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Unit: College of Arts and Sciences

Department: Department of Mathematics

##### Office location and address

323 Kerchof Hall

141 Cabell Dr

Charlottesville,
Virginia
22904
##### Publications

##### Sponsored Awards

AS-MATH Canonical bases, categorification, and modular representations

Source: U.S. NSF - Directorate Math. & Physical Sciences

June 01, 2017 – May 31, 2020

AS-MATH Representation theory and quantum symmetric pairs

Source: U.S. NSF - Directorate Math. & Physical Sciences

June 15, 2014 – May 31, 2017

Representations of Lie Superalgebras, Hecke Algebras and Affine Algebras

Source: U.S. NSF - Directorate Math. & Physical Sciences

August 15, 2011 – July 31, 2014

##### Courses

Credits: 4

Covers basic concepts with an emphasis on writing mathematical proofs. Topics include logic, sets, functions and relations, equivalence relations and partitions, induction, and cardinality. Prerequisite: Math 1320; and students with a grade of B or better in Math 3310, 3354, or any 5000-level Math course are not eligible to enroll in Math 3000.

Credits: 3

Surveys major topics of modern algebra: groups, rings, and fields. Presents applications to areas such as geometry and number theory; explores rational, real, and complex number systems, and the algebra of polynomials. Students without prior experience constructing rigorous proofs are encouraged to take Math 3000 before or concurrently with Math 3354. Prerequisite: MATH 1320.

Credits: 3

Includes combinatorial principles, the binomial and multinomial theorems, partitions, discrete probability, algebraic structures, trees, graphs, symmetry groups, Polya's enumeration formula, linear recursions, generating functions and introduction to cryptography, time permitting. Prerequisite: MATH 1320 and a proof-based course (MATH 3000, MATH 3310 or MATH 3354) or instructor permission.

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 will introduce students to the techniques and methods of mathematical research. Students will independently work with mathematical literature on a topic assigned by the instructor and present their findings in various formats (presentation, paper etc.).

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

Further topics in algebra.

Credits: 3

Studies basic results concerning Lie groups, Lie algebras, and the correspondence between them.

Credits: 3

Studies the foundations of representation and character theory of finite groups.

Credits: 3–9

Independent Research

Credits: 1–12

The Mathematics Colloquium is held weekly, the sessions being devoted to research activities of students and faculty members, and to reports by visiting mathematicians on current work of interest. For doctoral dissertation, taken under the supervision of a dissertation director.