Mathematics: A Concise History and Philosophy

1994
ISBN: 978-0-387-94280-3
Verlag: Springer

Buch, Englisch, 265 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 1270 g

Reihe: Readings in Mathematics

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.

Zielgruppe

Lower undergraduate

Autoren/Hrsg.

Anglin, W. S.

Fachgebiete

• Interdisziplinäres Wissenschaften Wissenschaften: Allgemeines Wissenschaften: Theorie, Epistemologie, Methodik
• Naturwissenschaften Physik Physik Allgemein
• Geisteswissenschaften Geschichtswissenschaft Geschichtliche Themen Kultur- und Ideengeschichte
• Mathematik | Informatik Mathematik Mathematik Allgemein Philosophie der Mathematik
• Interdisziplinäres Wissenschaften Wissenschaften: Allgemeines Geschichte der Human- und Sozialwissenschaften
• Interdisziplinäres Wissenschaften Wissenschaften: Allgemeines Geschichte der Naturwissenschaften, Formalen Wissenschaften & Technik
• Geisteswissenschaften Philosophie Philosophie der Mathematik, Philosophie der Physik
• Geisteswissenschaften Geschichtswissenschaft Geschichtliche Themen Wissenschafts- und Universitätsgeschichte
• Geisteswissenschaften Philosophie Wissenschaftstheorie, Wissenschaftsphilosophie

Inhaltsverzeichnis

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.