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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