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Gene Abrams


About the topic

Recommended resources





Gene Abrams is Professor of Mathematics at the University of Colorado at Colorado Springs. He earned his Ph.D. in mathematics at the University of Oregon in 1981. He is the coordinator of the UCCS MathOnLine program, a distance-learning delivery method for mathematics which allows advanced high school students to take UCCS mathematics courses via the Internet. He has written and spoken widely on issues in mathematics education, and has been actively involved in mathematics-oriented community outreach K-12 educational activities. Gene has published research articles and lectured extensively (both in the U.S. and Europe) on the topic of associative rings and their modules. His current area of mathematics investigation, a subject called Leavitt path algebras, is a topic of interest in both algebra and C*-analysis research circles. Gene has been honored with various teaching awards, including: the “2002 Teacher of the Year” by the Mathematical Association of America Rocky Mountain Section, “President’s Teaching Scholar” by the University of Colorado System (lifetime designation made in 1996), and the 1988 campuswide “Outstanding Teaching Award” by UCCS. He spends his spare time mountain biking, cross country skiing, and living / eating / sleeping baseball.

The Café management, in the interests of full disclosure, must point out that Gene is capable of writing stuff like this:
Abstract: For any row finite graph E and any field K we construct the Leavitt path algebra L(E) having coefficients in K. When K is the field of complex numbers, then L(E) is the algebraic analog of the Cuntz Krieger algebra C*(E). The matrix rings Mn(K) and the Leavitt algebras L(1, n) appear as algebras of the form L(E) for various graphs E. In our main result, we give necessary and sufficient conditions on E which imply that L(E) is simple.

We assume that last phrase is humor. Gene promises he won't talk like this at the Café.

About the topic

Math Quiz

1. (10 points) Circle the response which best describes the phrase “research in mathematics”.

a. Only done by pocket-protectored non-communicative personal-hygienically-deficient socially-challenged mentally-unstable white male geeks
b. Hasn’t happened since Euclid died over 2000 years ago
c. Has no impact on my everyday life
d. Something that non-mathematicians could never begin to understand
e. None of the above

2. (10 points) Circle the response which best describes the phrase “research in mathematics”.

a. Currently done by people throughout the world, in both academia and applications-oriented environments
b. An endeavor which facilitates the advancement of science and technology
c. An endeavor similar to the “basic research” work which goes on in all sciences
d. An endeavor similar to the “creative work” done by artists, writers, musicians,
e. All of the above.

This Café Scientifique will provide all participants (pocket-protectored beer drinkers and non-beer-drinkers alike) all the information they need to earn a perfect 20 / 20 on the quiz.

Recommended resources


Chaos: Making a New Science
By James Gleick. Penguin (Non-Classics); ISBN: 0140092501

Uncle Petros and Goldbach's Conjecture
by Apostolos Doxiadis Bloomsbury Publishing (New York); ISBN: 1582340676

Gödel, Escher, Bach: An Eternal Golden Braid
by Douglas R. Hofstadter Basic Books; ISBN 0465026567

Incompleteness: The Proof and Paradox of Kurt Godel
by Rebecca Goldstein W. W. Norton & Company; ISBN: 0393051692

The Man Who Knew Infinity: A Life of the Genius Ramanujan
by Robert Kanigel Washington Square Press; ISBN: 0671750615

Film and TV

Good Will Hunting
Starring: Robin Williams, Matt Damon ASIN: 6305216088

A Beautiful Mind
Starring: Russell Crowe ASIN: B00005JKQZ

Starring: Gwyneth Paltrow, Anthony Hopkins, Jake Gyllenhaal ASIN: B00005JNM3

The Proof
(PBS interview with Andrew Wiles about Fermat’s Last Theorem)

Numb3rs (CBS TV show)


Clay Mathematics Institute Million Dollar Millennium problems
Great Internet Mersenne Prime Search
American Mathematical Society Public Awareness program
Mathematics Association of America


© 2004 Colorado Café Scientifique