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

Format:

Book

Author/Creator:

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

Contributor:

Mathematical Association of America.

Series:

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 (xiii, 381 pages)

Place of Publication:

[Washington, DC] : Mathematical Association of America, c2010.

System Details:

Mode of access : World Wide Web

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:

Chapter 1. The Ancient Greeks and the Foundations of Mathematics Chapter 2. Zeno's Paradox and the Concept of Limit Chapter 3. The Mystical Mathematics of Hypatia Chapter 4. The Islamic World and the Development of Algebra Chapter 5. Cardano, Abel, Galois, and the Solving of Equations Chapter 6. René Descartes and the Idea of Coordinates Chapter 7. Pierre de Fermat and the Invention of Differential Calculus Chapter 8. The Great Isaac Newton Chapter 9. The Complex Numbers and the Fundamental Theorem of Algebra Chapter 10. Carl Friedrich Gauss: The Prince of Mathematics Chapter 11. Sophie Germain and the Attack on Fermat's Last Problem Chapter 12. Cauchy and the Foundations of Analysis Chapter 13. The Prime Numbers Chapter 14. Dirichlet and How to Count Chapter 15. Bernhard Riemann and the Geometry of Surfaces Chapter 16. Georg Cantor and the Orders of Infinity Chapter 17. The Number Systems Chapter 18. Henri Poincaré, Child Phenomenon Chapter 19. Sonya Kovalevskaya and the Mathematics of Mechanics Chapter 20. Emmy Noether and the Birth of Modern Algebra Chapter 21. Methods of Proof Chapter 22. Alan Turing and Cryptography

Notes:

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

Electronic reproduction. Providence, Rhode Island : American Mathematical Society. 2012

Description based on print version record.

Other Format:

Print version: Krantz, Steven G. 1951- episodic history of mathematics :

ISBN:

9781614446057 (online)

Access Restriction:

Restricted for use by site license.