A History of Mathematics, 3rd Edition provides 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.
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Höhe: 231 mm
Breite: 203 mm
Dicke: 38 mm
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ISBN-13
978-0-13-468952-4 (9780134689524)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Klassifikation
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.
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
