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Catalog Course Descriptions

View the Course Descriptions from the University Catalog

Spring 2024 Graduate Courses

  • MATH 4510/5700-Abstract Algebra II & Selected Topics in Contemporary Mathematics: William Cherry (Syllabus Math 4510/5700)

  • MATH 5290-Numerical Methods: Yanyan He (MATH 5290)

  • MATH 6010-Logic and Foundations: John Krueger

    • The topic of this course is set theory, and more specifically, the theory of trees. After reviewing some basic set theory, including ordinal and cardinal numbers, cardinal arithmetic, and club and stationary sets, we concentrate on the subject of trees, linear orders, and the connections of these objects with topology. We will study Aronszajn, Suslin, and Kurepa trees and lines, and set theoretic principles such as Martin's axiom and diamond principles which have implications concerning the existence of such trees and their properties. Prerequisites of the course include some familiarity with ordinal and cardinal numbers and Math 5610. Required work will include solving homework problems and presenting solutions in class. There will be no exams. Grading is based on attendance and homework.

  • MATH 6110-Topics in Analysis: Kirill Lazebnik

    • This course will explore some phenomena in the field known as "complex dynamics". One starting point is the following definition. Let f_c(z):=z^2+c for z and c complex numbers, and consider what happens when iterating the function f_c at a point z, in other words consider the sequence (z^2+c, (z^2+c)^2+c, ((z^2+c)^2+c)^2+c, …). The set of z having the property that perturbing z slightly results in the behavior of the above sequence changing predictably is known as the Fatou set, and the complement of the Fatou set is known as the Julia set (making this precise is not too difficult). The Fatou and Julia sets exhibit fractal behavior, and they depend on the parameter c in a surprisingly intricate manner. We will attempt to explain this dependence from more or less first principles, incorporating a diverse set of tools along the way.

  • MATH 6710-Applied Math (Bioinformatics): Serdar Bozdag

    • In this course, machine learning methods on graphs, particularly biological graphs will be covered. Graphs are natural data structures to represent multiple data modalities, which are currently abundant in multiple domains such as social networks and biology. We will cover shallow machine learning methods such as DeepWalk, node2vec and deep learning methods such as Graph Neural Networks and Graph Attention Networks. Discussion on more advanced methods for more complex graphs such as multiplex heterogeneous graphs will be discussed. Prior knowledge in programming and machine learning is highly recommended. No prior knowledge in biology is needed.

Fall 2024 Graduate Courses

Math 6510 - Representation Theory Charles Conley

  • See information here

Math 6810 - Probability Pieter Allaart

Overview: The purpose of this course is to explore the interface between probability theory and fractal geometry. The first four weeks or so will be spent on a rigorous development of probability based on measure theory. Topics will include the law of large numbers, conditional expectation and martingales. In the middle part of the course, we will introduce Hausdorff dimension, iterated function systems, self-similar sets (including the ternary Cantor set) and their generalizations. We will then learn some important probabilistic techniques for computing the Hausdorff dimension of these sets. In the third part of the course, probability and fractal geometry come together in the study of random fractals, with randomized versions of the classical Weierstrass function as one of the main examples. The course ends with a detailed study of the various fractal properties of Brownian motion.

Text: There is no required text for this course, but recommended reading includes:

  • P. Billingsley, Probability and Measure (3rd edition), Wiley
  • K. Falconer, Fractal geometry. Mathematical foundations and applications (2nd or 3rd edition), Wile

Prerequisites: Math 5320 (measure theory). Some knowledge of undergraduate-level probability is helpful, but not required.

Grading: Your grade will be based on attendance, active class participation and one or two 30-50 minute presentations, depending on the number of students in the class.

Breadth requirement: This course satisfies the Analysis breadth requirement.