Fall 2020

Convex Optimization

    • Instructor: Kevin Bui

    • Students: Abhishek Devarajan and Xinhan Huang

    • Book: Convex Optimization by Boyd and Vandenberghe.

Introduction to Graph Theory

  • Instructor: Zhijian Li

  • Students: Anthony Chen and Hursh Naik

  • Book: Invitation to Discrete Mathematics by Jiří Matoušek

Introduction to Ultrafilters in Analysis

  • Instructor: Jennifer Pi

  • Students: Mason Shurman and Joseph Yecco

  • Notes: "Ultrafilters Throughout Mathematics" by Isaac Goldbring

Mathematical Modeling of Cancer Dynamics

  • Instructor: Jesse Kreger

  • Students: Jingyi Wang and Xingdian Zhao

  • Book: Dynamics of Cancer (Mathematical Foundations of Oncology) by Dominik Wodarz and Natalia Komarova

Mathematics and Theory of Computation

  • Instructor: Adam Marks

  • Students: Jaylin Mantanic and Junyu Sui

  • Books: Computational Complexity, A Modern Approach by Sanjeev Arora and Boaz Barak and Mathematics and Computation by Avi Widgerson

Modular Forms and Elliptic Curves

  • Instructor: Shichen Tang

  • Students: Lorenzo Alesiani and Tianshu Chu

  • Books: A First Course in Modular Forms by Diamond and Shurman and A Course in Arithmetic by Serre

Numerical Modeling of Bio Fluid Dynamics

  • Instructor: Jinghao Chen

  • Students: Songchen Xie and Hongyang Cai

  • Book and Notes: Finite Difference Schemes and Partial Differential Equations by John Strikwerda and "A one-dimensional model of cell diffusion and aggregation, incorporating volume filling and cell-to-cell adhesion" by K. Anguige and C. Schmeiser

Quadratic Forms

  • Instructor: Luke Fredericks

  • Student: Lori Cha

  • Book: Primes of the form x^2+ny^2 by David Cox

Random Matrix Theory

  • Instructor: John Peca-Medlin

  • Students: Dajun Xu and Zongjie Yin

  • Notes: "Topics in Random Matrix Theory" by Terry Tao

Similarities in Number Theory Over the Integers and Function Fields

  • Instructor: Hua Lin

  • Students: Sylar Chow

  • Book: Number Theory over Function Fields by M. Rosen

Solving Systems of Polynomials Using Gröbner Bases

  • Instructor: Kelly Isham

  • Students: Anh Hoang and Lily McBeath

  • Book: Ideals, Varieties, and Algorithms by Cox, Little, and O'Shea

Topics in Logic and Model Theory

  • Instructor: Jessica Schirle

  • Student: Arturo Pantoja

  • Book and Notes: Model Theory by David Marker and "Mathematical Logic" by Anush Tserunyan