Mathematics: A Concise History and Philosophy

This is a concise introductory textbook for a one semester 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.

Inhalt
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.