Mark Kac, Gian-Carlo Rota, Jacob T. Schwartz (auth.)9780817636364, 9780817647742, 9783764336363, 0817636366, 0817647740, 3764336366
This is a volume of essays and reviews that delightfully explore mathematics in all its moods — from the light and the witty, and humorous to serious, rational, and cerebral. Topics include: logic, combinatorics, statistics, economics, artificial intelligence, computer science, and applications of mathematics broadly. You will also find history and philosophy covered, including discussion of the work of Ulam, Kant, Heidegger among others.
“…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
“‘Mathematicians, like Proust and everyone else, are at their best when writing about their first love’ … They are among the very best we have; and their best is very good indeed. … One approaches this book with high hopes. Happily, one is not disappointed.”— From The Mathematical Intelligencer
“Mathematics is shaped by the consistent concerns and styles of powerful minds —three of which are represented here. Kac’s work is marked by deep commitment and breadth of inquiry. Rota is the easiest of these authors to read…a delight: witty and urbane, with a clear and interesting agenda and an astonishing intellectual range. To read him is to be a part of a pleasant and rewarding conversation.—Mathematics Magazine
Table of contents :
Front Matter….Pages i-xii
Discrete Thoughts….Pages 1-3
Front Matter….Pages 5-5
Mathematics: Tensions….Pages 7-18
The Pernicious Influence of Mathematics on Science….Pages 19-25
Statistics….Pages 27-36
Statistics and Its History….Pages 37-48
Combinatorics….Pages 49-62
Computer Science….Pages 63-76
Mathematics: Trends….Pages 77-103
The Future of Computer Science….Pages 105-116
Economics, Mathematical and Empirical….Pages 117-149
Front Matter….Pages 151-151
Complicating Mathematics….Pages 153-155
Mathematics and Its History….Pages 157-161
Academic Responsibility….Pages 163-166
Husserl and the Reform of Logic….Pages 167-173
Husserl….Pages 175-181
Artificial Intelligence….Pages 183-190
Computing and Its History….Pages 191-193
Will Computers Replace Humans?….Pages 195-206
Computer-Aided Instruction….Pages 207-230
Misreading the History of Mathematics….Pages 231-234
Front Matter….Pages 151-151
The Wonderful World of Uncle Stan….Pages 235-237
Ulam….Pages 239-241
Kant….Pages 243-246
Heidegger….Pages 247-252
Doing Away with Science….Pages 253-262
More Discrete Thoughts….Pages 263-264
Back Matter….Pages 265-266
Reviews
There are no reviews yet.