Cover image for An episodic history of mathematics : mathematical culture through problem solving
An episodic history of mathematics : mathematical culture through problem solving
Personal Author:
MAA textbooks
1st ed.
Publication Information:
Washington, DC : Mathematical Association of America, 2010
Physical Description:
381 p. : ill. ; 26 cm.
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Item Category 1
30000010283095 QA21 K72 2010 Open Access Book Book

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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 be an encyclopedic history of mathematics, but to give the reader a sense of mathematical culture and history. The book abounds with stories, and personalities play a strong role. The book will introduce readers to some of the genesis of mathematical ideas. Mathematical history is exciting and rewarding, and is a significant slice of the intellectual pie. A good education consists of learning different methods of discourse, and certainly mathematics is one of the most well-developed and important modes of discourse that we have. The focus in this text is on getting involved with 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.

Reviews 1

Choice Review

This important work is not as detailed as Howard Eves's An Introduction to the History of Mathematics (6th ed., 1990; 1st ed., 1953), but it is more manageable and better suited to teaching the subject. Krantz (Washington Univ., St. Louis) selects key eras and topics to illustrate how mathematics in the Western world evolved from the ancient Greeks to the early modern era. The only non-Western mathematical topic discussed is the essential Islamic role in the development of algebra. Readers must look elsewhere for materials on Chinese, African, and other cultural contributions. Still, the thread of mathematics history leading to the mathematics that academic students perform today is well established. Krantz illustrates Greek and Arab mathematics and discusses the contributions of Cardono, Able, and Galois on the theory of equations. He shows calculus development through Descartes, Fermat and, of course, Newton. The discussions on the foundations of analysis cover the work of Gauss, Cauchy, and Riemann. Additional chapters cover Cantor, Poincare, Kovaleskaya, and Noether. The book ends with "Methods of Proof" and "Alan Turing and Cryptography." The carefully written work contains numerous examples, an excellent selection of problems and projects, and an extensive bibliography. Useful for history of mathematics or senior capstone courses. Summing Up: Highly recommended. Upper-division undergraduates. R. L. Pour Emory and Henry College

Table of Contents

1 The Ancient Greeks
2 Zeno's Paradox and the concept of limit
3 The mystical mathematics of Hypatia
4 The Islamic world and the development of algebra
5 Cardano, Abel, Galois, and the solving of equations
6 Rene Descartes and the idea of coordinates
7 The invention of differential calculus
8 The great Isaac Newton
9 Complex numbers and polynomials
10 The prince of mathematics
11 Sophie Germain and Fermat's Problem
12 Cauchy and the foundations of analysis
13 The prime numbers
14 Dirichlet and how to count
15 Riemann and the geometry of surfaces
16 Georg Cantor and the orders of infinity
17 The natural numbers
18 Henri Poincaré, child phenomenon
19 Sonya Kovalevskaya and mechanics
20 Emmy Noether and algebra
21 Methods of proof
22 Alan Turing and cryptography