Subject(s) 
Mathematics  History  Study and teaching (Higher)


Mathematics  Problems, exercises, etc


Mathematics  Study and teaching (Higher)


Mathematicians

Physical Description 
xiii, 381 p. : ill. ; 27 cm 
Note 
Includes bibliographical references (p. 365369) and index 
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  RenĂ© 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 PoincarĂ©, child phenomenon  Sonya Kovalevskaya and the mathematics of mechanics  Emmy Noether and algebra  Methods of proof  Alan Turing and cryptography 
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 
Series 
MAA textbooks

Alternate Author 
Mathematical Association of America

