History of Mathematics, A

Victor J. Katz  
Total pages
November 2013
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History of Mathematics, A
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A History of Mathematics, Third Edition, provides students with a solid background in the history of mathematics and focuses on the most important topics for today’s elementary, high school, and college curricula. Students will gain a deeper understanding of mathematical concepts in their historical context, and future teachers will find this book a valuable resource in developing lesson plans based on the history of each topic.

This book is ideal for a junior or senior level course in the history of mathematics for mathematics majors intending to become teachers.


  • 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 to this Edition

  • 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 palimpsest
    • A new section on Ptolemy’s Geography
    • Expanded coverage of Chinese, Indian, and Islamic mathematicians.
    • Increased material on ancient Egyptian and Babylonian mathematics.
    • New material on statistics in the nineteenth and twentieth centuries
    • The eighteenth century translation of some of Newton's work in the Principia into analysis
    • The solution to the Poincarè Conjecture, the first Clay Institute problem

Table of Contents

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