counted towards a minor or secondary undergraduate major.

MS in Mathematics: Students must complete all usual requirements for the MS in Mathematics ( https://catalog.gatech.edu/programs/mathematics-ms/#requirementstext ). In particular, students may choose between the thesis or non-thesis options for the degree, outlined below.

Course Requirements:

Note that Math 6701 or 6702 are not applicable toward the MS in Mathematics.

For questions about the BS portion of the program, please contact your major advisor.

For questions about the MS portion of the program, please contact Chris Jankowski at [email protected] .

For general academic questions, please contact [email protected] .

• The Bursar's website lists the yearly tuition and fees for graduate students here:  https://www.bursar.gatech.edu/tuition-fees . Undergraduate scholarships cannot be used for the MS portion.
• Full-time status for graduate students is 12 credits/semester, and F-1/J-1 students do need to be enrolled full-time unless they have an approved reduced course load.  MS students may apply for reduced course load during their semester of graduation.  The OIE website here  https://isss.oie.gatech.edu/content/enrollment-requirements has detailed rules.
• Ordinarily, all students are notified by April 15.  
• No, it is optional.
• One letter of recommendation is required.
• Yes - we cannot guarantee that anything received after the deadline will be considered.
• At present, there are only fall admissions.

• Bachelor of Science in Mathematics (BSMTH) with specialization in  Business Applications (BSMTH-BAP)
• College of Science
• Undergraduate Degree Programs (COS)
• To prepare the student for a mathematics - oriented career in industry, business and public administration.
• To provide the student with the mathematical training that will enable him to teach basic service courses in mathematics.
• To prepare the student for more advanced studies in mathematics.
• To develop the creative potential of the student through research.

MTH101A FOUNDATION COURSE IN MATHEMATICS (5 units)

This is a course on pre-calculus covering the following topics: Basics of algebra, equations and inequalities in one variable, functions and their graphs, exponential and logarithmic functions, trigonometric functions, trigonometric identities, inverse trigonometric functions, trigonometric equations, polar coordinate system, coordinates and lines, curve sketching, conic sections, systems of equations, sequences, mathematical induction, and the binomial theorem. 

STT101A FOUNDATION COURSE IN STATISTICS (3 units)

This is a course covering basic rules of probability, discrete and continuous probability distributions, and introduction to inferential statistics.

GEMATMW MATHEMATICS IN THE MODERN WORLD (3 units)

This course aims to discuss the nature of mathematics leading to appreciation of its practical, intellectual, social, and aesthetic dimensions.  It includes the study of the nature of mathematics and how the perception of this leads to different tools for understanding and dealing with various aspects of present day living such as managing personal finances, making social choices, appreciating geometric designs, understanding codes used in data transmissions and security, and dividing limited resources fairly.

STT201A EXPLORATORY DATA ANALYSIS (3 units)

This is a course covering statistical concepts, statistical measurements, statistical notations, collection, organization and presentation of data, measures of central tendency, location, dispersion, skewness, kurtosis; boxplots and stem-and-leaf display; measures of association and relationships; rates, ratios and proportions; construction of index numbers and indicators/official statistics.

MTH201A MATHEMATICAL ANALYSIS 1 (5 units)

This is the first course in the calculus series for majors.  It covers limits, continuity, derivatives of algebraic and transcendental functions, applications of derivatives, differentials, antiderivatives, definite integrals, the Fundamental Theorem of Calculus, and some applications of the definite integral.

MTH210A INTRODUCTION TO SET THEORY (3 units)

This is a course covering the principles of symbolic logic, valid arguments and methods of proof; axioms on sets, algebra of sets; relations and functions, the natural numbers, finite and infinite sets, and cardinal numbers.

MTPROG1 COMPUTATIONAL THINKING IN PYTHON (3 units)

This course covers the fundamentals of logic formulation, computational thinking and problem solving together with their implementation in the Python programming language. This course serves as a foundation for future courses that the students will encounter throughout their program. This course will cover topics on data representation, I/O, control structures, loops and functions as well as discussions on how to use them appropriately in constructing program code.

MTH202A MATHEMATICAL ANALYSIS 2 (5 units)

This is the second course in the calculus series for majors.  It covers techniques of integration, indeterminate forms, improper integrals, sequences and series, parametric equations, polar coordinates, functions of several variables and a quick look at evaluating multiple integrals.

STT203A STATISTICAL PACKAGES (3 units)

This is a course designed for Statistics/Mathematics majors, to familiarize students on the use of different statistical software (Microsoft Excel/PHStat2/MegaStat, SAS, and R) for creating and managing databases, as well as conducting simple statistical data analyses. 

MTH220A NUMBER THEORY (3 units)

This is an introductory course in Number Theory taken up as a major course by students in the mathematics programs.  Topics discussed include divisibility, the greatest common divisor and least common multiple, prime numbers and their properties, the unique factorization theorem, basic properties of congruences, linear congruences and linear Diophantine equations, the Chinese Remainder Theorem, applications of congruences, the theorems of Fermat, Euler and Wilson, arithmetic functions and their properties, quadratic congruences, quadratic residues and the Quadratic reciprocity law, and primitive roots.

MTH221A LINEAR ALGEBRA (3 units)

This is an introductory course in linear algebra taken up as a major course by students in the mathematics programs.  Topics discussed include matrices, vector spaces, linear transformation and its matrix representations, eigenvalues and eigenvectors, and diagonalization.

MTH203A MATHEMATICAL ANALYSIS 3 (5 units)

This is the third course in the calculus series for majors.  It covers multiple integration, vector spaces, and planes and lines in in , calculus of functions of several variables, and line and surface integrals.

MTH223A ABSTRACT ALGEBRA 1 (3 units)

This course is an introduction to group theory. It covers abelian and cyclic groups, subgroups, dihedral and permutation groups, normal subgroups and factor groups, Lagrange’s Theorem, fundamental homomorphism theorems and Cayley’s theorem.

MTH257A STATISTICAL THEORY 1 (3units)

A course in probability theory. Topics include the concept of sample space and events, conditional probability, probability density function, cumulative distribution functions, mathematical expectations, joint and marginal distribution functions of several random variables. Special distributions such as uniform, binomial, poisson, geometric, gamma, beta, exponential, normal, etc. are covered.

MTH258A STATISTICAL THEORY 2 (3 units)

A course in estimation of parameters and tests of hypotheses.  Topics include order statistics, limiting distributions, methods of estimation, properties of estimators and hypothesis testing.

MTH224A ABSTRACT ALGEBRA 2 (3 units)

This is a major course for BS Mathematics students.  It is a second course in Abstract Algebra which introduces students to other algebraic structures such as rings, integral domains and fields.  It is designed to enhance the students’ skills in logical reasoning and analysis.

MTH300A THEORY OF INTEREST (3 units)

A three-unit course on the theory of measurement of interest, annuities, extinction of debts by amortization and sinking funds, bonds and other securities.

STT141A LINEAR MODELS (3 units)

A study of the various linear statistical models that arise in practice. Topics include multivariate normal distribution, distribution of quadratic forms, general linear models, estimation and tests of hypotheses about linear hypotheses and design matrices giving rise to analysis of variance models.

MTH241A DIFFERENTIAL EQUATIONS (3 units)

A course in the solution of first order differential equations and higher order differential equations, Laplace Transformations, power series method and boundary value problems.

MTH253A OPERATIONS RESEARCH 1 (3 units)

As an introductory course in Operations Research, this course focuses on the basic models, the analysis and the solution of linear optimization models.  The thrust is in the analysis of problems and their solution approaches.  This course provides a firsthand exposure to vast and highly relevant area of operations research.

MTH242A NUMERICAL ANALYSIS (3 units)

This is a course for mathematics and statistics majors. It introduces the students to numerical methods of approximating solutions to different classes of mathematics problems. It is designed to provide the students with real-life approaches to solving problems for which closed form solutions are not feasible.

STT161A APPLIED MULTIVARIATE ANALYSIS (3 units)

A course dealing with applications of the following multivariate techniques in real-life data: discriminant analysis, multivariate analysis of variance, canonical correlation, factor analysis and cluster analysis.

MTH254A OPERATIONS RESEARCH 2 (3 units)

This course is designed for BS Mathematics students who are majoring in Business Applications covering topics on game theory and dynamic programming.

MTH245A ADVANCED CALCULUS (3 units)

This course presents the real number system as a complete, ordered field. It discusses topological properties of Euclidean n-space, limits and continuity, sequences of constants, and sequences of functions. It also covers differentiation and pertinent results such as the Mean Value Theorem.

MTH243A COMPLEX ANALYSIS (3 units)

This course covers the definition of the complex number system.  It discusses functions of a complex variable and their derivatives and integrals. Topics include the Cauchy-Riemann conditions, contour integrals, the Cauchy – Goursat Theorem, the Cauchy Integral theorem, Taylor and Laurent series, and the applications of residues.

STT163A TIME SERIES ANALYSIS AND FORECASTING (3 units)

A course dealing with the different methods of forecasting time series data – classical smoothing procedures, time series decomposition  and deseasonalization, ARIMA models, and Box-Jenkins method.

MTH230A MODERN GEOMETRY (3 units)

A course dealing with the geometries of the Euclidean plane, the sphere and the projective plane.  The topics include congruence, isometrics, affine transformations, Desargues Theorem and Pappus Theorem.

MTH301A SELECTED TOPICS (3 units)

An introductory course in Stochastic Processes. It covers Markov chains, Poisson process, renewal, Markov chains, continuous time Markov chains and Brownian motion

MTH255A OPERATIONS RESEARCH 3 (3 units)

This course is designed for BS Mathematics students who are majoring in Business Applications covering topics on minimum cost network flow, transportation and assignment problems, integer programming, and nonlinear programming problems.

MTH421A MATHEMATICS SEMINAR (1 unit)

A course requiring eight hours of attendance in lectures or seminars conducted by visiting professors or faculty members on various topics and the remaining hours for lectures/presentations by the students.

MTH422A THESIS WRITING 1 (2 units)

This course introduces research techniques and research topics in Mathematics to enhance students’ capacity in developing a thesis proposal. The students are required to submit a thesis proposal and present it in the form of a proposal defense.

MTH411A PRACTICUM (3 units)

This is a course taken by students to allow them to apply what they have learned in class. This will also expose them to the work environment, and to the different companies employing mathematicians/statisticians.

MTH423A THESIS WRITING 2 (3 units)

The course requirement is a bachelor’s thesis done by student under the guidance of an adviser.

• 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 2024 graduates is Monday, April 1 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. 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 2021, theses submitted in 2020, theses submitted in 2019, theses submitted in 2018 , 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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Department of Mathematics

Honors thesis.

• Undergraduate Program

The honors thesis is a research project, original or expository, or a combination of both, typically performed under the direction of a faculty member at the University of Rochester. If a compelling case is made, work may be performed under the direction of a faculty member from another department, another university or research center or a private corporation or by a graduate student. In all instances, you must have a faculty member of the mathematics department of the University of Rochester as a co-advisor to your thesis if your primary advisor is not a faculty member or is outside the department.

The Honors thesis write-up must be at least 20 pages long (counting bibliography and figures) and include a thorough introduction and reference section. The honors thesis must be presented in a public lecture at the Department of Mathematics in the presence of the Thesis Committee, consisting of the thesis advisor and at least two members of the Undergraduate Research Committee. If the advisor is a member of the Undergraduate Research Committee, one of the remaining members of the thesis committee need not be a member.

Upon the completion of the presentation, the advisor and committee member must fill out and sign the honors form if they feel the honors thesis meets the requirements.

Undergraduate Research Committee (2023-2024):

• Jonathan Pakianathan (chair)
• Alex Iosevich
• Naomi Jochnowitz
• Saul Lubkin

The following professors have also volunteered to help fill Honors Talk Committees and are considered official delegates of the undergrad research committee also.

• Steve Gonek
• Allan Greenleaf
• Sevak Mkrtchyan
• Carl Mueller
• Dinesh Thakur

Students who wish to write an honors thesis are strongly encouraged to begin the planning process early.

They must register for two units of Math 395W in the either the spring of fall semester of senior year (or, rarely, Spring of junior year).

By the end of February of the semester of graduation , they should provide the following information to the Undergraduate Research Committee:

• The name of the advisor
• The names of the remaining two members of the Thesis Committee (Note that at least two out of the three members of the thesis committee must be members of the Undergraduate Research Committee.)
• A tentative title and a rough description of the research

By noon on April 10 , the student must send a good draft of the honors thesis to the Thesis Committee and the chair of the Undergraduate Research Committee, Jonathan Pakianathan. The Thesis Committee members are expected to send a list of corrections and suggestions to the author within a week. This will give the author an opportunity to make the appropriate adjustments to the thesis prior to the presentation.

By noon on April 12 ,   the honors thesis presentation is to be scheduled so that the Thesis Committee can all attend. The scheduled date and time should be sent to Undergraduate Research Committee chair Jonathan Pakianathan and Math Department Coordinator Kimberly Toal, so as to be announced to the larger community and so that we can reserve a room if the talk is "in person" or set up a zoom room if it is online. Ideally, your honors thesis presentation is scheduled on a weekday, between 9AM and 5PM and avoids conflicts with other thesis talks. Most thesis presentations should aim to scheduled between Monday, April 15 and Friday, May 10.  The presentation outcome will be reported by your committee to Prof. Carl Mueller who will communicate it to the registrar by the senior grade deadline of Tuesday, May 14.

The presentation is a 50-minute talk, with 10 minutes of questions by the general audience, followed by anywhere from 10 to 40 minutes of closed-door questions from the committee.

The student then steps out, the committee discusses, and then the committee should then communicate the results to the student, sign the form, and turn it in to the front office.

See samples of past honors papers .

BS Thesis Guidelines and Timeline

Bachelor of science in biological sciences.

Bachelor of Science (BS): The BS is designed for students who wish to delve more deeply into the field of their major through additional electives, participation in scientific research, and completion of a BS thesis that summarizes their research. Successful BS students will (1) learn how scientists design and conduct scientific experiments; (2) collect data as part of a research effort; (3) evaluate the strengths and weaknesses of that data; (4) interpret the data in the context of a specific scientific discipline; and (5) describe their work in a BS Thesis

Students can earn a Bachelor of Science (BS) degree in Biological Sciences in any of the tracks by:

(1) completing three upper-level elective courses in Biological Sciences beyond those required for the BA degree, including  BIOS 28900  Undergraduate Bachelor of Science Research (or both quarters of  BIOS 00296  Undergraduate Honors Research if also pursuing Biology Research Honors)

(2) writing a BS thesis under the supervision of an adviser who is a member of the Biological Sciences Division research faculty.

Guidelines and Timeline for the BS in Biological Sciences

If you are participating in the BSCD honors program or a specialization that requires a thesis, you do not need to prepare a separate proposal (or thesis) for the BS degree, but you should submit copies of these materials to the BS program. Honors and specialization students are required to submit the BS Faculty Consent form in Spring of the 3rd year as directed below. You should adhere to the honors or specialization guidelines as you prepare your proposal, select faculty readers, and write your thesis. BS students who are writing a specialization thesis but are not in the BSCD Honors program are required to register for the BS research course (BIOS 28900) as directed below.

Spring of 2nd year

Declare your major as BA or BS in Biological Sciences. Remember that, in addition to the thesis, a BS requires three upper-level BIOS courses (numbered BIOS 21xxxx through 28xxx) beyond the five required for the BA degree. One of these courses must be BIOS 28900 unless you are taking BIOS 00296 for Research Honors.

Autumn of 3rd year

Start looking for a member of the BSD research faculty to serve as your thesis adviser and start developing ideas for your thesis research.

Description of the BS thesis

BS students will write a thesis based on original research. The topic must be a current issue in Biology, including basic science, medicine, and other applied fields, be described in a compelling thesis proposal, and be supported by a willing and appropriate Mentor. In most cases the thesis will present and analyze primary data collected by the student during their time in a mentor's lab. Students may also conduct critical and novel analysis of existing primary data (e.g., a critique of a healthcare policy such as methadone maintenance, a meta-analysis of recent clinical trials of antidepressants, or an argument against punctuated equilibria based on a fossil collection or genomic data). In either case, the work must be hypothesis driven and present evidence that tests the hypothesis. Topics related to global and public health will be accepted only for majors in the global and public health track. Please contact Chris Andrews if you have questions about the appropriateness of your topic. The thesis should follow the format of a published paper in a target journal appropriate for your topic but should include more extensive literature review and context in the introduction and conclusion.  A typical BS thesis is approximately 30 pages of double-spaced text (not including figures, tables and references).

Spring of 3rd year

To declare your interest in pursuing the BS in Biological Sciences, please submit the BS Faculty Consent Form  by 11:59 PM on Friday of finals week. If you have not already done so, please make sure you have officially declared your major as a BS in Biological Sciences so your college adviser can correctly slot courses into your degree program.

All BS students who will not be registered for BIOS 00296 (Undergraduate Honors Research) must register to take the BS research course (BIOS 28900 Undergraduate BS Research) in Autumn of their 4th year. We will add BIOS 00296 students to the BIOS 28900 Canvas site as unregistered students so they will receive announcements and can submit their materials for the BS degree. BS students who are writing a specialization thesis but are not in the BSCD Honors program are required to register for BIOS 28900.

Summer between 3rd and 4th year

BS students will typically conduct the bulk of their thesis research during this summer.

Autumn of 4th year

Unless you are in the BSCD Honors program and registered for BIOS 00296, make sure you are registered for the BS research course (BIOS 28900, Undergraduate BS Research) and have access to the associated Canvas site. BS students who are writing a specialization thesis but are not in the BSCD Honors program are required to register for the BS research course.

Submit a 1-2 page (single-spaced) thesis proposal (approved by your thesis adviser) as an assignment on the BIOS 28900 Canvas site by the end of Week 1.

Minimally, this proposal should include:

• the name, e-mail address, and department of your thesis adviser.
• a working title for your thesis.
• one introductory paragraph giving the background and rationale for your project.
• three to five paragraphs outlining your research question, hypotheses, predictions, and proposed methods.
• a few sentences regarding your proposed research timeline.
• a list of references cited in the proposal.

Winter of 4th year (by end of quarter)

During finals week , submit the names and e-mail addresses of two faculty readers from BSD research departments (other than your thesis adviser) to review your thesis in the spring. You will submit these names as an assignment on the BIOS 28900 Canvas site.

Spring of 4th year

By 11:59 PM on Friday of Week 4

Submit your thesis to your thesis adviser, who must approve it before you send it to readers for review. You do not need to submit this version of the thesis to the BSCD. This checkpoint allows your adviser to confirm that your thesis is in acceptable shape to send to readers.

By 11:59 PM on Friday of Week 5

Submit your thesis, approved by your thesis adviser, to your two faculty readers, along with the faculty review form (make a copy of the review form to share with readers here ). You should request that these readers return their reviews to you by Wednesday of Week 7 so you have time to respond to their feedback by the final deadline at the end of Week 8.

Between Weeks 7 and 8

In collaboration with your thesis adviser, revise your thesis in accordance with the feedback from your faculty reviewers. Both your thesis adviser and your two readers must sign off on the revisions before your final submission.  

By 11:59 PM on Friday of Week 8 

Submit the final version of the approved thesis, with confirmation of approval by your thesis adviser and two additional readers. You may collect signatures on a cover page ( here's the TEMPLATE)  or ask your adviser and readers to provide confirmation of approval by email to: [email protected]. 

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Guidelines for writing a thesis

These guidelines are intended for students writing a thesis or project report for a  Third Year Project Course ,  Honours year  or  Postgraduate Coursework Project . Postgraduate research students should see  Information about Research Theses  for postgraduate research students.

Before you start your Honours or Project year, you should speak to members of staff about possible thesis topics. Find out who works in the areas that you are interested in and who you find it easy to talk mathematics with. If at all possible, settle on a topic and supervisor before the start of the first semester of your Honours or Project year.

Most students see their supervisor about once a week, although this is usually open to negotiation between the student and the supervisor. Even if you haven't done much between visits it is a good idea to have a regular chat so that your supervisor can keep track of how you are going. You can expect your supervisor to:

• Help you select - and modify - your topic.
• Direct you to useful references on your topic.
• Help explain difficult points.
• Provide feedback on the direction of your research.
• Read and comment on drafts of your thesis.
• Help prepare you for your talk.
• Give general course advice.

Your thesis or project report is an overview of what you have been studying in your Honours or Project year. Write it as if you were trying to explain the area of mathematics or statistics that you have been looking at to a fellow student.

• Include an introduction that explains what the project is all about, and what its contents are. (It is sometimes better to leave writing this part to the end!) For many reports, a conclusion or summary is appropriate.
• Your thesis should be a coherent, self-contained piece of work.
• Your writing should conform to the highest standards of English. Aim at clarity, precision and correct grammar. Start sentences with capital letters and end them with full-stops. Don't start sentences with a symbol.
• Take great care with bibliographic referencing. Wherever some material has an external source, this should be clear to the reader. Don't just write in the introduction: 'This report contains material from [1],[2] and [3]' - give the references for the material wherever it is used. Don't gratuitously pad your reference list with references that are not referred to in the text. Check current journals for acceptable referencing styles.
• Be careful not to plagiarise. What constitutes plagiarism is perhaps a little different in mathematics and statistics compared to some other subjects since there is a limit to how different you may be able to make a proof (at least in its basic structure). We do, however, expect the report to be written in your own words. A basic rule is: if you put a fact or an idea in your report which is not your own, the reader should be able to tell where you got this fact or idea.
• The University has  policies on academic honesty and plagiarism  which all students should familiarise themselves with.

Generally, mathematics reports and theses are almost always typed in LaTeX. If you are going to type it yourself, you should allow a certain amount of time to become familiar with this software. Indeed, starting to learn LaTeX well before you actually want to write is a very good idea.

You should not underestimate the time it takes to produce a polished document. You will almost certainly need several drafts. It is very difficult to concentrate on getting the mathematics, spelling, grammar, layout, etc., all correct at once. Try getting another student to proofread what you have written - from their different viewpoint they may pick up on lots of things that you can't see.

P R Halmos (1970) in  How to write mathematics, Enseignement Math.  ((2) 16, 123-152) has the following advice: "The basic problem in writing mathematics is the same as in writing biology, writing a novel, or writing directions for assembling a harpsichord: the problem is to communicate an idea. To do so, and to do it clearly:

• you must have something to say (i.e., some ideas), and you must have someone to say it to (i.e., an audience)
• you must organize what you want to say, and you must arrange it in the order you want it said in
• you must write it, rewrite it, and re-rewrite it several times
• and you must be willing to think hard about and work hard on mechanical details such as diction, notation, and punctuation.

That's all there is to it."

His other advice includes:

• Say something: "To have something to say is by far the most important ingredient of good exposition---so much so that if the idea is important enough, the work has a chance to be immortal even if it is confusingly misorganized and awkwardly expressed..... To get by one the first principle alone is, however, only rarely possible and never desirable."
• Audience: "The second principle of good writing is to write for someone. When you decide to write something, ask yourself who it is that you want to reach." Your broad audience will be fellow Masters and Honours students, who may not be experts in your thesis topic. "The author must anticipate and avoid the reader's difficulties. As he(/she) writes, he(/she) must keep trying to imagine what in the words being written may tend to mislead the reader, and what will set him(/her) right."
• Organise: "The main contribution that an expository writer can make is to organize and arrange the material so as to minimize the resistance and maximize the insight of the reader and keep him(/her) on the track with no unintended distractions". 
• Think about the alphabet: "Once you have some kind of plan of organization, an outline, which may not be a fine one but is the best you can do, you are almost ready to start writing. The only other thing I would recommend that you do first is to invest an hour or two of thought in the alphabet; you'll find it saves many headaches later. The letters that are used to denote the concepts you'll discuss are worthy of thought and careful design. A good, consistent notation can be a tremendous help".
• Write in spirals: "The best way to start writing, perhaps the only way, is to write on the spiral plan. According to the spiral plan the chapters get written in the order 1,2,1,2,3,1,2,3,4 etc. You think you know how to write Chapter 1, but after you've done it and gone on to Chapter 2, you'll realize that you could have done a better job on Chapter 2 if you had done Chapter 1 differently. There is no help for it but to go back, do Chapter 1 differently, do a better job on Chapter 2, and then dive into Chapter 3... Chapter 3 will show up the weaknesses of Chapters 1 and 2".
• Write good English: "Good English style implies correct grammar, correct choice of words, correct punctuation, and, perhaps above all, common sense."

More information on how to write mathematics:

• Lee, K. A guide to writing mathematics
• Lee, K. Some notes on writing mathematics 
• Jackson, M. Some notes on writing in mathematics
• Reiter, A. Writing a research paper in mathematics
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Bachelor- and Master thesis in Mathematics

The legal regulations for Bachelor's and Master's theses can be found in each case in the general part of the examination regulations, currently ( February 2022 ) in the following paragraphs: 2-Hf.-Bachelor: § 19 - B.Sc. : § 21 - M.Ed.: § 19 - M. Ed. as extension subject: § 19 - M. Sc .: § 20 (Links to the examination regulations on the information pages of the study programs ) The current regulations of the examination regulations are legally binding; the information below is informal and legally without guarantee.

In the information below, the study program "M.Ed. as extension subject" is still missing, for which the same should apply as for the "normal M.Ed. should apply (but still has to be checked!).

Requirements for a Bachelor's or Master's thesis, Duration, ECTS credits

The processing period begins on the day on which the topic is officially assigned. This date is entered on the registration form.

Who is allowed to supervise Bachelor and Master theses?

Supervision at the Mathematical Institute:

The supervision of Bachelor's and Master's theses is primarily the responsibility of the professors (including junior professors and private lecturers) of the Institute of Mathematics. They are listed with their research and interest areas on the webpage Lecturers and Research Areas .

Non-professorial academic staff (i.e. who do not hold the title "Privatdozent/in" or "Dr. habil") may only officially supervise Bachelor's or Master's theses if they have been authorized to do so. In case of doubt, this must be inquired about.

It may well be that the work is de facto supervised by a research assistant. However, this is not legally relevant - the term "supervisor" always refers to the person officially designated and responsible for supervising the work.

External care:

Co-opted professors also have the right to supervise mathematical theses. These are usually mathematicians who hold a professorship at another faculty, but by virtue of their co-optation are eligible to examine within mathematics. They are also listed on the Lecturers and Research Areas page.

In exceptional cases, a thesis may also be supervised by a professor or a private lecturer of another faculty or another university if this is done in agreement with a professor or a private lecturer of the Mathematical Institute of the University of Freiburg. Such external supervision must be applied for informally via the examination office and approved by the subject examination board.

Master of Education theses in didactics of mathematics can only be supervised externally, usually by professors of mathematics at the University of Education Freiburg . This is possible within the framework of the supervision capacity of the University of Teacher Education and requires the completion of the module "Fachdidaktische Forschung". Please register your interest with the Department for Didactics of Mathematics. For the agreement with a professor of the Department of Mathematics of the University of Freiburg please contact either someone who is professionally close to the topic of the thesis, or to the Executive Director of the Department for Didactics of Mathematics .

A Bachelor's or Master's thesis can also be written in cooperation with a company . In this case, however, either the official supervision takes place at the Institute of Mathematics or the contact person in the company is by chance a habilitated professor or even a professor and the exception described in the previous section is possible. In the first case, experience has shown that a thorough consultation between the official supervisor of the thesis and the de-facto supervisor in the company is necessary.

How do you get a supervisor and a topic?

It is best if you already have an idea of the direction in which your work should go or in which focus area you want to write your paper. Then you can specifically contact lecturers who work in this direction or are active in this focus area. Please have a look at the pages Lecturers and Research Areas and Typical Study Processes in the Focus Areas . It is best to make an appointment to speak with them. Lecturers with whom you are currently listening to a lecture or attending a seminar you are of course welcome to speak to them on the sidelines.

If you do not find anyone to supervise your work in this way, you can apply to the examination office for the assignment of a supervisor. However, this is rather unusual.

Two-Major Bachelor's : Due to the fact that the curriculum leaves few choices, the topics for bachelor's theses are somewhat limited. You can connect to the advanced lectures in algebra and number theory, elementary geometry, numerics or stochastics, possibly also to the topic of the undergraduate seminar you have attended. Some instructors also assign topics that build on the basic lectures in calculus and linear algebra. Don't be afraid to approach lecturers; take advantage of office hours ! If you would like to write your thesis in mathematics, but have no real idea who should supervise your work, it may also be useful to talk to the student advisory service of the Department of Mathematics.

Bachelor of Science : In the course of your studies, through your required and elective courses, you will usually develop an idea of, in which focus area your work should be located. In this area you should then ideally also listen to an lecture and attend a seminar. Helpful is the page Typical study procedures in the focus areas . Feel free to approach the lecturers in this focus area early on. It may be advisable (as was still mandatory in the old examination regulations of 2012), to write the paper based on a seminar presentation. However, this does not have to be the case, especially if no suitable seminar is offered.

Master of Education : You can write your Master's thesis in one of the two subjects in subject-specific science or subject-specific didactics, or in educational science. Interdisciplinary theses or theses combining subject-specific and subject-specific didactical aspects are also possible. (At times there was a rumor that you had to write your Master's thesis in the other subject than your Bachelor's thesis; this is not true). If you want to write your thesis in mathematics, it is important to decide whether it should be in subject didactics or subject science, because the study plan depends on this:

• For a thesis in didactics of mathematics you have to complete the module "Fachdidaktische Forschung" at the PH Freiburg. Within the framework of this seminar you will then also find your supervisor.
• A specialized scientific paper can build well on the in-depth lecture or on a seminar taken in the module "Mathematische Ergänzung". If you already know in which area you would like to write your thesis, it is worthwhile to contact the lecturers of this area: Then you can take the module "Wissenschaftliches Arbeiten" instead of the in-depth lecture, in which you can familiarize yourself with the topic of the master's thesis.

Master of Education as an additional field : For the "major subject variant" with 120 ECTS credits, the same applies as for the M.Ed. program; for the "minor subject variant" with 90 ECTS credits, one can orientate oneself on the specifications for the two-main subject bachelor.

Master of Science : Students in the Master of Science program usually already have a good insight into mathematics and an idea of in which area they want to specialize. It is useful to have a look at the page Typical Study Sequences in the Focus Areas . Feel free to approach lecturers on the sidelines of lectures and seminars. Ideally, you should work your way into the topic of the Master's thesis in the specialization module or in the elective module in a reading course "Wissenschaftliches Arbeiten".

Work registration

Registration must be made in writing at the Examinations Office using the form provided for this purpose (available online on the Examinations Office website under "Forms and Information Sheets"). The form must also be signed by the supervisor of the thesis. Then it must be handed in immediately to the Examinations Office (mailbox in front of the Examinations Office or by e-mail). The processing time begins with the date of topic assignment noted on the registration form.

In the B.Sc. degree program Mathematics according to the "old" examination regulations of 2012, the registration of the thesis must be done at the latest on the day of the presentation in the Bachelor seminar. There are no requirements in the opposite direction: The presentation can take place as long as desired after the registration of the paper.

When registering for a Bachelor's or Master's thesis, one must confirm that one is familiar with the rules of good scientific practice . These rules are on the examination office website under "A to Z", keyword "Regeln wissenschaftlicher Redlichkeit".

When registering, the topic of the work is determined, the working title given for it can be adapted later. The topic may be changed once within certain deadlines (see under "New topic").

When registering the work, you can request, with the consent of the supervisor, to write the paper in English (or another language).

New topic / extension of the processing time

• Dual-Major Bachelor: two weeks
• B.Sc.: two weeks
• M.Ed.: four weeks
• M.Sc.: two months
• Dual-Major Bachelor: maximum six weeks
• B.Sc.: maximum one and a half months
• M.Ed.: maximum six weeks
• M.Sc.: maximum six weeks

Language, Formatting and the like

Theses must be written in German, unless, when registering the thesis, the student applies, with the consent of the supervisor, to write the thesis in another language. This must then be approved by the examination board, the review (with possibly second and third reviews) must be ensured and the thesis must contain a German abstract. It is usually no problem to write a paper in English. French may also be possible; all other languages are likely to be difficult.

The examination regulations do not specify the number of pages or the formatting of a paper. (i.e. font size, line spacing, size of margins, citation style, etc.). Please discuss all these points with the supervisor of your paper. Depending on the topic, there will certainly be ideas from the supervisor about the size of the paper; In our experience, formatting issues are of secondary importance. However, it is usual to prepare the paper in DIN A4 format and to use the mathematical word processing program LaTeX. (LaTeX is not mandatory, but makes life easier).

This sample can be used for the title page. The name of the supervisor can, but does not have to be mentioned on the title page. For Bachelor's and Master's theses as well as internal doctoral theses the title page with Unilogo may be used (however, without changes to the corporate design, i.e. in particular with regard to the size and position of the logo).

Submission of the work and formal requirements

Two copies of the thesis - or three copies for the M.Sc. program in Mathematics - printed and bound must be submitted to the examination office of the Mathematics Department in due time (in person, in the mailbox in front of the examination office or by mail - in this case the date of the postmark is the date of submission). In addition, the paper must be submitted (preferably by e-mail) as a pdf file. As a rule, the supervisor would also like to have the final version of the thesis as a pdf file by e-mail.

To meet the deadline, electronic submission is sufficient; the printed copies must then be subsequently delivered within the next two weeks together with a written assurance that the printed version matches the pdf version.

• that one has written the submitted work independently,
• that one has not used any sources or aids other than those indicated and that one has not copied any and that all content taken verbatim or in spirit from other works has been marked as such.
• and that the submitted work is not or has not been the subject of any other examination procedure, either in its entirety of another examination procedure.

If the thesis contains a programming part, the corresponding programming code must be submitted electronically as a separate file together with the abstract of the thesis. You should clarify in advance with your supervisor whether this is sufficient, or whether a printout of the programming code (if necessary as part of the thesis) is required.

Presentation of the work

A presentation of the Bachelor's thesis is only required in the B.Sc. program according to the new examination regulations of 2021; a presentation of the Master's thesis only in the M.Sc. program. The presentations are ungraded study achievements of 1 ECTS point in the B.Sc. program and 3 ECTS points in the M.Sc. program.

There is no separate registration for the presentation, neither in writing nor via HISinOne.

The presentation of the bachelor's thesis should be about 30 minutes long, but can also be longer by mutual agreement. Beyond that, there are no formal and temporal requirements, especially not for the presentation of master's theses. A presentation may take place before the end of the submission of a thesis (sensibly not too early) and should not take place too late afterwards. At one extreme, it may be a discussion with the supervisor and the assessor in an office or, at the other extreme, it may consist of an ordinary presentation in a senior seminar or a project seminar. Both the date and the closer circumstances must be agreed upon with the supervisor.

A thesis is reviewed and evaluated by the official supervisor. In some cases there is also a second examiner, always in the M.Sc. Mathematics and in exceptional cases in the M.Ed. Mathematics. (These exceptional cases are: in case of interdisciplinary work; in case of work with external supervision, unless it is a subject didactic paper supervised at the PH Freiburg, for which there is only one reviewer). The second examiner is appointed by the responsible examination office, usually on the suggestion of the supervisor. Students do not have to take care of this.

The duration of the assessment should not exceed six weeks. If you need the assessment in a hurry (e.g. because of matriculation in a Master's program or starting a job), please discuss this with your supervisor as early as possible. If the assessment is delayed, please contact your supervisor and the examination office.

If there is only one expert opinion and it evaluates the thesis as passed, the grade of the expert opinion is the grade for the thesis. If the expert opinion evaluates the thesis as not passed, a second expert opinion is ordered by the examination board. If the second expert opinion also evaluates the thesis as not passed, the thesis is not passed. If the second expert opinion evaluates the work as passed with grade x, a third expert opinion is ordered by the subject examination committee, which determines the final grade y with x ≤ y ≤ 5.0 and thus in particular determines whether the thesis has been passed or not. If there are two expert opinions, the arithmetic mean of the two individual grades, rounded down to one decimal place, is the grade for the paper, unless the two individual grades x1 and x2 differ by at least two grade levels. (Grade levels are "very good ", "good ", etc. - so it is not about the difference of the two grades). In this case, a third opinion is ordered by the subject examination board, which determines the final grade y with min{x1,x2} ≤ y ≤ max{x1,x2} and, if applicable, thus determines in particular whether the thesis has been passed or not.

Repeat of a thesis

A thesis can be repeated exactly once in case of failure. For this purpose, the student must apply for a re-submission of the thesis within two months after the or submit an application for the assignment of a new topic.

The retake may be supervised by another person and the topic may be from a different area of mathematics concentration. However, the repetition of a thesis in the Dual-Major Bachelor or M.Ed. must be in the same subject.

A return of the topic is only allowed in case of a repetition if this possibility has not yet been used in the first attempt.

Follow-up studies: What needs to be considered?

Master at the University of Freiburg

The general rule at the University of Freiburg is that in order to apply for a Master's program the underlying Bachelor's program does not have to have been completed. Important: The application deadline (in mathematics July 15 or January 15 - as of 2022) must not be missed under any circumstances, completely independent of the status of the Bachelor's thesis! For matriculation , however, the Bachelor's program must have been completed. For Bachelor graduates from Freiburg, it is sufficient if the completion of the Bachelor program is documented in HISinOne; the certificate does not necessarily have to be available yet. (Applicants from other countries need the certificate for matriculation). For matriculation, a deadline is normally set at the beginning of October for the winter semester or at the beginning of April for the summer semester. However, this deadline can be extended until approximately the end of the second week of lectures in consultation with the Student Secretariat, if, for example, the reports for the Bachelor's thesis are still outstanding. (Matriculation under reserve is not possible - this only existed during the Corona pandemic in case, that the completion of the Bachelor's program was delayed for corona-related reasons).

In concrete terms, this means for Freiburg students who want to follow a Master's program at the University of Freiburg: If you are running short of time, you should re-register for the following semester in the Bachelor's program and plan the registration of the Bachelor's thesis in such a way, that the report is available at the beginning of the lecture period at the latest, so that you can then transfer to the Master's program. How much time the supervisor needs for the expert opinion should be discussed with him/her in advance. The examination office usually only needs one day to enter the grade in HISinOne, but may not be staffed every day. If you would like to write the thesis in June, July and August, for example, the six weeks allotted for the assessment are sufficient, in order to be able to transfer to the master's program in mid-October. If, on the other hand, you would like to write the thesis in the months of July to September, the report must be prepared within two to three weeks, in order to be able to enroll or transfer in time: This is only possible after prior consultation with the supervisor!

Master at other universities

For matriculation at other universities, the certificate must usually be available and, of course, the matriculation deadlines of the respective university must be observed, which may end much earlier. It is therefore difficult to give a general timetable. In addition, the examination office also needs more time to prepare the certificate and have it signed, especially if the typical summer vacation period is involved. A few universities allow conditional matriculation; however, one must clarify this with the university.

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