Discrete Thoughts

This is a volume of essays and reviews that delightfully explores mathematics in all its moods from the light and the witty, and humorous to serious, rational, and cerebral. These beautifully written articles from three great modern mathematicians will provide a source for supplemental reading for almost any math class. Topics include: logic, combinatorics, statistics, economics, artificial intelligence, computer science, and broad applications of mathematics. Readers will also find coverage of history and philosophy, including discussion of the work of Ulam, Kant, and Heidegger, among others.

Beautifully written articles from three great modern mathematicians Ideas provoke thought and debate Provides a source for supplemental reading for almost any math class

Résumé

From the reviews of the second edition:

"...These papers reflect on mathematics and its influence on human society. They can help the specialist to notice what is going on around him, and they may lead educated people from other domains to a better understanding of mathematics. Many of these papers can advise educators how to form a modern mathematics education, which develops approved ideas and institutions...I admire the stimulating perspectives of the authors"

--American Mathematical Society

"Kac, Rota, and Schwartz have collected here: occasional essays about mathematics, mathematicians, and surrounding subjects. ... The essays are fun to read, light in manner but serious in content. Many of them are provocative. ... As a result, the book would make wonderful fodder for a reading course or seminar. ... Discrete Thoughts is a classic indeed." (Fernando Q. Gouvêa, MathDL, January, 2008)

Contenu
Discrete Thoughts.- Discrete Thoughts.- I.- Mathematics: Tensions.- The Pernicious Influence of Mathematics on Science.- Statistics.- Statistics and Its History.- Combinatorics.- Computer Science.- Mathematics: Trends.- The Future of Computer Science.- Economics, Mathematical and Empirical.- II.- Complicating Mathematics.- Mathematics and Its History.- Academic Responsibility.- Husserl and the Reform of Logic.- Husserl.- Artificial Intelligence.- Computing and Its History.- Will Computers Replace Humans?.- Computer-Aided Instruction.- Misreading the History of Mathematics.- The Wonderful World of Uncle Stan.- Ulam.- Kant.- Heidegger.- Doing Away with Science.- More Discrete Thoughts.