An Episodic History of Mathematics

by Krantz, Steven G.

• ISBN13: 9780883857663
• ISBN10: 0883857669
• Format: Hardcover
• Copyright: 2010-03-22
• Publisher: Mathematical Assn of Amer

Summary

An Episodic History of Mathematics delivers a series of snapshots of the history of mathematics from ancient times to the twentieth century. The intent is not to provide an encyclopaedic history of mathematics, but to give the reader a sense of mathematical culture and history. The book also acquaints the reader with the nature and techniques of mathematics through its exercises. The book introduces the genesis of many mathematical ideas. For example, while Krantz does not get into the nuts and bolts of Andrew Wiles's solution of Fermat's Last Theorem, he does describe some of the stream of thought that created the problem and led to its solution. The focus in this text is on doing - getting involved with the mathematics and solving problems. Every chapter ends with a detailed problem set that will provide the student with many avenues for exploration and many new entrees into the subject.

Table of Contents

Preface

The Ancient Greeks

Zeno's Paradox and the concept of limit

The mystical mathematics of Hypatia

The Islamic world and the development of algebra

Cardano, Abel, Galois, and the solving of equations

Rene Descartes and the idea of coordinates

The invention of differential calculus

The great Isaac Newton

Complex numbers and polynomials

The prince of mathematics

Sophie Germain and Fermat's Problem

Cauchy and the foundations of analysis

The prime numbers

Dirichlet and how to count

Riemann and the geometry of surfaces

Georg Cantor and the orders of infinity

The natural numbers

Henri Poincaré, child phenomenon

Sonya Kovalevskaya and mechanics

Emmy Noether and algebra

Methods of proof

Alan Turing and cryptography

Bibliography

Index

Table of Contents provided by Publisher. All Rights Reserved.