Directed Reading Program
# Indiana University Mathematics

## Past reading projects

### Spring 2022

**Mentee:** Jacob Renner

**Mentor:** Nathan Lowry

**Subject:** Elliptic Curves

**Book:** Rational Points over Elliptic Curves by Joseph Silverman and John Tate

**Mentee:** Enoch Ayeh

**Mentor:** Alex Glickfield

**Subject:** Invertibility in Infinite Dimensions

**Book:** The Lebesgue Integral for Undergraduates by William Johnston

**Mentee:** Jessica Missey

**Mentor:** Yi-Lin Lee

**Subject:** Knot Colorability

**Book:** Topology by James Munkres

**Mentee:** Nick Adkins

**Mentor:** Tom Yerger

**Subject:** Differential Geometry via Moving Frames and Exterior Differential Systems

**Book:** Cartan for Beginners: Differential Geometry via Moving Frames and Exterior Differential Systems by Thomas Ivey and Joseph Landsberg

**Mentee:** Tianshu Yu

**Mentor:** Kai Smith

**Subject:** Lie Groups, Lie Algebras, and Matrix Exponentiation

**Book:** Lie Groups, Lie Algebras, and Representations by Brian Hall

### Spring 2018

**Mentee**: Alexandra Embry

**Mentor**: Emily Rudman

**Subject**: Introduction to Ciphers

**Book**: Introduction to Cryptography by Johannes Buchmann

**Mentee**: Xuan Li

**Mentor**: Raghavendra Venkatraman

**Subject**: Some Theorems from Elementary Number Theory

**Book**: Topics from the Theory of Numbers by Emil Grosswald

**Mentee**: Nathanial Lowry

**Mentor**: Dylan Spence

**Subject**: A Tour of Algebraic Geometry

**Book**: Algebraic Geometry: A Problem Solving Approach by Thomas Garrity

**Mentee**: Elio Seni

**Mentor**: Cong Zhou

**Subject**: An Interpretation of Black-Scholes Formula by Change of Measure

**Book**: Measures, Integrals, and Martingales by Rene L. Schilling

**Mentee**: Derek Wenning

**Mentor**: Brady Thompson

**Subject**: Having FUN with FUNctional Analysis

**Book**: A Course in Functional Analysis by John B. Conway

### Fall 2017

**Mentee**: Lu Li

**Mentor**: Brady Thompson

**Subject**: Queuing Theory

**Book**: Introduction to Queuing Theory by B. V. Gnedenko

**Mentee**: Li Liu

**Mentor**: Samantha Allen

**Subject**: The Mathematics of PageRank

**Book**: Graph Theory with Applications to Engineering and Computer Science by Narsingh Deo

**Mentee**: Jue Wang

**Mentor**: Hongming Nie

**Subject**: Valuations

**Book**: Non-Archimedean Operator Theory by Toka Diagana and François Ramaroson

**Mentee**: Sijie Wang

**Mentor**: Eduardo Fischer

**Subject**: The Equivalence of Simplicial and Singular Homology

**Book**: Algebraic Topology by Allen Hatcher

### Spring 2017

**Mentee**: Nanjie Chen

**Mentor**: Didac Martinez-Granado

**Subject**: A Study of the Hex Game via the Fixed Point Theorem

**Mentee**: Tang Jiawei

**Mentor**: Calvin Woo

**Subject**: Towards Infinity-Category Enrichment

**Book**: Categorical Homotopy Theory by Emily Riehl

**Mentee**: Manasse Kwete

**Mentor**: Yining Zhang

**Subject**: Lie Algebra, a Short Introduction

**Book**: Lie Algebras of Finite and Affine Type by Roger Carter

**Mentee**: Elio Seni

**Mentor**: Kursat Sozer

**Subject**: Introduction to Manifolds

**Book**: An Introduction to Manifolds by Loring W. Tu

**Mentee**: Derek Wenning

**Mentor**: Brady Thompson

**Subject**: Monopoly and Markov Chains

**Book**: An Introduction to Markov Processes by Daniel W. Stroock

### Fall 2016

**Mentee**: Christopher Audretsch

**Mentor**: Kin Wai Chan

**Subject**: The Prime Number Theorem

**Book**: Introduction to Analytic Number Theory by Tom M. Apostol

**Mentee**: Taylor Ball

**Mentor**: Ryan Vitale

**Subject**: Rings of Invariants

**Book**: The Symmetric Group: Representations, Combinatorial Algorithms, and Symmetric Functions by Bruce E. Sagan

**Mentee**: Anthony Coniglio

**Mentor**: Anthony Conway

**Subject**: Computing Lower Bounds for the Splitting Number of Links

**Book**: An Introduction to Knot Theory by W.B. Raymond Lickorish

**Mentee**: William Hargis

**Mentor**: Xuqiang Qin

**Subject**: Introduction to Representation Theory

**Book**: Linear Representations of Finite Groups by Jean-Pierre Serre

**Mentee**: Cally McGee

**Mentor**: Josh Edge

**Subject**: Graph Theory and the Bridges of Königsberg

**Book**: Combinatorics and Graph Theory by John M. Harris, Jeffry L. Hirst and Michael J. Mossinghoff

### Spring 2016

**Mentee**: Evgueni Alexeev

**Mentor**: Calvin Woo

**Subject**: Differential forms on smooth manifolds, with applications

**Book**: Geometry of Differential Forms by Shigeyuki Morita

**Mentee**: Elizabeth Duteau

**Mentor**: Pawan Patel

**Subject**: How Markov chains revolutionized the way we surf the web

**Book**: Markov Chains: Gibbs Fields, Monte Carlo Simulation, and Queues by Pierre Bremaud

**Mentee**: Zachary Hay

**Mentor**: Maxime Scott

**Subject**: Showing the equivalence of the hypothesis of cardinal comparability and the axiom of choice

**Book**: Notes on Set Theory by Yiannis Moschovakis

**Mentee**: Sam McKay

**Mentor**: Patrick Haggerty

**Subject**: Hyperbolic geometry in knot theory

**Books**: Knots and Links by Dale Rolfsen

The Knot Book by Colin Adams

**Mentee**: Andrew Vander Werf

**Mentor**: David Sprunger

**Subject**: A look at hyperreals

**Book**: Lectures on the Hyperreals by Robert Goldblatt

### Fall 2015

**Mentee**: Chase Abram

**Mentor**: Ranjan Rohatgi

**Subject**: Playing games with numbers

**Book**: On Numbers and Games by John Conway

**Mentee**: Taylor Ball

**Mentor**: Ryan Vitale

**Subject**: Proving Euclidean Geometry by Gröbner Bases

**Book**: Sheaves in Geometry and Logic: A first introduction to topos theory by Saunders Mac Lane and Ieke Moerdijk

**Mentee**: Beixi Lei

**Mentor**: Wai Kit Lam

**Subject**: Mathematical finance

**Book**: Options, Futures, and Other Derivatives by John Hull

**Mentee**: Jordan Lenchitz

**Mentor**: Ash Lightfoot

**Subject**: Low-dimensional musical pitch and chord spaces

**Books**: A Geometry of Music: Harmony and Counterpoint in the Extended Common Practice (Oxford Studies in Music Theory) by Dmitri Tymoczko

Generalized Musical Intervals and Transformations by David Lewin

**Mentee**: Sam Pilgrim

**Mentor**: Nikhil Gupta

**Subject**: The fundamental group

**Book**: Topology by James Munkres

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