An Episodic History of Mathematics: Mathematical Culture Through Problem Solving

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MAA, Apr 1, 2010 - Mathematics - 381 pages
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An Episodic History of Mathematics will acquaint students and readers with mathematical language, thought, and mathematical life by means of historically important mathematical vignettes. It will also serve to help prospective teachers become more familiar with important ideas of in the history of mathematicsboth classical and modern.Contained within are wonderful and engaging stories and anecdotes about Pythagoras and Galois and Cantor and Poincar, which let readers indulge themselves in whimsy, gossip, and learning. The mathematicians treated here were complex individuals who led colorful and fascinating lives, and did fascinating mathematics. They remain interesting to us as people and as scientists.This history of mathematics is also an opportunity to have some fun because the focus in this text is also on the practicalgetting involved with the mathematics and solving problems. This book is unabashedly mathematical. In the course of reading this book, the neophyte will become involved with mathematics by working on the same problems that, for instance, Zeno and Pythagoras and Descartes and Fermat and Riemann worked on.This is a book to be read, therefore, with pencil and paper in hand, and a calculator or computer close by. All will want to experiment; to try things; and become a part of the mathematical process.
 

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i r8 8/8 m8 no deb8 or h8 or masterb8

Contents

Zenos Paradox and the Concept of Limit
25
The Mystical Mathematics of Hypatia
43
The Islamic World and the Development of Algebra
55
Cardano Abel Galois and the Solving of Equations
73
Rene Descartes and the Idea of Coordinates
95
Pierre de Fermat and the Invention of Differential Calculus
109
The Great Isaac Newton
125
The Complex Numbers and the Fundamental Theorem of Algebra
151
Bernhard Riemann and
247
Georg Cantor
261
The Number Systems
275
Henri Poincare Child Phenomenon
289
Sonya Kovalevskaya and the Mathematics of Mechanics
305
Emmy Noether and Algebra
319
Methods of Proof
331
Alan Turing and Cryptography
345

The Prince of Mathematics
169
Sophie Germain and the Attack on Fermats Last Problem
195
Cauchy and the Foundations of Analysis
207
The Prime Numbers
223
Dirichlet and How to Count
237
Bibliography
365
Index
371
About the Author
381
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About the author (2010)

Steven G. Krantz received his BA from the University of California, Santa Cruz, and his Ph.D. from Princeton University. He has taught at UCLA, Princeton University, Penn State University, and Washington University in St Louis. He has directed 17 Ph.D. theses, authored over 50 books, and over 150 scholarly papers. He has served on several editorial boards, and is Editor-in-Chief of three journals. Krantz is the holder of the Chauvenet Prize, the Beckenbach Book Award, and the Kemper Foundation Award.

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