Author | Anglin, W. S. author |
---|---|

Title | Mathematics: A Concise History and Philosophy [electronic resource] / by W. S. Anglin |

Imprint | New York, NY : Springer New York : Imprint: Springer, 1994 |

Connect to | http://dx.doi.org/10.1007/978-1-4612-0875-4 |

Descript | XI, 265 p. online resource |

SUMMARY

This is a concise introductory textbook for a one-semester (40-class) course in the history and philosophy of mathematics. It is written for mathematยญ ics majors, philosophy students, history of science students, and (future) secondary school mathematics teachers. The only prerequisite is a solid command of precalculus mathematics. On the one hand, this book is designed to help mathematics majors acยญ quire a philosophical and cultural understanding of their subject by means of doing actual mathematical problems from different eras. On the other hand, it is designed to help philosophy, history, and education students come to a deeper understanding of the mathematical side of culture by means of writing short essays. The way I myself teach the material, stuยญ dents are given a choice between mathematical assignments, and more hisยญ torical or philosophical assignments. (Some sample assignments and tests are found in an appendix to this book. ) This book differs from standard textbooks in several ways. First, it is shorter, and thus more accessible to students who have trouble coping with vast amounts of reading. Second, there are many detailed explanations of the important mathematical procedures actually used by famous matheยญ maticians, giving more mathematically talented students a greater opporยญ tunity to learn the history and philosophy by way of problem solving

CONTENT

1 Mathematics for Civil Servants -- 2 The Earliest Number Theory -- 3 The Dawn of Deductive Mathematics -- 4 The Pythagoreans -- 5 The Pythagoreans and Perfection -- 6 The Pythagoreans and Polyhedra -- 7 The Pythagoreans and Irrationality -- 8 The Need for the Infinite -- 9 Mathematics in Athens Before Plato -- 10 Plato -- 11 Aristotle -- 12 In the Time of Eudoxus -- 13 Ruler and Compass Constructions -- 14 The Oldest Surviving Math Book -- 15 Euclidโ{128}{153}s Geometry Continued -- 16 Alexandria and Archimedes -- 17 The End of Greek Mathematics -- 18 Early Medieval Number Theory -- 19 Algebra in the Early Middle Ages -- 20 Geometry in the Early Middle Ages -- 21 Khayyam and the Cubic -- 22 The Later Middle Ages -- 23 Modern Mathematical Notation -- 24 The Secret of the Cubic -- 25 The Secret Revealed -- 26 A New Calculating Device -- 27 Mathematics and Astronomy -- 28 The Seventeenth Century -- 29 Pascal -- 30 The Seventeenth Century II -- 31 Leibniz -- 32 The Eighteenth Century -- 33 Lagrange -- 34 Nineteenth-Century Algebra -- 35 Nineteenth-Century Analysis -- 36 Nineteenth-Century Geometry -- 37 Nineteenth-Century Number Theory -- 38 Cantor -- 39 Foundations -- 40 Twentieth-Century Number Theory -- References -- Appendix A Sample Assignments and Tests -- Appendix ? Answers to Selected Exercises

Philosophy
Philosophy and science
Mathematics
Physics
Philosophy
Philosophy of Science
Mathematics general
Physics general