AA

Unit: College of Arts and Sciences

Department: Department of Mathematics

##### Office location and address

227 Kerchof Hall

141 Cabell Dr

Charlottesville,
Virginia
22904
##### Publications

##### Sponsored Awards

AS-MATH Conference on Recent Mathematical Advances in Classical, Quantum & Statistical Mechanics

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

December 01, 2012 – November 30, 2014

Measures on function spaces, statistical mechanics and the rigorous renormalization group

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

July 01, 2009 – June 30, 2013

##### Courses

Credits: 3

Introduces fundamental concepts/techniques of probability/the theory of randomness. Focuses on problem solving/understanding key theoretical ideas. Topics include sample spaces combinatorial analysis/discrete and continuous random variables/classical distributions/expectation/Chebyshev's inequality/independence/central limit theorem/conditional probability/generating functions. Prerequisite: MATH 1320. Recommended: knowledge of double integrals.

Credits: 4

Introduces the methods, theory, and applications of differential equations. Includes first-order, second and higher-order linear equations, series solutions, linear systems of first-order differential equations, and the associated matrix theory. May include numerical methods, non-linear systems, boundary value problems, and additional applications. Prerequisite: MATH 1320 or its equivalent.

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

Topics in probability selected from Random walks, Markov processes, Brownian motion, Poisson processes, branching processes, stationary time series, linear filtering and prediction, queuing processes, and renewal theory. Prerequisites: MATH 3100 and MATH 3351.

Credits: 3

Geometric study of curves/surfaces/their higher-dimensional analogues. Topics vary and may include curvature/vector fields and the Euler characteristic/the Frenet theory of curves in 3-space/geodesics/the Gauss-Bonnet theorem/and/or an introduction to Riemannian geometry on manifolds. Prerequisites: MATH 2310 and MATH 3351 or instructor permission.

Credits: 3

Topics include abstract topological spaces & continuous functions/connectedness/compactness/countability/separation axioms. Rigorous proofs emphasized. Covers myriad examples, i.e., function spaces/projective spaces/quotient spaces/Cantor sets/compactifications. May include intro to aspects of algebraic topology, i.e., the fundamental group. Prerequisites: MATH 2310 or 2315 or APMA 2120 and MATH 3315 or MATH 3351 or MATH 4651 or APMA 3080

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: 3

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

Credits: 3

Additional topics in measure theory. Banach and Hilbert spaces, and Fourier analysis. Prerequisite: MATH 7310, 7340, or equivalent.

Credits: 3

Studies the basic principles of linear analysis, including spectral theory of compact and selfadjoint operators. Prerequisite: MATH 7340 and 7310, or equivalent.

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.