A History of Mathematics: An Introduction

Part I. Ancient Mathematics 1. Egypt and Mesopotamia 1.1 Egypt 1.2 Mesopotamia 2. The Beginnings of Mathematics in Greece 2.1 The Earliest Greek Mathematics 2.2 The Time of Plato 2.3 Aristotle 3. Euclid 3.1 Introduction to the Elements 3.2 Book I and the Pythagorean Theorem 3.3 Book II and Geometric Algebra 3.4 Circles and the Pentagon 3.5 Ratio and Proportion 3.6 Number Theory 3.7 Irrational Magnitudes 3.8 Solid Geometry and the Method of Exhaustion 3.9 Euclid's Data 4. Archimedes and Apollonius 4.1 Archimedes and Physics 4.2 Archimedes and Numerical Calculations 4.3 Archimedes and Geometry 4.4 Conic Sections Before Apollonius 4.5 The Conics of Apollonius 5. Mathematical Methods in Hellenistic Times 5.1 Astronomy Before Ptolemy 5.2 Ptolemy and The Almagest 5.3 Practical Mathematics 6. The Final Chapter of Greek Mathematics 6.1 Nichomachus and Elementary Number Theory 6.2 Diophantus and Greek Algebra 6.3 Pappus and Analysis Part II. Medieval Mathematics 7. Ancient and Medieval China 7.1 Introduction to Mathematics in China 7.2 Calculations 7.3 Geometry 7.4 Solving Equations 7.5 Indeterminate Analysis 7.6 Transmission to and from China 8. Ancient and Medieval India 8.1 Introduction to Mathematics in India 8.2 Calculations 8.3 Geometry 8.4 Equation Solving 8.5 Indeterminate Analysis 8.6 Combinatorics 8.7 Trigonometry 8.8 Transmission to and from India 9. The Mathematics of Islam 9.1 Introduction to Mathematics in Islam 9.2 Decimal Arithmetic 9.3 Algebra 9.4 Combinatorics 9.5 Geometry 9.6 Trigonometry 9.7 Transmission of Islamic Mathematics 10. Medieval Europe 10.1 Introduction to the Mathematics of Medieval Europe 10.2 Geometry and Trigonometry 10.3 Combinatorics 10.4 Medieval Algebra 10.5 The Mathematics of Kinematics 11. Mathematics Elsewhere 11.1 Mathematics at the Turn of the Fourteenth Century 11.2 Mathematics in America, Africa, and the Pacific Part III. Early Modern Mathematics 12. Algebra in the Renaissance 12.1 The Italian Abacists 12.2 Algebra in France, Germany, England, and Portugal 12.3 The Solution of the Cubic Equation 12.4 Viete, Algebraic Symbolism, and Analysis 12.5 Simon Stevin and Decimal Analysis 13. Mathematical Methods in the Renaissance 13.1 Perspective 13.2 Navigation and Geography 13.3 Astronomy and Trigonometry 13.4 Logarithms 13.5 Kinematics 14. Geometry, Algebra and Probability in the Seventeenth Century 14.1 The Theory of Equations 14.2 Analytic Geometry 14.3 Elementary Probability 14.4 Number Theory 14.5 Projective Geometry 15. The Beginnings of Calculus 15.1 Tangents and Extrema 15.2 Areas and Volumes 15.3 Rectification of Curves and the Fundamental Theorem 16. Newton and Leibniz 16.1 Isaac Newton 16.2 Gottfried Wilhelm Leibniz 16.3 First Calculus Texts Part IV. Modern Mathematics 17. Analysis in the Eighteenth Century 17.1 Differential Equations 17.2 The Calculus of Several Variables 17.3 Calculus Texts 17.4 The Foundations of Calculus 18. Probability and Statistics in the Eighteenth Century 18.1 Theoretical Probability 18.2 Statistical Inference 18.3 Applications of Probability 19. Algebra and Number Theory in the Eighteenth Century 19.1 Algebra Texts 19.2 Advances in the Theory of Equations 19.3 Number Theory 19.4 Mathematics in the Americas 20. Geometry in the Eighteenth Century 20.1 Clairaut and the Elements of Geometry 20.2 The Parallel Postulate 20.3 Analytic and Differential Geometry 20.4 The Beginnings of Topology 20.5 The French Revolution and Mathematics Education 21. Algebra and Number Theory in the Nineteenth Century 21.1 Number Theory 21.2 Solving Algebraic Equations 21.3 Symbolic Algebra 21.4 Matrices and Systems of Linear Equations 21.5 Groups and Fields - The Beginning of Structure 22. Analysis in the Nineteenth Century 22.1 Rigor in Analysis 22.2 The Arithmetization of Analysis 22.3 Complex Analysis 22.4 Vector Analysis 23. Probability and Statistics in the Nineteenth Century 23.1 The Method of Least Squares and Probability Distributions 23.2 Statistics and the Social Sciences 23.3 Statistical Graphs 24. Geometry in the Nineteenth Century 24.1 Differential Geometry 24.2 Non-Euclidean Geometry 24.3 Projective Geometry 24.4 Graph Theory and the Four Color Problem 24.5 Geometry in N Dimensions 24.6 The Foundations of Geometry 25. Aspects of the Twentieth Century 25.1 Set Theory: Problems and Paradoxes 25.2 Topology 25.3 New Ideas in Algebra 25.4 The Statistical Revolution 25.5 Computers and Applications 25.6 Old Questions Answered