Author | Laubenbacher, Reinhard. author |
---|---|
Title | Mathematical Expeditions [electronic resource] : Chronicles by the Explorers / by Reinhard Laubenbacher, David Pengelley |
Imprint | New York, NY : Springer New York : Imprint: Springer, 1999 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-0523-4 |
Descript | X, 278 p. online resource |
1 Geometry: The Parallel Postulate -- 1.1 Introduction -- 1.2 Euclidโs Parallel Postulate -- 1.3 Legendreโs Attempts to Prove the Parallel Postulate -- 1.4 Lobachevskian Geometry -- 1.5 Poincarรฉโs Euclidean Model for Non-Euclidean Geometry. -- 2 Set Theory: Taming the Infinite -- 2.1 Introduction -- 2.2 Bolzanoโs Paradoxes of the Infinite -- 2.3 Cantorโs Infinite Numbers -- 2.4 Zermeloโs Axiomatization -- 3 Analysis: Calculating Areas and Volumes -- 3.1 Introduction -- 3.2 Archimedesโ Quadrature of the Parabola -- 3.3 Archimedesโ Method -- 3.4 Cavalieri Calculates Areas of Higher Parabolas -- 3.5 Leibnizโs Fundamental Theorem of Calculus -- 3.6 Cauchyโs Rigorization of Calculus -- 3.7 Robinson Resurrects Infinitesimals -- 3.8 Appendix on Infinite Series -- 4 Number Theory: Fermatโs Last Theorem -- 4.1 Introduction -- 4.2 Euclidโs Classification of Pythagorean Triples -- 4.3 Eulerโs Solution for Exponent Four -- 4.4 Germainโs 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 Euclidโs Application of Areas and Quadratic Equations -- 5.3 Cardanoโs Solution of the Cubic -- 5.4 Lagrangeโs Theory of Equations -- 5.5 Galois Ends the Story -- References -- Credits