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, thesis directed by O.T. O’Meara, 1970

Bio

Positions Held

1970-71 NSF Fellow at the University of Zürich, Switzerland
1971-72 SFB Scholar at the University of Bonn, West Germany
1972, 1978 Assistant, Associate Professor, University of Notre Dame
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, 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

Overview of Publications

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. Over two dozen articles, see zbMath Open, 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 Robert Steinberg in Bull. Amer. Math. Soc. (N.S.), Vol 23, No 2, 1990.

• A. J. Hahn, Quadratic Algebras, Clifford Algebras and Arithmetic Witt Groups, UNIVERSITEXT Series, Springer-Verlag, Berlin, Heidelberg, New York, 1994. Reviewed by A. R. Wadsworth in Bull. Amer. Math. Soc. (N.S.), Vol 33, No 2, 1996.

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. Comment by Van Dyck.

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. Reviewed by David Halliday in PHYSICS TODAY, APRIL 1999. 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, by Springer, Tokyo, 2001, 2002.
• A. J. Hahn,  Mathematical Excursions to the World's Great Buildings | Princeton University Press, Princeton University Press, 2012. Comments from the author. Reviews by Ian Anderson in The Mathematical Gazette, Volume 97, Issue 540, 2013, pp. 566–567, Phill Schultz in Gazette of the Australian Mathematical Society, Volume 40, No 3, pp. 212–2013, Sylvie Duvernoy and Jesper Matthiasen in Nexus Netw J, Volume 15, No 2, 2013, pp. 381–383, and Stephen Wassel and Kim Williams in The Mathematical Intelligencer, Vol 5, No 3, 2013, pp. 69-73. Translated into Chinese by Posts & Telecom Press in 2014 and 2023. The edition of 2023 is a revised translation that appeared in the Turing New Knowledge imprint of the Press. Both translations by Li Li (李莉).

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. Resources for using the Text. Reviews by Peter Shiu in Mathematical Gazette, Volume 102, Issue 554, 2018, pp. 372-374, Megan Sawyer and William Frascella in MAA Reviews 08/4/2017, David Kollosche in zbMATH Open. Zbl 1379.26002, 2018, and N. W. Schillow in CHOICE: Current Reviews for Academic Libraries 55, no. 2 (October 2017). See also the Editorial Reviews on Amazon.
• A. J. Hahn, Basic Calculus of Planetary Orbits and Interplanetary Flight, The Missions of the Voyagers, Cassini, and Juno, 2020, Springer Nature, Switzerland AG. Assessed by NASA and Lockheed Martin engineer Mario Zoccoli and reviewed by Klaus Rohe in the Journal für Astronomie Nr 75 (2020), pg. 92. See also the Editorial Reviews on Amazon. Translated into Japanese by Kano Satoru and Takashi Kasuga in two volumes in 2023. Vol 1. Development of Space Science & Mathematical Preparation. Vol. 2. Motion by Gravity and Spacecraft Trajectories, Asakura Publishing Co., Ltd, Shinjuku City, Tokyo 162-0814, Japan.