William H. Barker

Isaac Henry Wing Professor of Mathematics

Bill Barker

Contact Information

barker@bowdoin.edu
207-725-3571
Mathematics

Searles Science Building - 105


Teaching this semester

MATH 1800. Multivariate Calculus, A

Multivariate calculus in two and three dimensions. Vectors and curves in two and three dimensions; partial and directional derivatives; the gradient; the chain rule in higher dimensions; double and triple integration; polar, cylindrical, and spherical coordinates; line integration; conservative vector fields; and Green’s theorem. An average of four to five hours of class meetings and computer laboratory sessions per week.

MATH 2404. Geometry

A survey of modern approaches to Euclidean geometry in two dimensions. Axiomatic foundations of metric geometry. Transformational geometry: isometries and similarities. Klein’s Erlanger Programm. Symmetric figures. Other topics may be chosen from three-dimensional geometry, ornamental groups, area, volume, fractional dimension, and fractals.

Teaching next 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.

Education

  • 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.