A History of Mathematics

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  • Edition: 3rd
  • Format: Paperback
  • Copyright: 2008-07-02
  • Publisher: Pearson
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One of the leading historians in the mathematics field, Victor Katz provides a world view of mathematics, balancing ancient, early modern, and modern history.

Author Biography

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.

Table of Contents

Ancient Mathematics
Egypt and Mesopotamia
The Beginnings of Mathematics in Greece
The Earliest Greek Mathematics
The Time of Plato
Introduction to the Elements
Book I and the Pythagorean Theorem
Book II and Geometric Algebra
Circles and the Pentagon
Ratio and Proportion
Number Theory
Irrational Magnitudes
Solid Geometry and the Method of Exhaustion
Euclids Data
Archimedes and Apollonius
Archimedes and Physics
Archimedes and Numerical Calculations
Archimedes and Geometry
Conic Sections Before Apollonius
The Conics of Apollonius
Mathematical Methods in Hellenistic Times
Astronomy Before Ptolemy
Ptolemy and The Almagest
Practical Mathematics
The Final Chapter of Greek Mathematics
Nichomachus and Elementary Number Theory
Diophantus and Greek Algebra
Pappus and Analysis
Medieval Mathematics
Ancient and Medieval China
Introduction to Mathematics in China
Solving Equations
Indeterminate Analysis
Transmission to and from China
Ancient and Medieval India
Introduction to Mathematics in India
Equation Solving
Indeterminate Analysis
Transmission to and from India
The Mathematics of Islam
Introduction to Mathematics in Islam
Decimal Arithmetic
Transmission of Islamic Mathematics
Medieval Europe
Introduction to the Mathematics of Medieval Europe
Geometry and Trigonometry
Medieval Algebra
The Mathematics of Kinematics
Mathematics Elsewhere
Mathematics at the Turn of the Fourteenth Century
Mathematics in America, Africa, and the Pacific
Early Modern Mathematics
Algebra in the Renaissance
The Italian Abacists
Algebra in France, Germany, England, and Portugal
The Solution of the Cubic Equation
Viete, Algebraic Symbolism, and Analysis
Simon Stevin and Decimal Analysis
Mathematical Methods in the Renaissance
Navigation and Geography
Astronomy and Trigonometry
Geometry, Algebra and Probability in the Seventeenth Century
The Theory of Equations
Analytic Geometry
Elementary Probability
Number Theory
Projective Geometry
The Beginnings of Calculus
Tangents and Extrema
Areas and Volumes
Rectification of Curves and the Fundamental Theorem
Newton and Leibniz
Isaac Newton
Gottfried Wilhelm Leibniz
First Calculus Texts
Modern Mathematics
Analysis in the Eighteenth Century
Differential Equations
The Calculus of Several Variables
Calculus Texts
The Foundations of Calculus
Probability and Statistics in the Eighteenth Century
Theoretical Probability
Statistical Inference
Table of Contents provided by Publisher. All Rights Reserved.

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