# History of Mathematics, A (Classic Version), 3rd edition

Published by Pearson (March 21, 2017) © 2018

**Victor J. Katz**University of the District of Columbia

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For junior- to senior-level courses in the history of mathematics for mathematics majors intending to become teachers.

### A modern classic

**A History of Mathematics, 3rd 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 title is part of the Pearson Modern Classics series. Pearson Modern Classics are acclaimed titles at a value price.

### Hallmark features of this title

**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.

### New and updated features of this title

**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 19th and 20th centuries; the 18th-century translation of some of Newton's work in the Principia into analysis; the solution to the Poincarè Conjecture, the first Clay Institute problem.

**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### About our author

**Victor J. Katz** received his PhD in mathematics from Brandeis University in 1968 and has been Professor of Mathematics at the University of the District of Columbia for many years. He has long been interested in the history of mathematics and, in particular, in its use in teaching. He is the editor of **The Mathematics of Egypt, Mesopotamia, China, India and Islam: A Sourcebook** (2007). He has edited or co-edited two recent books dealing with this subject, **Learn from the Masters** (1994) and **Using History to Teach Mathematics** (2000). Dr. Katz also co-edited a collection of historical articles taken from MAA journals of the past 90 years, **Sherlock Holmes in Babylon and other Tales of Mathematical History**. He has directed two NSF-sponsored projects to help college teachers learn the history of mathematics and learn to use it in teaching. Dr. Katz has also involved secondary school teachers in writing materials using history in the teaching of various topics in the high school curriculum. These materials, **Historical Modules for the Teaching and Learning of Mathematics**, have now been published by the MAA. Currently, Dr. Katz is the PI on an NSF grant to the MAA that supports Convergence, an online magazine devoted to the history of mathematics and its use in teaching.

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