Preface 0 Introduction PART Ⅰ: History and Philosophy of Mathematics 1 Egyptian Mathematics 2 Scales of Notation 3 Prime Numbers 4 Sumerian-Babylonian Mathematics 5 More about Mesopotamian Mathematics 6 The Dawn of Greek Mathematics 7 Pythagoras and His School 8 Perfect Numbers 9 Regular Polyhedra 10 The Crisis of Incommensurables 11 From Heraclitus to Democritus 12 Mathematics in Athens 13 Plato and Aristotle on Mathematics 14 Constructions with Ruler and Compass 15 The Impossibility of Solving the Classical Problems 16 Euclid 17 Non-Euclidean Geometry and Hilbert's Axioms 18 Alexandria from 300 BC to 200 BC 19 Archimedes 20 Alexandria from 200 BC to 500 AD 21 Mathematics in China and India 22 Mathematics in Islamic Countries 23 New Beginnings in Europe 24 Mathematics in the Renaissance 25 The Cubic and Quartic Equations 26 Renaissance Mathematics Continued 27 The Seventeenth Century in France 28 The Seventeenth Century Continued 29 Leibniz 30 The Eighteenth Century 31 The Law of Quadratic Reciprocity PART Ⅱ: Foundations of Mathematics 1 The Number System 2 Natural Numbers (Peano's Approach) 3 The Integers …… References Index
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