ZG

Unit: College of Arts and Sciences

Department: Department of Mathematics

##### Office location and address

331 Kerchof Hall

141 Cabell Dr

Charlottesville,
Virginia
22904
##### Publications

##### Sponsored Awards

Toward criticality of the Navier-Stokes regularity problem

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

July 01, 2020 – June 30, 2023

AS-MATH Turbulent cascades and dissipation in the 3D Navier-Stokes model

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

September 01, 2015 – March 31, 2019

AS-MATH Nonlinear PDE in Spaces of Analytic Functions

Source: University of Bergen

January 01, 2012 – December 31, 2015

AS-MATH Turbulent Cascades and Regularity Theory in Physical Scales of 3D Incompressible Fluid Flows

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

September 01, 2012 – August 31, 2015

Analysis, Control and Inverse Theory of Fluids, Waves, Materials Structures, and Their Interactions

Source: U.S. DOD - Air Force - Afosr

July 01, 2012 – June 30, 2015

AS-MATH Zachary Bradshaw VSGC Fellowship 2012-13

Source: Virginia Space Grant Consortium

June 01, 2012 – May 31, 2014

##### Courses

Credits: 3

Introduces fundamental ideas of probability, the theory of randomness. Focuses on problem solving and understanding key theoretical ideas. Topics include sample spaces, counting, random variables, classical distributions, expectation, Chebyshev's inequality, independence, central limit theorem, conditional probability, generating functions, joint distributions. Prerequisite: MATH 1320 or equivalent. Strongly recommended: MATH 2310

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: 3

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 is a beginning course in partial differential equations/Fourier analysis/special functions (such as spherical harmonics and Bessel functions). The discussion of partial differential equations will include the Laplace and Poisson equations and the heat and wave equations. Prerequisites: MATH 3250 and either MATH 3351 or MATH 4210.

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

Studies the fundamental theorems of analytic function theory.

Credits: 1–12

For master's thesis, taken under the supervision of a thesis director.

Credits: 3

Harmonic Analysis and PDEs seminar

Credits: 1–12

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

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.