Alexander J. Hahn

Professor and Director of the Kaneb Center for Teaching and Learning

B.S., Loyola University of Los Angeles, 1965
M.S., University of Notre Dame, 1968
Ph.D., University of Notre Dame, 1970

Research Interests

My research over the years has had a focus on the following algebraic concerns: Orthogonal groups and other classical matrix groups both over fields and integral domains and in number theoretic situations, and related structures such as Clifford algebras, Azumaya algebras, quadratic and hermitian forms and their Witt groups, and linear and hermitian K-Theory.

• A.J. Hahn and O.T. O'Meara, The Classical Groups and K-Theory, Grundlehren der Mathematik, Vol. 291, Springer-Verlag, Berlin and New York, 576 pp. of print, 1989.

• A.J. Hahn, Quadratic Algebras, Clifford Algebras and Arithmetic Witt Groups, UNIVERSITEXT Series, Springer-Verlag, Berlin and New York, 286 pp. of print, 1994.

• A. J. Hahn, The Zassenhaus Decomposition for the Orthogonal Groups: Properties and Applications,
  Documenta Mathematica (2001), 165-181. See Documenta Mathematica at http://www.mathematik.uni-bielefeld.de/documenta/

• A. J. Hahn, The Clifford Algebra in the Theory of Algebras, Quadratic Forms, and Classical Groups, invited article, submitted for publication, Proceedings of the 6th International Conference On Clifford Algebras and Their Applications, Birkhauser.

More recently, I have also become interested in the history of mathematics and science:

• A. J. Hahn, The Pendulum Swings again: A Mathematical Reassessment of Galileo's Experiments with Inclined Planes, Arch. Hist. Exact Sci. 56 (2002), 339-361.

Finally, my appreciation for the importance of the teaching of mathematics from the points of view of both content and communication has moved me to write:

• A. J. Hahn, Basic Calculus: From Archimedes to Newton to its Role in Science, Texts in Mathematics, Springer-Verlag, New York, 1998. Translated into Japanese in two volumes by Kano Satoru, Department of Physics, Hosei University, Tokyo: Volume 1, Basic Calculus: From Archimedes to Newton; Volume 2, Basic Calculus: Differential and Integral Calculus and Science, Springer-Verlag, Tokyo, 2001, 2002.

Please direct questions and comments to: Alexander.J.Hahn.1@nd.edu