William H. Barker

Isaac Henry Wing Professor of Mathematics

Bill Barker

Contact Information


Searles Science Building - 105

Teaching this semester

MATH 2020. Introduction to Mathematical Reasoning

William Barker
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

William Barker
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

Research Interests

  • 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.