An episodic history of mathematics: mathematical culture through problem solving

An 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 provide an encyclopaedic history of mathematics, but to give the readera sense of mathematical culture and history. The book also acquaints the reader with the nature and techniques of mathematics through its exercises. The book introduces the genesis of many mathematical ideas. For example, while Krantz does not get into the nuts and bolts of Andrew Wiles's solution of Fermat's Last Theorem, he does describe some of the stream of thought that created the problem and led to its solution. The focus in this text is on doing – getting involved with the 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. INDICE: Preface; 1. The Ancient Greeks; 2. Zeno's Paradox and the concept of limit; 3. The mystical mathematics of Hypatia; 4. The Islamic world and thedevelopment of algebra; 5. Cardano, Abel, Galois, and the solving of equations; 6. Rene Descartes and the idea of coordinates; 7. The invention of differential calculus; 8. The great Isaac Newton; 9. Complex numbers and polynomials; 10. The prince of mathematics; 11. Sophie Germain and Fermat's Problem; 12. Cauchy and the foundations of analysis; 13. The prime numbers; 14. Dirichlet andhow to count; 15. Riemann and the geometry of surfaces; 16. Georg Cantor and the orders of infinity; 17. The natural numbers; 18. Henri Poincaré, child phenomenon; 19. Sonya Kovalevskaya and mechanics; 20. Emmy Noether and algebra; 21. Methods of proof; 22. Alan Turing and cryptography; Bibliography; Index.

• ISBN: 978-0-88385-766-3
• Editorial: Mathematical Association of America
• Encuadernacion: Cartoné
• Páginas: 381
• Fecha Publicación: 01/04/2010
• Nº Volúmenes: 1
• Idioma: Inglés