A history of mathematics: an introduction

Content: Part I. Ancient Mathematics 1. Egypt and Mesopotamia1.1 Egypt1.2 Mesopotamia 2. The Beginnings of Mathematics in Greece2.1 The Earliest Greek Mathematics2.2 The Time of Plato2.3 Aristotle 3. Euclid3.1 Introduction to the Elements3.2 Book I and the Pythagorean Theorem3.3 Book II and Geometric Algebra3.4 Circles and the Pentagon3.5 Ratio and Proportion3.6 Number Theory3.7 Irrational Magnitudes3.8 Solid Geometry and the Method of Exhaustion3.9 Euclid's Data 4. Archimedes and Apollonius4.1 Archimedes and Physics4.2 Archimedes and Numerical Calculations4.3 Archimedes and Geometry4.4 Conic Sections Before Apollonius4.5 The Conics of Apollonius 5. Mathematical Methods in Hellenistic Times5.1 Astronomy Before Ptolemy5.2 Ptolemy and The Almagest5.3 Practical Mathematics 6. The Final Chapter of Greek Mathematics6.1 Nichomachus and Elementary Number Theory6.2 Diophantus and Greek Algebra6.3 Pappus and Analysis Part II. Medieval Mathematics 7. Ancient and Medieval China7.1 Introduction to Mathematics in China7.2 Calculations7.3 Geometry7.4 Solving Equations7.5 Indeterminate Analysis7.6 Transmission to and from China 8. Ancient and Medieval India8.1 Introduction to Mathematics in India8.2 Calculations8.3 Geometry8.4 Equation Solving8.5 Indeterminate Analysis8.6 Combinatorics8.7 Trigonometry8.8 Transmission to and from India 9. The Mathematics of Islam9.1 Introduction to Mathematics in Islam9.2 Decimal Arithmetic9.3 Algebra9.4 Combinatorics9.5 Geometry9.6 Trigonometry9.7 Transmission of Islamic Mathematics 10. Medieval Europe10.1 Introduction to the Mathematics of Medieval Europe10.2 Geometry and Trigonometry10.3 Combinatorics10.4 Medieval Algebra10.5 The Mathematics of Kinematics 11. Mathematics Elsewhere11.1 Mathematics at the Turn of the Fourteenth Century11.2 Mathematics in America, Africa, and the Pacific Part III. Early Modern Mathematics 12. Algebra in the Renaissance12.1 The Italian Abacists12.2 Algebra in France, Germany, England, and Portugal12.3 The Solution of the Cubic Equation12.4 Viete, Algebraic Symbolism, and Analysis12.5 Simon Stevin and Decimal Analysis 13. Mathematical Methods in the Renaissance13.1 Perspective13.2 Navigation and Geography13.3 Astronomy and Trigonometry13.4 Logarithms13.5 Kinematics 14. Geometry, Algebra and Probability in the Seventeenth Century14.1 The Theory of Equations14.2 Analytic Geometry14.3 Elementary Probability14.4 Number Theory14.5 Projective Geometry 15. The Beginnings of Calculus15.1 Tangents and Extrema15.2 Areas and Volumes15.3 Rectification of Curves and the Fundamental Theorem 16. Newton and Leibniz16.1 Isaac Newton16.2 Gottfried Wilhelm Leibniz16.3 First Calculus Texts Part IV. Modern Mathematics 17. Analysis in the Eighteenth Century17.1 Differential Equations17.2 The Calculus of Several Variables17.3 Calculus Texts17.4 The Foundations of Calculus 18. Probability and Statistics in the Eighteenth Century18.1 Theoretical Probability18.2 Statistical Inference18.3 Applications of Probability 19. Algebra and Number Theory in the Eighteenth Century19.1 Algebra Texts19.2 Advances in the Theory of Equations19.3 Number Theory19.4 Mathematics in the Americas 20. Geometry in the Eighteenth Century20.1 Clairaut and the Elements of Geometry20.2 The Parallel Postulate20.3 Analytic and Differential Geometry20.4 The Beginnings of Topology20.5 The French Revolution and Mathematics Education 21. Algebra and Number Theory in the Nineteenth Century21.1 Number Theory21.2 Solving Algebraic Equations21.3 Symbolic Algebra21.4 Matrices and Systems of Linear Equations21.5 Groups and Fields - The Beginning of Structure 22. Analysis in the Nineteenth Century22.1 Rigor in Analysis22.2 The Arithmetization of Analysis22.3 Complex Analysis22.4 Vector Analysis 23. Probability and Statistics in the Nineteenth Century23.1 The Method of Least Squares and Probability Distributions23.2 Statistics and the Social Sciences23.3 Statistical Graphs 24. Geometry in the Nineteenth Century24.1 Differential Geometry24.2 Non-Euclidean Geometry24.3 Projective Geometry24.4 Graph Theory and the Four Color Problem24.5 Geometry in N Dimensions24.6 The Foundations of Geometry 25. Aspects of the Twentieth Century25.1 Set Theory: Problems and Paradoxes25.2 Topology25.3 New Ideas in Algebra25.4 The Statistical Revolution25.5 Computers and Applications25.6 Old Questions Answered