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 3404. Projective and Non-Euclidean Geometries
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
- 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.