Mathematical expeditions : chronicles by the explorers
 Author/Creator
 Laubenbacher, Reinhard.
 Language
 English.
 Imprint
 New York : Springer, c1999.
 Physical description
 x, 275 p. : ill. ; 25 cm.
 Series
 Undergraduate texts in mathematics. Readings in mathematics.
Access
Available online

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QA21 .L34 1999

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QA21 .L34 1999
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Contributors
 Contributor
 Pengelley, David.
Contents/Summary
 Bibliography
 Includes bibliographical references (p. [259]267) and index.
 Contents

 1 Geometry: The Parallel Postulate. 1.1 Introduction. 1.2 Euclid's Parallel Postulate. 1.3 Legendre's Attempts to Prove the Parallel Postulate. 1.4 Lobachevskian Geometry. 1.5 Poincare's Euclidean Model for NonEuclidean Geometry.. 2 Set Theory: Taming the Infinite. 2.1 Introduction. 2.2 Bolzano's Paradoxes of the Infinite. 2.3 Cantor's Infinite Numbers. 2.4 Zermelo's Axiomatization. 3 Analysis: Calculating Areas and Volumes. 3.1 Introduction. 3.2 Archimedes' Quadrature of the Parabola. 3.3 Archimedes' Method. 3.4 Cavalieri Calculates Areas of Higher Parabolas. 3.5 Leibniz's Fundamental Theorem of Calculus. 3.6 Cauchy's Rigorization of Calculus. 3.7 Robinson Resurrects Infinitesimals. 3.8 Appendix on Infinite Series. 4 Number Theory: Fermat's Last Theorem. 4.1 Introduction. 4.2 Euclid's Classification of Pythagorean Triples. 4.3 Euler's Solution for Exponent Four. 4.4 Germain's General Approach. 4.5 Kummer and the Dawn of Algebraic Number Theory. 4.6 Appendix on Congruences. 5 Algebra: The Search for an Elusive Formula. 5.1 Introduction. 5.2 Euclid's Application of Areas and Quadratic Equations. 5.3 Cardano's Solution of the Cubic. 5.4 Lagrange's Theory of Equations. 5.5 Galois Ends the Story. References. Credits.
 (source: Nielsen Book Data)
 Publisher's Summary
 The stories of five mathematical journeys into new realms, pieced together from the writings of the explorers themselves. Some were guided by mere curiosity and the thrill of adventure, others by more practical motives. In each case the outcome was a vast expansion of the known mathematical world and the realisation that still greater vistas remain to be explored. The authors tell these stories by guiding readers through the very words of the mathematicians at the heart of these events, providing an insightinto the art of approaching mathematical problems. The five chapters are completely independent, with varying levels of mathematical sophistication, and will attract students, instructors, and the intellectually curious reader. By working through some of the original sources and supplementary exercises, which discuss and solve  or attempt to solve  a great problem, this book helps readers discover the roots of modern problems, ideas, and concepts, even whole subjects. Students will also see the obstacles that earlier thinkers had to clear in order to make their respective contributions to five central themes in the evolution of mathematics.
(source: Nielsen Book Data)  Supplemental links

Publisher description
Table of contents only
Subjects
Bibliographic information
 Publication date
 1999
 Responsibility
 Reinhard Laubenbacher, David Pengelley.
 Series
 Undergraduate texts in mathematics. Readings in mathematics
 ISBN
 0387984348
 9780387984346
 038798433X
 9780387984339