Discrete Thoughts: Essays on Mathematics, Science and Philosophy / Edition 2

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Overview

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
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Editorial Reviews

Booknews
Over two dozen essays, originally published during the 1960s and 1970s, stroll through the wide terrain of mathematics, noting logic, economics, history, philosophy, and other topics. Assumes an undergraduate level of mathematical sophistication. Revised from the first edition (ca. 1985). No index. Annotation c. Book News, Inc., Portland, OR (booknews.com)
From the Publisher

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)

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Product Details

  • ISBN-13: 9780817636364
  • Publisher: Springer-Verlag New York, LLC
  • Publication date: 6/28/1993
  • Edition description: REV
  • Edition number: 2
  • Pages: 284
  • Product dimensions: 6.16 (w) x 9.27 (h) x 0.65 (d)

Table of Contents

Preface
Acknowledgments
1 Discrete Thoughts 1
2 Mathematics: Tensions 7
3 The Pernicious Influence of Mathematics on Science 19
4 Statistics 27
5 Statistics and Its History 37
6 Combinatorics 49
7 Computer Science 63
8 Mathematics: Trends 77
9 The Future of Computer Science 105
10 Economics, Mathematical and Empirical 117
11 Complicating Mathematics 153
12 Mathematics and Its History 157
13 Academic Responsibility 163
14 Husserl and the Reform of Logic 167
15 Husserl 175
16 Artificial Intelligence 183
17 Computing and Its History 191
18 Will Computers Replace Humans? 195
19 Computer-Aided Instruction 207
20 Misreading the History of Mathematics 231
21 The Wonderful World of Uncle Stan 235
22 Ulam 239
23 Kant 243
24 Heidegger 247
25 Doing Away with Science 253
26 More Discrete Thoughts 263
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