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 3404. Projective and Non-Euclidean Geometries

William Barker
A survey of affine, projective, and non-Euclidean geometries in two-dimensions, unified by the transformational viewpoint of Klein’s Erlanger Programm. Special focus placed on conic sections and projective embeddings. Additional topics as time permits: complex numbers in plane geometry, quaternions in three-dimensional geometry, and the geometry of four-dimensional space-time in special relativity. Mathematics 2404 is helpful but not required.


  • 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.