BH

Unit: College of Arts and Sciences

Department: Department of Mathematics

##### Office location and address

219 Kerchof Hall

141 Cabell Dr

Charlottesville,
Virginia
22904
##### Publications

##### Sponsored Awards

CAREER: L^{2}-invariants and entropy of square integrable functions managing division abbreviation:DMS

Source: U.S. National Science Foundation (NSF)

September 01, 2022 – August 31, 2027

Entropy theory methods in von Neumann algebras

Source: U.S. National Science Foundation (NSF)

June 01, 2020 – May 31, 2023

ECOAS 2020 - Participant Support

Source: U.S. National Science Foundation (NSF)

October 01, 2020 – September 30, 2022

Aspects of Sofic Entropy and Algebraic Actions

Source: U.S. National Science Foundation (NSF)

September 28, 2017 – May 31, 2020

##### Courses

Credits: 4

A rigorous development of the properties of the real numbers and the ideas of calculus including theorems on limits, continuity, differentiability, convergence of infinite series, and the construction of the Riemann integral. Students without prior experience constructing rigorous proofs are encouraged to take Math 3000 before or concurrently with Math 3310. Prerequisite: MATH 1320.

Credits: 3

This course covers the basic topology of metric spaces/continuity and differentiation of functions of a single variable/Riemann-Stieltjes integration/convergence of sequences and series. Prerequisite: MATH 3310 or permission of instructor.

Credits: 3

Differential and integral calculus in Euclidean spaces. Implicit and inverse function theorems, differential forms and Stokes' theorem. Prerequisites: MATH 2310 or MATH 2315; MATH 3351 or MATH 4651 or APMA 3080; and MATH 3310 or MATH 4310

Credits: 3

Review of topics from Math 3351 including vector spaces, bases, dimension, matrices and linear transformations, diagonalization; however, the material is covered in greater depth with emphasis on theoretical aspects. The course continues with more advanced topics including Jordan and rational canonical forms of matrices and introduction to bilinear forms. Additional topics such as modules and tensor products may be included. Prerequisite: MATH 3351

Credits: 3

This course provides a framework for the completion of a Distinguished Major Thesis, a treatise containing an exposition of a chosen mathematical topic. A faculty advisor guides a student through the beginning phases of the process of research and writing. Prerequisite: Acceptance into the Distinguished Major Program.

Credits: 3

This is the second semester of a two semester sequence for the purpose of the completion of a Distinguished Major Thesis. A faculty member guides the student through all phases of the process which culminates in an open presentation of the thesis to an audience including a faculty evaluation committee. Prerequisite: MATH 4900.

Credits: 1–3

Reading and study programs in areas of interest to individual students. For third- and fourth-years interested in topics not covered in regular courses. Students must obtain a faculty advisor to approve and direct the program.

Credits: 3

Introduces measure and integration theory. Prerequisite: MATH 5310 or equivalent.

Credits: 3

Studies the fundamental theorems of analytic function theory.

Credits: 3

Topics in the theory of operators on a Hilbert space and related areas of function theory.

Credits: 3

Studies the basic structure theory of groups, especially finite groups.

Credits: 1–12

For doctoral research, taken before a dissertation director has been selected.