1.

Record Nr.

UNINA9910955955503321

Autore

Krantz Steven G (Steven George), <1951->

Titolo

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

Pubbl/distr/stampa

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

ISBN

1-61444-605-9

Edizione

[1st ed.]

Descrizione fisica

1 online resource (396 p.)

Collana

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

MAA textbooks

Classificazione

31.01

Disciplina

510.9

Soggetti

Mathematics - History - Study and teaching (Higher)

Mathematics

Mathematics - Study and teaching (Higher)

Mathematicians

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Description based upon print version of record.

Nota di bibliografia

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

Nota di contenuto

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.

Sommario/riassunto

"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.