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 flexible presentation organizes the book by chronological period and then by topic, which gives instructors the option of following a specific theme throughout the course.Discussions of the important textbooks of major time periods show students how topics were historically treated, allowing students to draw connections to modern approaches.A global perspective integrates non-Western coverage, including contributions from Chinese, Indian, and Islamic mathematicians. An additional chapter discusses the mathematical achievements of early Africa, America, and Asia.Chapter openers include a vignette and quotation to add motivation and human interest.Focus essays are boxed features that are set apart from the main narrative of the text for easy reference. Biographies outline the lives and achievements of notable mathematicians. Other essays explore special topics, such as Egyptian influence on Greek mathematics.A chronology of major mathematicians at the end of every chapter gives an overview of important individuals and their contribution to the field of mathematics.Problems from primary sources enable students to understand how mathematicians were able to solve problems at various times and places.Discussion questions promote group work and can be used by future teachers to design lessons for elementary and secondary level math classes.An annotated bibliography at the end of each chapter provides easy reference to primary and secondary sources for research and further study.A phonetic pronunciation guide is included to aid in the pronunciation of historical names and places.

New exercises include more basic exercises to ensure that students understand and retain the material.Shorter chapters and sections allow for increased flexibility of coverage.New and updated coverage based on the latest research and findings: New material on Archimedes discovered in the analysis of theMethod palimpsestA new section on Ptolemy’s GeographyExpanded coverage of Chinese, Indian, and Islamic mathematicians.Increased material on ancient Egyptian and Babylonian mathematics.New material on statistics in the nineteenth and twentieth centuriesThe eighteenth century translation of some of Newton's work in the Principia into analysisThe solution to the Poincarè Conjecture, the first Clay Institute problem