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