Alexander Hahn

Emeritus - Full

Education

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

Research Group

Algebra and Algebraic Geometry

Research Area

Clifford Algebras, Azumaya Algebras, Quadratic and Hermitian forms and their Witt groups, and Linear and Hermitian K-Theory, Applied mathematics

Bio

1982-83 Visiting Professor at the University of California at Santa Barbara
1984-2017 Professor, University of Notre Dame
2017-present Professor Emeritus, University of Notre Dame
1987-88 Visiting Professor, University of Innsbruck, Innsbruck, Austria
1992-93 Guest Professor, University of Innsbruck, Austria
1996-2000 Chair, Department of Mathematics, University of Notre Dame
2000-2014 Director, Glynn Family Honors Program, Notre Dame
2002-2009 Director, Kaneb Center for Teaching and Learning, Notre Dame

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, 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. Two dozen articles and the two books

• A.J. Hahn and O.T. O’Meara, The Classical Groups and K-Theory, Grundlehren der Mathematik, Vol. 291, Springer-Verlag, Berlin, Heidelberg, New York, 1989. (Reviewed by R. Steinberg, Bull. Amer. Math. Soc. (N.S.), Volume 23, Number 2, (1990), 594-598.)

• A. J. Hahn, Quadratic Algebras, Clifford Algebras and Arithmetic Witt Groups, UNIVERSITEXT Series, Springer-Verlag, Berlin, Heidelberg, New York, 1994. (Reviewed by A. Wadsworth, Bull. Amer. Math. Soc. (N.S.), Volume 33, Number 2, (1996), 263-267.)

deal with these areas of mathematics. The article

• 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.

responds to my interests in the history of mathematics and science. My sense of the importance of the communication of mathematics with an emphasis on its broad relevance and applicability stimulated the books:

• 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.
• A. J. Hahn, Mathematical Excursions to the World’s Great Buildings, Princeton University Press, 2012. Translated into Chinese by Posts & Telecom Press, 2013.

I have continued to pursue these themes with an edited volume and two more books:

• Catesby Taliaferro, Rational Mechanics: The Classic Notre Dame Course, Alexander Hahn, Thomas Banchoff, Fred Crosson editors, Dover Books on Physics, Dover, 2014.
• A. J. Hahn, Calculus in Context: Background, Basics, and Applications, Johns Hopkins University Press, 2017. It is astonishing that this text has been selected by BookAuthority as the Best Basic Calculus Book of All Time. See https://bookauthority.org/books/best-basic-calculus-books?t=w3jsq3&s=award&book=1421422301,
• A. J. Hahn, Basic Calculus of Planetary Orbits and Interplanetary Flight, The Missions of the Voyagers, Cassini, and Juno, April 2020, Springer, New York, NY.  https://www.springer.com/us/book/9783030248673. Translation into Japanese by Asakura Publishing in progress (approved in July, 2021).