An Episodic History of Mathematics
Subtitle: Mathematical Culture Through Problem Solving
Publisher: Mathematical Association of America
Published: 2010
Language: eng
Format: Hardcover
Number of pages: 381
ISBN-13: 9780883857663
Description: "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.
Table of contents: title: Preface
pagenum: xi; label: 1
title: The Ancient Greeks and the foundations of Mathematics
pagenum: 1; label: 2
title: Zeno's Paradox and the Concept of Limit
pagenum: 25; label: 3
title: The Mystical mathematics of Hypatia
pagenum: 43; label: 4
title: The Islamic World and the Development of Algebra
pagenum: 55; label: 5
title: Cardano, Abel, Galois, and the Solving of Equations
pagenum: 73; label: 6
title: Rene Descartes and the Idea of Coordinates
pagenum: 95; label: 7
title: Pierre de Fermat and the Invention of Differential Calculus
pagenum: 109; label: 8
title: The Great Isaac Newton
pagenum: 124; label: 9
title: The Complex Numbers and the Fundamental Theorem of Algebra
pagenum: 151; label: 10
title: Carl Friedrich Gauss: The Prince of Mathematics
pagenum: 169; label: 11
title: Sophie Germain and the Attack on Fermat's Last Problem
pagenum: 195; label: 12
title: Cauchy and the Foundations of Analysis
pagenum: 207; label: 13
title: The Prime Numbers
pagenum: 223; label: 14
title: Dirichlet and How to Count
pagenum: 237; label: 15
title: Bernard Riemann and the Geometry of Surfaces
pagenum: 247; label: 16
title: Georg Cantor and the Orders of Infinity
pagenum: 261; label: 17
title: The Number Systems
pagenum: 275; label: 18
title: Henri Poincare, Child Phenomenon
pagenum: 289; label: 19
title: Sonya Kovalevskaya and the Mathematics of Mechanics
pagenum: 305; label: 20
title: Emmy Noether and Algebra
pagenum: 319; label: 21
title: Methods of Proof
pagenum: 331; label: 22
title: Alan Turing and Cryptography
pagenum: 345; title: Bibliography
pagenum: 365; title: Index
pagenum: 371; title: About the Author
pagenum: 381