History of Mathematics: An Introduction, A, 4th edition
Title overview
For junior- to senior-level courses in the history of mathematics for mathematics majors intending to become teachers.
Fosters a deeper understanding of math concepts in their historical context
A History of Mathematics focuses on the most important topics for today's elementary, high school and college curricula. The flexible presentation organizes the book by chronological period and then by topic, which gives instructors the option to follow a specific theme throughout the course. Future teachers will find it a valuable resource to develop lesson plans based on the history of each topic. The 4th Edition includes 14 new interactive GeoGebra figures, adds a section on mathematics in the U.S. in the 20th century, and much more.
Hallmark features of this title
- Discussions of the important textbooks of major time periods show students how topics were treated historically, 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
- 14 new interactive GeoGebra figures illustrate concepts like Ptolemy’s theorem and Mercator projection.
- New material on Babylonian and Egyptian mathematics is provided, especially developments during Greek rule in the eastern Mediterranean.
- New discussion of the conchoid of Nicomedes and on Islamic mathematics accomplished in Spain is added.
- Details on the work of Citrabhānu in the chapter on India is provided.
- Expanded material on advanced geometry in medieval Europe is provided.
- A new section on mathematics in the United States in the 20th century is added.
Table of contents
I. ANCIENT MATHEMATICS
- 1: Egypt and Mesopotamia
- 2: The Beginnings of Mathematics in Greece
- 3: Euclid
- 4: Archimedes and Apollonius
- 5: Mathematical Methods in Hellenistic Times
- 6: The Final Chapters of Greek Mathematics
II. MEDIEVAL MATHEMATICS
- 7: Ancient and Medieval China
- 8: Ancient and Medieval India
- 9: The Mathematics of Islam
- 10: Mathematics in Medieval Europe
- 11: Mathematics around the World
III. EARLY MODERN MATHEMATICS
- 12: Algebra in the Renaissance
- 13: Mathematical Methods in the Renaissance
- 14: Algebra, Geometry, and Probability in the Seventeenth Century
- 15: The Beginnings of Calculus
- 16: Newton and Leibniz
IV. MODERN MATHEMATICS
- 17: Analysis in the Eighteenth Century
- 18: Probability and Statistics in the Eighteenth Century
- 19: Algebra and Number Theory in the Eighteenth Century
- 20: Geometry in the Eighteenth Century
- 21: Algebra and Number Theory in the Nineteenth Century
- 22: Analysis in the Nineteenth Century
- 23: Probability and Statistics in the Nineteenth Century
- 24: Geometry in the Nineteenth Century
- 25: Aspects of the Twentieth Century and Beyond
Appendix A: Using This Textbook in Teaching Mathematics
General References in the History of Mathematics
Index and Pronunciation Guide
Author bios
About our author
Victor J. Katz received his PhD in mathematics from Brandeis University in 1968. He is now a Professor of Mathematics emeritus at the University of the District of Columbia, where he taught for 37 years. He has long been interested in the history of mathematics, and particularly in its use in teaching. He has edited or co-edited 3 books dealing with this subject: Learn from the Masters (1994), Using History to Teach Mathematics: An International Perspective (2000), and Recent Developments on Introducing a Historical Dimension in Mathematics Education (2011). He is also the editor of 3 sourcebooks in mathematics: The Mathematics of Egypt, Mesopotamia, China, India and Islam: A Sourcebook (2007), Sourcebook in the Mathematics of Medieval Europe and North Africa (2016), and Sourcebook in the Mathematics of Ancient Greece and the Eastern Mediterranean (2024).
Dr. Katz also co-edited 2 volumes of historical articles taken from MAA journals of the past 100 years: Sherlock Holmes in Babylon and Other Tales of Mathematical History and Who Gave You the Epsilon? & Other Tales of Mathematical History. He co-directed the NSF-sponsored projects entitled the Institute in the History of Mathematics and Its Use in Teaching designed to help college teachers learn the history of mathematics and how to use it in teaching. This project also included secondary school teachers, who ultimately wrote materials using the history of mathematics in the teaching of numerous topics in the high-school curriculum. These materials (Historical Modules for the Teaching and Learning of Mathematics) have been published by the MAA. With the late Frank Swetz, he was the founding editor of Convergence, the MAA’s online magazine devoted to the history of mathematics and its use in teaching (a magazine now more than 20 years old). In 2023, Dr. Katz received the MAA’s Yueh-Gin Gung and Charles Y. Hu Award for Distinguished Service to Mathematics.
Dr. Katz had been married for 55 years to Dr. Phyllis Katz, herself an accomplished researcher in science education outside of schools. Together they have 3 adult children and 8 grandchildren.