Krantz S.G. An Episodic History of Mathematics: Mathematical Culture through Problem Solving

Mathematical Association of America, 2010. — 381 p. — ISBN 978-0883857663An Episodic History of Mathematics delivers a series of snapshots of the history of mathematics from ancient times to the twentieth century. The intent is not to be an encyclopedic history of mathematics, but to give the reader a sense of mathematical culture and history. The book abounds with stories, and personalities play a strong role. The book will introduce readers to some of the genesis of mathematical ideas. Mathematical history is exciting and rewarding, and is a significant slice of the intellectual pie. A good education consists of learning different methods of discourse, and certainly mathematics is one of the most well-developed and important modes of discourse that we have. The focus in this text is on getting involved with mathematics and solving problems. Every chapter ends with a detailed problem set that will provide the student with many avenues for exploration and many new entrees into the subject.The Ancient Greeks
Zeno’s Paradox and the Concept of Limit
The Mystical Mathematics of Hypatia
The Arabs and the Development of Algebra
Cardano, Abel, Galois, and the Solving of Equations
Ren´ e Descartes and the Idea of Coordinates
The Invention of Differential Calculus
Complex Numbers and Polynomials
Sophie Germain and Fermat’s Last Problem
Cauchy and the Foundations of Analysis
The Prime Numbers
Dirichlet and How to Count
Riemann and the Geometry of Surfaces
Georg Cantor and the Orders of Infinity
The Number Systems
Henri Poincar´e, Child Prodigy
Sonya Kovalevskaya and Mechanics
Emmy Noether and Algebra
Methods of Proof
Alan Turing and Cryptography