All inquiries about our graduate program are warmly welcomed and answered daily:

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# Graduate Courses, Summer 2021-Spring 2022

## Contact

## Summer 2021

**For Detailed Course Outlines, click on ***course
numbers.*

*course numbers.*

## 7999-1 Problem Lab in Algebra—practice for PhD Qualifying Exam in Algebra.

- Instructor:
- Prerequisite:
- Text:

## 7999-2 Problem Lab in Analysis—practice for PhD Qualifying Exam in Analysis.

- Instructor:
- Prerequisite:
- Text:

## 7999-3 Problem Lab in Topology—practice for PhD Qualifying Exam in Topology.

- Instructor:
- Prerequisite:
- Text:

## 7999-n Assorted Individual Reading Classes

## 8000-n Assorted Sections of MS-Thesis Research

## 9000-n Assorted Sections of Doctoral Dissertation Research

## Fall 2021

**For Detailed Course Outlines, click on
***course numbers.*

*course numbers.*

Core courses and Breadth courses are listed in **bold**.

## 4997-1 Vertically Integrated Research:

- Instructor:
- Prerequisite:
- Text:

## 4997-2 Vertically Integrated Research:

- Instructor:
- Prerequisite:
- Text:

## 7001 Communicating Mathematics I. Prof. Oxley.

- Instructor: Prof. Oxley.
- Prerequisite: Consent of department. This course is required for all
incoming graduate students. It is a
*lab course*meeting for an average of two hours per week throughout the semester for one-semester-hour's credit. - This course provides practical training in the teaching of mathematics at
the pre-calculus level, how to write mathematics for publication, and treats
other issues relating to mathematical exposition.
*Communicating Mathematics I and II*are designed to provide training in all aspects of communicating mathematics. Their overall goal is to teach the students how to successfully teach, write, and talk about mathematics to a wide variety of audiences. In particular, the students will receive training in teaching both pre-calculus and calculus courses. They will also receive training in issues that relate to the presentation of research results by a professional mathematician. Classes tend to be structured to maximize discussion of the relevant issues. In particular, each student presentation is analyzed and evaluated by the class.

## 7210 **Algebra I.** Prof. Sage.

- Instructor: Prof. Sage.
- Prerequisite:
- Text:

## 7260 Homological Algebra. Prof. Achar

- Instructor: Prof. Achar
- Prerequisite:
- Text:

## 7290 Hopf Algebras & Finite Groups. Prof. Ng

- Instructor: Prof. Ng
- Prerequisite:
- Text:
- Hopf algebras, sometimes also known as quantum groups, are generalizations of groups and Lie algebras. Their representation categories are tensor categories which have many important applications to areas in mathematics and physics. In this course, we present an introduction to the theory of Hopf algebras and their representations. The basic theory of representations of finite groups will be introduced as motivation at the beginning of the course, and the course will be a great continuation of Math 7211. Prerequisites are some notions on finite groups and rings, and a good knowledge of linear algebra covered in Math 7210 or equivalent.

## 7311 **Real Analysis I.** Prof. Olafsson.

- Instructor: Prof. Olafsson.
- Prerequisite:
- Text:

## 7350 **Complex Analysis.** Prof. Antipov.

- Instructor:
- Prerequisite: Prof. Antipov.
- Text:

## 7360 **Probability Theory.** Prof. Chen.

- Instructor: Prof. Chen.
- Prerequisite:
- Text:

## 7365 Applied Stochastic Analysis. Prof. Ganguly.

- Instructor: Prof. Ganguly.
- Prerequisite:
- Text:

## 7380 Introduction to Applied Math. Prof. Shipman

- Instructor: Prof. Shipman.
- Prerequisite:
- Text:

## 7384 Topics in Material Science: Prof. Lipton.

- Instructor: Prof. Lipton.
- Prerequisite:
- Text:

## 7386 Partial Differential Equations. Prof. Bulut.

- Instructor: Prof. Bulut.
- Prerequisite:
- Text:

## 7390 Topics in Convex and Stochastic Optimization. Prof. Zhang.

- Instructor: Prof. Zhang.
- Prerequisite: Math 2057 Multidimensional Calculus; Math 2085 Linear Algebra
- Text: Class Notes
- Convex and stochastic optimization have played important role in modern optimization. This course will focus on the theory and algorithm development for solving convex optimization problems and optimization problems with stochastic features. Tentative topics include Convex sets, Convex functions, Duality theory, gradient and stochastic gradient methods for solving convex and nonconvex optimization problems.

## 7490 Matroid Theory. Prof. Oxley

- Instructor: Prof. Oxley.
- Prerequisites: Permission of the Department
- Text: J. Oxley,
*Matroid Theory, Second edition,*Oxford, 2011. - What is the essence of the similarity between forests in a graph and linearly independent sets of columns in a matrix? Why does the greedy algorithm produce a spanning tree of minimum weight in a connected graph? Can one test in polynomial time whether a matrix is totally unimodular? Matroid theory examines and answers questions like these.
This course will provide a comprehensive introduction to the basic theory of matroids. This will include discussions of the basic definitions and examples, duality theory, and certain fundamental substructures of matroids. Particular emphasis will be given to matroids that arise from graphs and from matrices.

## 7510 **Topology I.** Prof. Dasbach.

- Instructor: Prof. Dasbach.
- Prerequisite:
- Text:

## 7520 Algebraic Topology. Prof. Vela-Vick.

- Instructor: Prof. Vela-Vick.
- Prerequisite:
- Text:

## 7590 Arrangements and Configuration Spaces. Prof. Bibby.

- Instructor: Prof. Bibby
- Prerequisite:
- Text:

## 7999-n Assorted Individual Reading Classes

## 8000-n Assorted Sections of MS-Thesis Research

## 9000-n Assorted Sections of Doctoral Dissertation Research

## Spring 2022

**For Detailed Course Outlines, click on
***course numbers.*

*course numbers.*

Core courses and Breadth courses are listed in **bold**.

## 4997-1 Vertically Integrated Research:

- Instructor:
- Prerequisite:
- Text:

## 4997-2 Vertically Integrated Research:

- Instructor:
- Prerequisite:
- Text:

## 7002 Communicating Mathematics II. Prof. Oxley.

- Instructor: Prof. Oxley.
- Prerequisite:
- Text:

## 7211 **Algebra II.** Prof. Long.

- Instructor: Prof. Long.
- Prerequisite:
- Text:

## 7220 Commutative Algebra &: Algebraic Geometry. Prof. Hoffman

- Instructor: Prof. Hoffman.
- Prerequisite:
- Text:

## 7230 Topics in Number Theory. Prof. Tu

- Instructor: Prof. Tu.
- Prerequisite:
- Text:

## 7320 **Ordinary Differential Equations.** Prof. Estrada

- Instructor: Prof. Estrada.
- Prerequisite:
- Text:

## 7330 **Functional Analysis.** Prof. He.

- Instructor:
- Prerequisite: Prof. He.
- Text:

## 7366 Stochastic Analysis. Prof. Sundar.

- Instructor: Prof. Sundar.
- Prerequisite:
- Text:

## 7380 Topics in **C**^{*} algebras. Prof. Olafsson.

- Instructor: Prof. Olafsson.
- Prerequisite:
- Text:

## 7384 Topics in Material Science: Prof. Shipman.

- Instructor: Prof. Shipman.
- Prerequisite:
- Text:

## 7390-1 Topics in Analysis. Prof. Walker.

- Instructor: Prof. Walker.
- Prerequisite:
- Text:

## 7390-2 Topics in Elliptic Partial Differential Equations. Prof. Zhu.

- Instructor: Prof. Zhu.
- Prerequisite:
- Text:

## 7390-3 Several Complex Variables. Prof. Rubin.

- Instructor: Prof. Rubin.
- Prerequisite:
- Text:

## 7410 **Graph Theory.** Prof. Oporowski.

- Instructor: Prof. Oporowski.
- Prerequisite:
- Text:

## 7490 Combinatorial Optimization. Prof. Ding

- Instructor: Prof. Ding.
- Prerequisite:
- Text:

## 7512 **Topology II.** Prof. Dani.

- Instructor: Prof. Dani.
- Prerequisite:
- Text:

## 7550 **Differential Geometry.** Prof. Baldridge.

- Instructor: Prof. Baldridge.
- Prerequisite:
- Text:

## 7590-1 Geometric Topology: Braids. Prof. Cohen.

- Instructor: Prof. Cohen.
- Prerequisite:
- Text:

## 7590-2 Geometry and Physics. Prof. Zeitlin

- Instructor: Prof. Zeitlin.
- Prerequisite: Some basic knowledge of differential geometry: calculus on manifolds, differential forms, Lie groups (MATH 7550 is more than enough).
- Text: I will distribute my own notes.
- This course is a rigorous introduction to quantum field theory aimed at mathematicians. The primary target is path integral techniques, including Feynman diagrams, Batalin-Vilkovisky (BV) formalism, localization. The goal of the course is to understand basic notions needed to read papers in Quantum Field Theory and String Theory. The material will be also useful for students in the physics department interested in High Energy Physics.

## 7710 **Numerical Linear Algebra.** Prof. Sung.

- Instructor: Prof. Sung.
- Prerequisite:
- Text: