Special Topics Courses

Fall 2021

MA 493 Sec 001/ MA 591 Sec 003
Instructor: Tye Lidman
Title: Math for Social Justice

Description: In this class, we will study how mathematics can be applied to social justice issues. Potential topics, depending on the interests of the class, may include analyzing political districting (gerrymandering), modeling social change, and studying human trafficking. In the process, we will learn and develop significant mathematical theory in the areas relevant to the issues, such as metric geometry and graph theory. Prerequisites: MA225 and a willingness to engage in discussions around social issues. For math PhD students, this class will not count towards the 30 credit coursework requirement for math or applied math, but can be used for the 72 hour total credit requirement.

MA 591  Sec 002
Instructor:  Naihuan Jing
Title: Math Foundation of Quantum Computation

Description: Quantum computation and quantum information has been an active and far-reaching interdisciplinary research area recently. In 1994, Peter Shor shocked the scientific world with a quantum algorithm of factorizing integers that could potentially break the NP barrier in the usual computer science. In theory quantum computer is based on quantum mechanical principles to process information and computation. Though quantum computers have not be realized in reality, many experts agree that we are probably at the dawn of new era of quantum computers.

The course intends to introduce students to basic mathematical foundation of quantum computation to prepare for further research in the area. The course’s prerequisites are kept at minimum, as I will review the needed materials in the class, so the class should be accessible to undergraduate and beginning graduate students.

MA 591 Sec 004
Instructor:  Mette Olufsen
Title: Introduction to Fluid DynamicsDescription:  This course will offer an introduction to fluid dynamics and its applications in biology. The course will study fluid mechanics from a mathematical perspective, including examples from biological applications. The equations of fluid mechanics will be derived from first principles, and areas of active research will be discussed. The course is suitable for advanced undergraduate students and graduate students in mathematics, physics, engineering, and mathematical biology. Students will work on an independent project that can be taken from their research. Topics will include physical concepts such as viscosity, vorticity, viscous flow, shock waves, wave propagation, stokes flow, boundary layers, and potential flow. Biological applications will include swimming, flying, and blood flow in networks of arteries.

Background needed: Basic understanding of mechanics, vector calculus, matrices, ordinary differential equations. Other mathematics and physics will be reviewed as needed.
MA797 Sec 001:
Instructor: Patrick Combettes

Title: Convex Analysis
Description: Convex analysis was founded in the 1960s. It constitutes one of the main pillars of nonlinear analysis and it is an indispensable tool for pure and applied
mathematicians. Convex analysis has applications in various fields of mathematics and its applications: calculus of variations, optimization, machine learning, control theory, information theory, statistics, signal and image processing, nonlinear PDEs,
probability theory, transportation theory, mechanics, mean field games, etc. The objective of the course is to provide the main bases and techniques of convex analysis, discuss convex optimization algorithms, and explore concrete applications.

MA 810 Sec 001
Instructor:  Radmila Sazdanovic
Title: Advanced topics in algebraic topology and its applications

Course description:  Cohomology, homotopy groups, fiber bundles, and homological algebra are essential topics in topology. As tools, they are especially relevant to areas such as categorification, topological combinatorics, algebraic geometry, differential geometry, physics, and topological data analysis. Additional topics will be determined based on students’ interest and include, but are not limited to: Topological Quantum Field theories, Khovanov-type link homology theories, categorification, and topological data analysis and its relations to ML and DNN.

Course prerequisites:  MA 753 or equivalent.
Course materials: Algebraic Topology by Allen Hatcher and a collection of survey and recent research articles.