An episodic history of mathematics : mathematical culture through problem solving / Steven G. Krantz.

Format:

Book

Author/Creator:

Krantz, Steven G. (Steven George), 1951-

Contributor:

Mathematical Association of America.

Series:

MAA Textbooks

MAA textbooks

AMS/MAA Textbooks, 2577-1213 ; v. 19

Language:

English

Subjects (All):

Mathematics--History--Study and teaching (Higher).

Mathematics.

Mathematics--Problems, exercises, etc.

Mathematics--Study and teaching (Higher).

Mathematicians.

Physical Description:

1 online resource (396 p.)

Edition:

1st ed.

Place of Publication:

[Washington, D.C.] : Mathematical Association of America, c2010.

Language Note:

English

Summary:

"An Episodic History of Mathematics delivers a series of snapshots of mathematics and mathematicians from ancient times to the twentieth century. Giving readers a sense of mathematical culture and history, the book also acquaints readers with the nature and techniques of mathematics via exercises. It introduces the genesis of key mathematical concepts. For example, while Krantz does not get into the intricate mathematical details of Andrew Wiles's proof of Fermat's Last Theorem, he does describe some of the streams of thought that posed the problem and led to its solution. The focus in this text, moreover, is on doing - getting involved with the mathematics and solving problems. Every chapter ends with a detailed problem set that will provide students with avenues for exploration and entry into the subject. It recounts the history of mathematics; offers broad coverage of the various schools of mathematical thought to give readers a wider understanding of mathematics; and includes exercises to help readers engage with the text and gain a deeper understanding of the material."--Publisher's description.

Contents:

The ancient Greeks and the foundations of mathematics

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

René Descartes and the idea of coordinates

Pierre de Fermat and the invention of differential calculus

The great Isaac Newton

The complex numbers and the fundamental theorem of algebra

Carl Friedrich Gauss: the prince of mathematics

Sophie Germain and the attack on Fermat's last problem

Cauchy and the foundations of analysis

The prime numbers

Dirichlet and how to count

Bernhard Riemann and the geometry of surfaces

Georg Cantor and the orders of infinity

The number systems

Henri Poincaré, child phenomenon

Sonya Kovalevskaya and the mathematics of mechanics

Emmy Noether and algebra

Methods of proof

Alan Turing and cryptography.

Notes:

Description based upon print version of record.

Includes bibliographical references (p. 365-369) and index.

Description based on print version record.

ISBN:

1-61444-605-9

OCLC:

929120391