math senior thesis

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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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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Guidelines for Senior Theses in the Mathematics Department

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

Recent Senior Theses

Supervision

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

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

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

Public Lecture

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

Submitting the Completed Thesis

The supervisor must approve the student's thesis. No later than April 15th, the student must submit a completed thesis to the thesis supervisor. If the supervisor asks the student to make changes, the student has until April 30th to do so. By April 30th, the student must give the supervisor two paper copies and an electronic copy of the thesis in final form. The electronic copy will be posted on the department's web site. [Students who expect to graduate in January must submit a completed thesis by November 15th and the final form by November 30th.]

Form of the Thesis

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

• The student's name and graduating class.
• The title of the senior thesis.
• The name of the faculty supervisor. (If there is more than one supervisor, list both. If one of the supervisors is not in the Mathematics Department, list the department and institution.)
• The date of completion of the thesis.

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

Merit of the Senior Thesis

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

Honors Consideration

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

Mathematics Library Collection of Senior Theses

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

• Sustainability

Mathematics

Senior thesis information.

Both senior thesis and senior seminar satisfy the Bates W3 writing requirement and highlight mathematical research, writing, presentation, and group collaboration. Senior thesis is a good choice for students wanting to improve all these, with special emphasis on mathematical research on a topic chosen by the student. Senior theses also involve significant amounts of writing, presentations, and check-ins with other math thesis writers.

To ensure that each senior thesis writer has an enriching experience, the math department limits how many theses each faculty member advises, typically to no more than two theses per semester per advisor. To help the department determine senior thesis advisors, each junior math major who would like to write a senior thesis completes a request form by NOON on the last day of Winter Semester classes of the junior year, that is, by 12:00pm (noon) on Friday, April 12, 2024 . Some details:

• The request form seeks background information on the student, the student’s preferences regarding senior thesis, the student’s reasoning behind their preferences, and a description of the proposed senior thesis project. The project description should include enough information to show that the student has given their topic serious thought and that the project is feasible, given the student’s background and given the amount of time the student has to do the research.
• The math department strongly advises juniors to discuss senior thesis topics and ideas with faculty members before writing a request. The request form asks whether you have had such discussions.
• Students should plan to work at least 12 hours per week on thesis, and at least 15 hours per week if pursuing an Honors thesis.
• The math department meets to consider all senior thesis and senior seminar proposals. The department chair typically notifies students of the results of the meeting during Short Term.
• The mathematics department keeps copies of past senior theses in our lounge in Hathorn 209. We encourage prospective senior thesis writers to look through these past theses as part of deciding whether to write a thesis: past theses provide topic ideas, writing structures, and a sense of the scope of a senior thesis.

Types of thesis

• One-semester thesis: A one-semester thesis may be either in the fall (MATH 457) or winter (MATH 458). One-semester theses are due by the Friday of the final examination period of the semester in which the student is writing their thesis.
• Two-semester thesis: Two-semester theses (MATH 457 and MATH 458) not in the Honors Program are due by the last day of classes of the winter semester.
• Honors thesis: Honors theses (MATH 457 and MATH 458) are always two-semester theses and follow the procedures and deadlines of the Honors Program . While all capstone experiences expect students to demonstrate mathematical reading skills and ability to communicate mathematics, a thesis earning Honors in Mathematics is distinguished by an exceptional level of achievement in these areas. Students preferring to write an Honors thesis state this preference at the time of their senior thesis proposal. The Department then decides which students to nominate for the Honors Program, based on the thesis work presented at the end of the first semester.
• Double thesis with another major: A double thesis is a single year-long project that satisfies the thesis requirements of both mathematics and another department, and as such, requires a significant amount of mathematics. A student writing a double thesis signs up for their math thesis in one semester (either MATH 457 or MATH 458) and the other department thesis in the other semester. The math department requires the student to present a talk or poster in the “math semester.” A student who applies thesis course credit to another major may not apply that same credit to the Mathematics Major. The Department will not approve a proposal for a one-semester double thesis.

Completing the thesis

• Students turn in their thesis to their advisor, in a format determined by the advisor, and students give the department chair a final printed copy of the thesis to be placed on permanent display in the mathematics lounge.
• one-semester thesis students present a poster or a talk;
• two-semester non-honors thesis students present a talk in Fall Semester and a poster or a talk in Winter Semester;
• Honors thesis students present a talk in Fall Semester and give their Honors defense during a College-designated Honors defense time period;
• when there is a choice of a poster or a talk, this decision is to be made with the thesis advisor.

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Undergraduate Honors & Senior Thesis

Students excelling in their major coursework and interested in pure math should consider Departmental Honors. Departmental Honors means you will graduate “With Distinction” as opposed to College Honors which is “With Honors”.  The most important component of graduating with Departmental Honors is researching and writing a Senior Thesis.

Requirements for Departmental Honors:

• Must complete a B.S. Mathematics Degree.
• Must satisfactorily complete at least one three-quarter sequence 402-3-4, 424-5-6, or 441-2-3; or two two-quarter sequences from this list. Exceptions must be approved by the chair of the Departmental Honors Committee.
• Must earn a GPA of 3.5 or better in Math coursework completed at the UW.
• Must write a senior thesis (earn a numerical grade for MATH 496).
• Must have a 3.3 minimum cumulative GPA at UW.

Please note: If you are not interested in the College Honors or Departmental Honors in Mathematics, you may still write a Senior Thesis. The process is the same as above, but it does not need to be approved by the Honors Committee.

Research credit (Math 498) may be available with faculty permission.

Beginning of your final year at the UW : think about a thesis topic and seek out a faculty supervisor.  Read below for more details about selecting a topic.

First week of classes the quarter before you expect to graduate: submit a thesis proposal form to the Dept. Honors Committee.  The form is online here: Math Dept. Honors Thesis Proposal Form

Last day of your final quarter: Once your advisor approves the thesis, email it to [email protected] and cc your faculty advisor.  You may also wish to upload it to the University Libraries archive .

Nature of the thesis

The senior thesis shall be an expository account of a topic in pure or applied mathematics related to the student’s area of interest. (Original results or proofs are welcome but are definitely not expected.) The thesis must contain some nontrivial mathematical arguments. (E.g., a non-technical essay on “fractals in nature” would not be acceptable.) The thesis should normally be about 20 to 30 pages in length (double spaced, Times New Roman 12pt font, 1” margins). These figures are guidelines, not rigid requirements. The topic should be something that cannot simply be read out of a standard textbook. Writing the thesis should involve:

• obtaining material from the periodical literature, or
• consulting several books and synthesizing material from them, or
• reading an account of a topic in a book that is substantially more advanced than the student’s regular coursework, digesting it, and putting it into readable form.

Choosing a topic

Finding a topic is the students’ responsibility, although consultation with faculty members is encouraged. The topic must be approved by a faculty member of the Mathematics Department who will supervise the work (the “supervisor”) and by the chair of the Departmental Honors Committee. A Senior Thesis Topic Proposal form can be found at the link above, and should be filled out by the student with the supervisor's support (the Dept. will check in with your supervisor). The topic proposal must be submitted to the chair of the Departmental Honors Committee no later than the end of the first week of classes the quarter preceding the quarter in which the student expects to graduate. Exceptions to this deadline may be granted only by the chair of the Departmental Honors Committee. Students contemplating writing a thesis are strongly encouraged to start thinking about a topic in the autumn quarter of their senior year.

Writing the thesis

The student must register for Math 496 (Honors Senior Thesis) during the last quarter of thesis work. The student may receive three credit hours of W-course credit for writing the thesis. Normally, the students will register for a reading course (Math 498) with the supervisor during the preceding quarter (s). The student will receive three hours of credit for each of these courses, but in exceptional cases, with the approval of the supervisor, the number or credit hours may be increased. The supervisor may allow the student to replace Math 498 with a suitable topics course; however, it is still expected that the student will meet periodically with the supervisor.

There is no specific required thesis template for an undergraduate thesis.  Some students may choose to use a modified version of the graduate thesis templates, but this is not required.

Approval of thesis

The student shall submit a draft of the thesis to the supervisor for comments and criticisms, and then shall submit a final version with appropriate revisions. The supervisor shall read the thesis and certify its acceptability with respect to both content and exposition. In order to ensure sufficient time for these things, the student must submit the first draft no later than three weeks before the last day classes of the quarter in which the student expects to graduate, and the final draft no later than the last day of classes. Exceptions to these deadlines may be granted only by the chair of the Departmental Honors Committee.

Once the thesis has been approved by your faculty supervisor, you will need to email the document to [email protected] (required) as well as submit it to the ResearchWorks archive , part of the University Libraries (optional but strongly recommended).  Submission to the archive will allow your thesis to be included in the dissemination and preservation of scholarly work.  Your thesis will be made publicly available.

Interdisciplinary theses

Theses which are concerned with the application of some part of mathematics to some others field are acceptable, as long as they contain some substantial mathematics. In exceptional cases the student may wish to work most closely with a faculty member in another department in preparing the thesis. However, in such cases the thesis topic and the thesis itself must still be approved by a member of the Mathematics Department.

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Department of Mathematics - UC Santa Barbara

Senior Thesis Options

To enter the honors program in mathematics, a student must have completed 120 units of coursework with an overall grade-point average of at least 3.5 and at least 24 upper-division mathematics and statistics units with a grade-point average of at least 3.5 (excluding Mathematics 100A-B, 193, 195A-B, and PSTAT 133A-B-C and 193).

To complete the honors program, the student must maintain a grade-point average of at least 3.5 in all upper-division and graduate mathematics and statistics courses (excluding Mathematics 100A-B, 193, 195A-B, and PSTAT 133A-B-C and 193) and as well as complete one of the following: (a) a senior thesis, Math 197A-B; (b) a two-quarter graduate sequence; or (c) together with an advisor, submit a Distinction in the Major proposal for an interdisciplinary program of three mathematically oriented courses outside the math department to the undergraduate committee for its approval. Option C does not apply to economics/mathematics or financial mathematics majors.

Distinction in the Major for each option will be awarded at graduation pending final approval by the Department of Mathematics Undergraduate Committee. Written projects will be submitted to the committee, and grades will be evaluated for coursework options. To apply for the Honors Program in Mathematics, please email the Mathematics Undergraduate Advisors at  [email protected] .

University of Notre Dame

Department of Mathematics

College of Science

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Senior Thesis

Writing a senior thesis.

Begin by finding an advisor in the area of mathematics on which you wish to write a thesis. Any member of the department can serve as a senior thesis advisor. A list of faculty who have expressed particular interest in advising, along with some suggested topics, may be found here . You may also find it helpful to look at the list of recent senior theses topics (listed below). You can begin looking for an advisor towards the end of the fall semester, or during the spring semester, of your junior year. Your advisor will propose a collection of appropriate readings to get the process started. You should then register for 2 credits of Undergraduate Research (MATH 48800) for the coming semester. To get registration permission you have to contact the Director of Undergraduate Studies (currently Andrei Jorza ) telling him that you intend to complete a senior thesis, and telling him who your advisor is. (Don't forget to sign your email with your full name!) You should continue registering for 2 credits of MATH 48800 for each semester that you work on the thesis, until the final semester (spring of senior year) when you should instead register for 2 credits of Thesis (MATH 48900). Each registration period you will need to contact the DUS to get the necessary permissions; it would be helpful to him if each time you reminded him who your advisor is and what your topic is. Writing a senior thesis is a major undertaking. It is never too early to begin planning and writing it. Although the details of your progress will vary depending on the specific plan you've worked out with your advisor, one possible timeline might be as follows. You might meet with your advisor for about an hour a week during fall semester of senior year (and maybe spring semester of junior year, if you started earlier), and in most cases you should aim to have most of the research and reading completed, and be able to give an outline of the thesis to your advisor, by the end of fall of senior year. You can then turn to writing, aiming to submit a draft of the thesis to your advisor by mid March, so that a final version can be ready by early April. Regular meetings with your advisor during the spring semester will help this process along. Usually your advisor will help you work out a more detailed plan of study, but there is a great deal of flexibility in this as the work progresses. The length of your thesis will depend very much on the subject matter. Past theses have ranged from 15 to 60 pages, with most in the 30 to 50 page range. A good guideline is that the thesis should be long enough for you to convey enough details and explanations that a mathematics major would be able to follow it. Your advisor will help you with more precise guidelines specific to your chosen topic. There are just a few deadlines to keep in mind throughout the process:

• If you are an Honors student, then as soon as you know who your advisor is and what your topic will be, you should pass this information on to Liviu Nicolaescu (again, remembering to sign your email with your full name).
• By January 24 of senior year you need to write to the DUS letting him know the following information: your full name, ND email address, the exact title of the thesis, your majors and minors, and your advisor's name. This information is required by the registrar.
• By April 12 of senior year a hard copy of the thesis, with a cover page signed by your advisor, must be submitted to the DUS. He will then assign readers who will decide whether the thesis is acceptable. This decision will be made in time for the registrar to be informed, so that the appropriate citation can be put on your diploma.

Once your thesis has been approved, you should take the time to upload it to Curate ND so that it will be permanently available to future scholars. You should also consider giving a short talk about your thesis at the College of Science Joint Annual Meeting . Your advisor will help you figure out the deadline for this. A note for Glynn Family Honors students: Your Glynn Family Honors Thesis can be submitted to the Department of Mathematics. You should follow the schedule described above, but note that there might also be additional requirements specific to the Glynn Family Honors program.

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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

Applied Mathematics

• Undergraduate Program

Each of the Applied Mathematics concentrations allows exceptional students to pursue honors, which involves in-depth project work with faculty.

Outline of Honors Requirements

• Excellence in grades
• Completion of an in-depth, original research project carried out under the guidance of a Brown-affiliated faculty advisor
• Completion of an honors thesis describing this research 
• Completion of two semesters of independent study courses while working on the honors thesis

Deadlines and requirements for honors differ between joint concentrations due to the different needs and scales of each program. Check the details for each concentration below:

• Be in good academic standing by the end of the seventh (or penultimate) semester.
• Earn grades of A or S-with-distinction in at least 70% of the Brown University courses used for concentration credit, excluding calculus and linear algebra, or be in the upper 20% of the student's cohort (as measured by the fraction of grades of A or S-with-distinction among courses used for concentration credit, excluding calculus and linear algebra) by the end of the seventh (or penultimate) semester. (Since S-with-distinctions do not appear on the internal academic record or the official transcript, the department will consult directly with the Registrar’s Office to confirm a student’s grades in concentration courses.)
• Secure a faculty advisor and at least one second reader for the proposed honors thesis project. One of the advisors/readers must be an Applied Mathematics faculty member. 
• Meet regularly, as agreed upon, with their honors thesis advisor and provide regular written drafts on the thesis project.
• Complete an honors thesis that is approved by the faculty advisor and second reader(s) prior to the deadline in the students eighth (or final) semester. Deadlines and guidance about the honors thesis are described below. 
• Email a copy of their approved thesis to Student Affairs Manager Candida Hall ( [email protected] ) in Applied Math for archival purposes prior to the deadline.
• Give an oral presentation of the honors thesis at an approved venue, usually the senior thesis day in Applied Mathematics.
• Complete two semesters of independent study courses while working on the honors thesis, such as APMA 1970/1971 or BIOL 1950/1960 or ECON 1960/1970 or CS 1970. One of these courses can be used to fulfill the senior seminar requirement of the APMA ScB, but they cannot be used to fulfill other concentration requirements. 
• Obtain permission to pursue honors from the department by submitting a completed Honors Declaration Form to our Student Affairs Manager Candida Hall by the deadline (usually at the beginning of the seventh semester). The honors declaration form requires signatures from the thesis advisor, second reader, and concentration advisor, as well as, a brief description of the proposed thesis research. It also requires a preliminary check of eligibility requirements, including the fraction of quality grades.
• Secure a faculty advisor and at least one second reader for the proposed honors thesis project. One of the advisors/readers must be an Applied Mathematics faculty member and one must be a Biomed-affiliated faculty member. 
• Email a copy of their approved thesis to our Student Affairs Manager, Candida Hall ( [email protected] ) in Applied Math for archival purposes prior to the deadline.
• Give an oral presentation of the honors thesis at an approved venue, usually at the senior thesis day in Applied Mathematics or in Biology.
• Complete two semesters of independent study courses while working on the honors thesis, such as APMA 1970/1971 or BIOL 1950/1960. One of these courses can be used to fulfill the research course requirement of the concentration, but they cannot be used to fulfill other concentration requirements. These extra independent study courses are included in the calculation of quality grades described above.
• Obtain permission to pursue honors from the department by submitting a completed Honors Declaration Form to our Student Affairs Manager, Candida Hall ( [email protected] ) by the deadline (usually at the beginning of the seventh semester). The honors declaration form requires signatures from the thesis advisor, second reader, and concentration advisor, as well as, a brief description of the proposed thesis research. It also requires a preliminary check of eligibility requirements, including the fraction of quality grades.
• APMA-CS concentrators can choose to pursue honors within either APMA or CS, but their primary thesis advisor must be in the department that they choose. Students wishing to do honors research with a non-APMA or CS advisor should contact the Directors of Undergraduate Studies in APMA and CS to discuss options.
• Students pursuing honors within APMA should follow the APMA requirements described above.
• Students pursuing honors within CS should follow the CS requirements and deadlines described here: http://cs.brown.edu/degrees/undergrad/concentrating-in-cs/honors/
• Students pursuing honors in CS must also email a copy of their approved thesis to our Student Affairs Manager, Candida Hall ( [email protected] ) in Applied Math for archival purposes.
• APMA-Econ concentrators can choose to pursue honors within either APMA or Econ, but their primary thesis advisor must be in the department that they choose.
• Students pursuing honors within APMA should follow the APMA requirements described above. 
• Students pursuing honors within Econ should follow the Econ requirements and deadlines described here: https://economics.brown.edu/academics/undergraduate/honors-and-capstones/thesis
• Students pursuing honors in Econ must also email a copy of their approved thesis to our Student Affairs Manager, Candida Hall ( [email protected] ) in Applied Math for archival purposes.

APMA Deadlines for Honors Program

Applied Mathematics Honors Declaration Form

Honors Thesis Guidelines:

Mathematical Content :

• Research problem: The thesis should be written on a mathematical problem or on an application that is approached using mathematical techniques. The thesis should demonstrate that the research question is significant and important.
• Thoroughness: The thesis should put the research problem into a broader context, address it in a convincing and thorough manner, and use mathematical approaches that are sound, feasible, and appropriate to the research problem.
• Depth: The thesis should involve mathematics at the level of 1000-level APMA courses and should demonstrate a solid understanding of the mathematics used in the thesis.

Writing Quality :

• Organization: The thesis should have a clear and coherent organization that effectively develops the central idea. There is an introduction that includes a clear statement of the research problem and an outline of the research method. Throughout the paper, arguments are presented clearly and in logical order, and the conclusions are precise and concise. The thesis does not contain awkward or unexpected transitions.
• Clarity: The thesis must be clearly written; in particular, the mathematical content must be clear to the intended audience. It should be clear from the writing that the student has a correct and complete understanding of the mathematical content of the thesis. Assertions are clearly stated and well supported.
• Citations: All sources used in the thesis should be referenced and cited completely and correctly: it should become clear what information from other sources has been integrated into the thesis and where that information came from. The bibliography should also contain an accurate and reasonably complete list of related works and papers.
• Grammar and Orthography: The thesis should be properly formatted and free of errors of grammar, spelling, and punctuation. The tone should be professional.

'Applicable Algebra reshaped my understanding of math'

Zhenghui Zhang: Mathematics

A&S Communications

Zhenghui Zhang

Mathematics  China

What was your favorite class and why?

There are many classes I have taken that are truly inspirational, and it is tough to say which one is my favorite. However, I do think MATH 3360 Applicable Algebra, taught by Prof. Marcelo Aguiar, greatly impacted my thinking about mathematics. It is the first proof-based mathematics class I took at Cornell, and Prof. Aguiar demonstrated how to derive rich, intricate mathematical theorems in algebra from clear, simple definitions. In the class, deduction was the nutrition that fertilized the growth of mathematical ideas, and I often found myself shocked to realize how far we have gone, given how little we started with. Moreover, the class has the perpetual power to reassure and energize me whenever I get stuck in research math: I will think back about how we do proofs in MATH 3360, calm myself down, restart thinking, and end up proving something! By reshaping my understanding of math, the class's influence is truly everlasting.

What is your main extracurricular activity and why is it important to you?

While during semesters I devote myself primarily to math, during breaks I tend to push myself out of my bubble by traveling to different countries. In the past, I have been to Mexico, Peru, the Dominican Republic, Haiti, etc., and it is a fantastic experience to witness different cultures/lifestyles and see gorgeous scenery! I really like traveling to Latin American countries, especially given that my comparative literature minor has helped me understand some of their special historical backgrounds through novels/scholarly texts. Specifically, one novel that I find extremely motivating is "One Hundred Years of Solitude." This is a reading from my comparative literature class, and I can really relate to the plot. By reading Latin American literature and experiencing life there, I can understand social issues inherent in these countries after colonization and have intellectual discussions with my friends by putting myself in a global perspective. I believe traveling/reading can help me see the broader, more complex parts of life that are undetectable/incomprehensible by rationality but are worth understanding through sympathy and love.

What have you accomplished as a Cornell student that you are most proud of?

Since junior year, I have been working on connecting the (co)homology of specific linear quotient spaces with their associated matroids under the supervision of Prof. Ed Swartz. Unlike short-term REU projects, this long-term project shows me the side of research that values resilience and patience. Working on this research is like gradually clearing the mud and finding the scattered gems bit by bit. So far, we have obtained excellent partial results like long exact sequences based on matroid deletion, contraction and computations of rational homologies through characteristic polynomials of dual matroids. Recently, our primary focus has been on computing the cohomology ring structures of certain linear quotients of spheres using equivariant cohomology and Smith's theory. We have a concrete conjecture for the ring structure, which has proven true for certain examples. I hope to continue working on this research project over the summer and potentially prove some nice theorems! This year, I began working on my senior thesis, which focuses on the ends of spaces and boundaries of groups under the supervision of Prof. Jason Manning. Shape theory, a variant of homotopy theory, can be used to study local ‘bad’ spaces that arise as the boundaries of groups, like the Sierpinski carpet or the Menger cube. I am currently writing my senior thesis, which will show some applications of shape theory in geometric group theory and low-dimensional topology!

What are your plans for next year? 

I will attend graduate school and start doing research in topology, an area of mathematics that studies spaces and their shapes. Specifically, I want to understand low-dimensional topology; i.e., 3-dimensional or 4-dimensional spaces. While spaces in dimensions 1, 2, >=5 are somehow well understood by mathematicians, 3 or 4-dimensional spaces, those closest to the space we live in (because the physical world we live in is 3-dimensional and the spacetime is 4-dimensional), are the hardest to comprehend. One of the most famous unsolved conjectures in this area is the 4-dimensional smooth Poincare conjecture, which boils down to understanding whether the 4-dimensional sphere admits an additional differentiable structure. Low-dimensional topology is a very active area of research. I want to contribute to this area in the future, using methods like gauge theory, floer homology and hyperbolic/symplectic techniques.

Every year, our faculty nominate graduating Arts & Sciences students to be featured as part of our Extraordinary Journeys series.  Read more about the Class of 202 4.

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Guidelines for Senior Theses in the Mathematics Department

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

Recent Senior Theses

Supervision

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

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

Standard venues for senior theses. One obvious way in which a senior thesis can be produced is through an independent reading course (MATH 490); another way is through an REU experience, either at Cornell or elsewhere. (If the REU work was accomplished or initiated elsewhere, a "local expert" will still be needed to supervise or "vouch for" the work as a senior thesis.) In yet a third way, a student may present a faculty member with a solution or partial solution to an interesting problem. In such cases, this could form the core of a senior thesis. Faculty are invited to encourage such work from their students.

Public Lecture

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

Submitting the Completed Thesis

The supervisor must approve the student's thesis. No later than April 15th, the student must submit a completed thesis to the thesis supervisor. If the supervisor asks the student to make changes, the student has until April 30th to do so. By April 30th, the student must give the supervisor two paper copies and an electronic copy of the thesis in final form. The electronic copy will be posted on the department's web site. [Students who expect to graduate in January must submit a completed thesis by November 15th and the final form by November 30th.]

Form of the Thesis

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

• The student's name and graduating class.
• The title of the senior thesis.
• The name of the faculty supervisor. (If there is more than one supervisor, list both. If one of the supervisors is not in the Mathematics Department, list the department and institution.)
• The date of completion of the thesis.

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

Merit of the Senior Thesis

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

Honors Consideration

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

Mathematics Library Collection of Senior Theses

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

Last modified: June 20, 2008

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Out of the Centre

Savvino-storozhevsky monastery and museum.

Zvenigorod's most famous sight is the Savvino-Storozhevsky Monastery, which was founded in 1398 by the monk Savva from the Troitse-Sergieva Lavra, at the invitation and with the support of Prince Yury Dmitrievich of Zvenigorod. Savva was later canonised as St Sabbas (Savva) of Storozhev. The monastery late flourished under the reign of Tsar Alexis, who chose the monastery as his family church and often went on pilgrimage there and made lots of donations to it. Most of the monastery’s buildings date from this time. The monastery is heavily fortified with thick walls and six towers, the most impressive of which is the Krasny Tower which also serves as the eastern entrance. The monastery was closed in 1918 and only reopened in 1995. In 1998 Patriarch Alexius II took part in a service to return the relics of St Sabbas to the monastery. Today the monastery has the status of a stauropegic monastery, which is second in status to a lavra. In addition to being a working monastery, it also holds the Zvenigorod Historical, Architectural and Art Museum.

Belfry and Neighbouring Churches

Located near the main entrance is the monastery's belfry which is perhaps the calling card of the monastery due to its uniqueness. It was built in the 1650s and the St Sergius of Radonezh’s Church was opened on the middle tier in the mid-17th century, although it was originally dedicated to the Trinity. The belfry's 35-tonne Great Bladgovestny Bell fell in 1941 and was only restored and returned in 2003. Attached to the belfry is a large refectory and the Transfiguration Church, both of which were built on the orders of Tsar Alexis in the 1650s.  

To the left of the belfry is another, smaller, refectory which is attached to the Trinity Gate-Church, which was also constructed in the 1650s on the orders of Tsar Alexis who made it his own family church. The church is elaborately decorated with colourful trims and underneath the archway is a beautiful 19th century fresco.

Nativity of Virgin Mary Cathedral

The Nativity of Virgin Mary Cathedral is the oldest building in the monastery and among the oldest buildings in the Moscow Region. It was built between 1404 and 1405 during the lifetime of St Sabbas and using the funds of Prince Yury of Zvenigorod. The white-stone cathedral is a standard four-pillar design with a single golden dome. After the death of St Sabbas he was interred in the cathedral and a new altar dedicated to him was added.

Under the reign of Tsar Alexis the cathedral was decorated with frescoes by Stepan Ryazanets, some of which remain today. Tsar Alexis also presented the cathedral with a five-tier iconostasis, the top row of icons have been preserved.

Tsaritsa's Chambers

The Nativity of Virgin Mary Cathedral is located between the Tsaritsa's Chambers of the left and the Palace of Tsar Alexis on the right. The Tsaritsa's Chambers were built in the mid-17th century for the wife of Tsar Alexey - Tsaritsa Maria Ilinichna Miloskavskaya. The design of the building is influenced by the ancient Russian architectural style. Is prettier than the Tsar's chambers opposite, being red in colour with elaborately decorated window frames and entrance.

At present the Tsaritsa's Chambers houses the Zvenigorod Historical, Architectural and Art Museum. Among its displays is an accurate recreation of the interior of a noble lady's chambers including furniture, decorations and a decorated tiled oven, and an exhibition on the history of Zvenigorod and the monastery.

Palace of Tsar Alexis

The Palace of Tsar Alexis was built in the 1650s and is now one of the best surviving examples of non-religious architecture of that era. It was built especially for Tsar Alexis who often visited the monastery on religious pilgrimages. Its most striking feature is its pretty row of nine chimney spouts which resemble towers.

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