Mathematical Expeditions: Chronicles by the Explorers by Reinhard LaubenbacherMathematical Expeditions: Chronicles by the Explorers by Reinhard Laubenbacher

Mathematical Expeditions: Chronicles by the Explorers

byReinhard Laubenbacher, David Pengelley

Paperback | July 28, 1999

Pricing and Purchase Info


Earn 380 plum® points

Prices and offers may vary in store


In stock online

Ships free on orders over $25

Not available in stores


This book contains the stories of five mathematical journeys into new realms, told through the writings of the explorers themselves. Some were guided by mere curiosity and the thrill of adventure, while others had more practical motives. In each case the outcome was a vast expansion of the known mathematical world and the realization that still greater vistas remained to be explored. The authors tell these stories by guiding the reader through the very words of the mathematicians at the heart of these events, and thereby provide insight into the art of approaching mathematical problems. The book can be used in a variety of ways. The five chapters are completely independent, each with varying levels of mathematical sophistication. The book will be enticing to students, to instructors, and to the intellectually curious reader. By working through some of the original sources and supplemental exercises, which discuss and solve - or attempt to solve - a great problem, this book helps the reader 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.
Title:Mathematical Expeditions: Chronicles by the ExplorersFormat:PaperbackDimensions:278 pages, 23.5 × 15.5 × 0.01 inPublished:July 28, 1999Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:038798433X

ISBN - 13:9780387984339


Table of 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 Poincaré's Euclidean Model for Non-Euclidean 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.

From Our Editors

Explorers of all types are guided by mere curiosity, the thrill of adventure and, sometimes, by more practical motives. Mathematical Expeditions contains the stories of five mathematical journeys to new realms, pieced together through the writings of explorers who expanded what was known to the mathematical world and realized still greater vistas remained to be explored. Among the topics discussed are Fermat's last theorem and the taming of the infinite.