A Sample Thesis in Mathematics

BY

YOUR NAME AS IT APPEARS ON YOUR EXAM REPORT
BS, University of Wisconsin, 2005
Another Prior degree, if Appropriate

THESIS [PhD candidates may use DISSERTATION here instead]

Submitted as partial fulfillment of the requirements

for the degree of DEGREE in OFFICIAL PROGRAM NAME

in the Graduate College of the

University of Illinois Chicago, YEAR

Chicago, Illinois

Defense Committee:
Name, Chair, Advisor
Name
Name
Name, Outside Members Need Affiliation Here

Accessibility Statement

This document is in an accessible EPUB format. A PDF version of this document is available at [URL] or can be obtained by contacting [contact details].

Dedication

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Preface

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Contents

1. 1 Introduction
   1. 1.1 Motivation
      1. 1.1.1 Historical context
      2. 1.1.2 Open questions
2. 2 Background
   1. 2.1 Group theory
3. 3 Main Results
   1. 3.1 A computer simulation
   2. 3.2 Second main result
4. 4 Vitae
5. A Technical Lemmas

List of Figures

1. 1.1 This is a torus
2. 1.2 The Snake Lemma

List of Tables

1. 1.1 Example Table

List of Abbreviations

Summary

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Chapter 1 Introduction

This is the introduction chapter. We cite some classic works [1, 2].

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Theorem 1.1.

This is a theorem

We reference Theorem 1.1.

University of Illinois Chicago.

1.1. Motivation

Figure 1.1. This is a torus

Figure 1.2. The Snake Lemma

1.1.1. Historical context

A brief overview of how the problem developed.

$${\int }_0^{1}f(x)𝑑x=2$$ (1.1)

How to solve (1.1)

1.1.2. Open questions

Some questions remain open for future work.

Note: I have not tested the accessibility of this table.

Monkeys	Lions
100	200

Table 1.1. Example Table

Chapter 2 Background

This chapter gives necessary background.

2.1. Group theory

Definition 2.1.

A group is a set $G$ with a binary operation satisfying closure, associativity, identity, and inverses.

Theorem 2.2.

Every finite subgroup of the multiplicative group of a field is cyclic.

Proof.

This is a standard result from algebra. ∎

Chapter 3 Main Results

Here we present the main contributions of the thesis.

3.1. A computer simulation

⬇

def factorial(n):

"""Compute the factorial of n recursively."""

if n == 0:

return 1

else:

return n * factorial(n - 1)

print(f"5! = {factorial(5)}")

3.2. Second main result

Another significant theorem.

Chapter 4 Vitae

For UIC this can be a full CV or a short version (e.g. half a page) with previoius degrees, work experience and publications.

Appendix A Technical Lemmas

Here we collect some supporting lemmas.