William H. Barker
Isaac Henry Wing Professor of Mathematics, Chair of Department of Mathematics
Searles Science Building - 105
Teaching this semester
MATH 2603. Introduction to Analysis
Building on the theoretical underpinnings of calculus, develops the rudiments of mathematical analysis. Concepts such as limits and convergence from calculus are made rigorous and extended to other contexts, such as spaces of functions. Specific topics include metric spaces, point-set topology, sequences and series, continuity, differentiability, the theory of Riemann integration, and functional approximation and convergence.
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.