Mathematics, a concise history and philosophy
著者
書誌事項
Mathematics, a concise history and philosophy
（Undergraduate texts in mathematics, . Readings in mathematics）
Springer-Verlag, c1994
- : us
- : gw
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Mathematics: a concise history and philosophy
Mathematics : a concise history and philosophy
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注記
Includes bibliographical references and index
内容説明・目次
- 巻冊次
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: us ISBN 9780387942803
内容説明
This is a concise introductory textbook for a one-semester (40-class) course in the history and philosophy of mathematics. It is written for mathemat 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 ac 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, stu dents are given a choice between mathematical assignments, and more his 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 mathe maticians, giving more mathematically talented students a greater oppor tunity to learn the history and philosophy by way of problem solving.
目次
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 Euclid'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.
- 巻冊次
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: gw ISBN 9783540942801
内容説明
This is a concise introductory textbook for a one-term course in the history and philosophy of mathematics. It is written for mathematics majors, philosophy students, history of science students and secondary school mathematics teachers. The only prerequisite is a solid command of pre-calculus mathematics. Furthermore, there are many detailed explanations of the important mathematical procedures actually used by famous mathematicians, giving more mathematically talented students a greater opportunity to learn the history and philosophy by way of problem-solving. Several important philosophical topics are pursued throughout the text, giving the student an opportunity to come to a full understanding of their development. These topics include infinity, the nature of motion and Platonism.
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