03608nam a2200397 a 4500 ebr10733080 CaPaEBR m o u cr cn||||||||| 100121s2010 dcua sb 001 0deng d 2010921168 0883857669 9780883857663 9781614446057 (e-book) CaPaEBR CaPaEBR (OCoLC)811562988 QA21 .K72 2010eb 510.9 22 Krantz, Steven G. (Steven George), 1951- An episodic history of mathematics [electronic resource] : mathematical culture through problem solving / Steven G. Krantz. [Washington, D.C.] : Mathematical Association of America, c2010. xiii, 381 p. : ill. MAA textbooks Includes bibliographical references (p. 365-369) and index. 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 -- Ren�e 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 Poincar�e, child phenomenon -- Sonya Kovalevskaya and the mathematics of mechanics -- Emmy Noether and algebra -- Methods of proof -- Alan Turing and cryptography. "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. Electronic reproduction. Palo Alto, Calif. : ebrary, 2013. Available via World Wide Web. Access may be limited to ebrary affiliated libraries. Mathematics History Study and teaching (Higher) Mathematics Problems, exercises, etc. Mathematics Study and teaching (Higher) Mathematicians. Electronic books. local Mathematical Association of America. ebrary, Inc. http://site.ebrary.com/lib/rucke/Doc?id=10733080 An electronic book accessible through the World Wide Web; click to view 36728 36728