Tai Melcher headshot

Tai Alexis Melcher

Associate Professor
Unit: College of Arts and Sciences
Department: Department of Mathematics
Office location and address
205 Kerchof Hall
141 Cabell Dr
Charlottesville, Virginia 22904
AS-MATH CAREER Heat Kernel Measures in Infinite Dimensions
Source: U.S. NSF - Directorate Math. & Physical Sciences
June 01, 2013 – May 31, 2022
AS-MATH 2017 Seminar on Stochastic Processes
Source: U.S. NSF - Directorate Math. & Physical Sciences
December 01, 2016 – November 30, 2017
Stochastic Processes in non-Euclidean spaces
Source: U.S. NSF - Directorate Math. & Physical Sciences
June 01, 2009 – May 31, 2013
MATH 1220: A Survey of Calculus II
Credits: 3
A second calculus course for business/biology/and social-science students. Topics include differential equations/infinite series/analysis of functions of several variables/analysis of probability density functions of continuous random variables. The course begins with a review of basic single-variable calculus. Prerequisite: MATH 1210 or equivalent; at most one of MATH 1220 and MATH 1320 may be taken for credit.
MATH 3100: Introduction to Probability
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
MATH 3250: Ordinary Differential Equations
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.
MATH 4110: Introduction to Stochastic Processes
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. Prerequisite: MATH 3100 or APMA 3100; and a knowledge of matrix algebra
MATH 4993: Independent Study
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.
MATH 7000: Seminar on College Teaching
Credits: 1–3
Discussion of issues related to the practice of teaching, pedagogical concerns in college level mathematics, and aspects of the responsibilities of a professional mathematician. Credits may not be used towards a Master's degree. Prerequisite: Graduate standing in mathematics.
MATH 7360: Probability Theory I
Credits: 3
Rigorous introduction to probability, using techniques of measure theory. Includes limit theorems, martingales, and stochastic processes. Prerequisite: 7310 or equivalent.
MATH 9995: Independent Research
Credits: 3–9
Independent Research
MATH 9998: Non-Topical Research, Preparation for Doctoral Research
Credits: 1–12
For doctoral research, taken before a dissertation director has been selected.
MATH 9999: Non-Topical 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.