William H. Barker
Isaac Henry Wing Professor of Mathematics
Searles Science Building - 105
Teaching this semester
MATH 2020. Introduction to Mathematical Reasoning
An introduction to logical deductive reasoning and mathematical proof through diverse topics in higher mathematics. Specific topics include set and function theory, modular arithmetic, proof by induction, and the cardinality of infinite sets. May also consider additional topics such as graph theory, number theory, and finite state automata.
MATH 2351. Lie Groups and Lie Algebras
A Lie group is a smooth n-dimensional surface with a multiplication that is differentiable. Allowing for a theory of "continuous symmetry" of objects, Lie groups and their associated algebras are central tools of modern mathematics and theoretical physics. Although highly sophisticated in general, the most common Lie groups are groups of matrices under matrix multiplication. Matrix groups can be studied with only a background in multivariable calculus and linear algebra. Basic course topics include, among others, real and complex matrix Lie groups and Lie algebras, one-parameter subgroups, the exponential map, the adjoint representations, and applications in geometry and physics.
- A.B. Binghamton University
- Ph.D. Massachusetts Institute of Technology
- Geometry, Lie Theory, Analysis
Books, Reports, and Monographs
Continuous Symmetry: From Euclid to Klein
William Barker and Roger Howe
Supplemental Materials (Errata, Revisions, Course Resources)
Review of Continuous Symmetry from MAA Reviews.
Curriculum Foundations Project: Voices of the Partner Disciplines
The individual reports are available for downloading
CUPM Curriculum Guide 2004
Harmonic Analysis on Reductive Groups
Edited by William Barker and Paul Sally
Lp Harmonic Analysis on SL(2,R)
Further information on this Memoir.