# Past Projects

This page records past projects, including the mentor-mentee pairings, the topics they worked through, and the texts used.

# Fall 2019:

**Mentee**: Connor Lehmacher

**Mentor**: Julio Caceres

**Project Topic**: Functional Analysis

**Readings**:

**Mentee**: Jeffrey Cheng

**Mentor**: David Chan

**Project Topic**: Group Actions & Sylow’s Theorems

**Readings**: *A First Course in Abstract Algebra*, John B. Fraleigh

**Mentee**: Yujie Wang

**Mentor**: Ishan Ishan

**Project Topic**: Arzela-Ascoli Theorem

**Readings**: *Introduction to Topology and Modern Analysis*, G. F. Simmons; *Methods of Real Analysis*, Richard R. Goldberg

**Mentee**: Jackson Knox

**Mentor**: Hayden Jananthan

**Project Topic**: Descriptive Set Theory

**Readings**: *Classical Descriptive Set Theory*, Alexander S. Kechris

**Mentee**: Samuel Frank

**Mentor**: Andy Jarnevic

**Project Topic**: Fermat’s Little Theorem

**Readings**: *Number Theory*, George E. Andrews

**Mentee**: Kevin Gomez

**Mentor**: Zack Tripp

**Project Topic**: Dirichlet’s Theorem

**Readings**: *Introduction to Analytic Number Theory*, Tom M. Apostol

# Spring 2019:

(Co-organized by the Vanderbilt Math Club)

**Mentee**: Marcus Min

**Mentor**: Hayden Jananthan

**Project Topic**: Foundations of Mathematics

**Readings**: *A Tour Through Mathematical Logic*, Robert S. Wolf

**Mentee**: Yan Xu**
Mentor**: Sam Rizzo

**Project Topic**: Metric Spaces and Geometry

**Readings**: N/A

**Mentee**: Elijah Sheridan

**Mentor**: Robert Saskowski

**Project Topic**: Group Theory and Mathematical Physics

**Readings**: N/A

**Mentee**: Kevin Gomez

**Mentor**: Zack Tripp

**Project Topic**: Elementary and Analytic Number Theory

**Readings**: *Introduction to Analytic Number Theory*, Tom M. Apostol

**Mentee**: Connor Lehmacher

**Mentor**: Frank Wagner

**Project Topic**: Geometric Group Theory

**Readings**: *Algebra*, Michael Artin and *Topology*, James Munkres