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History of Mathematics, A (Classic Version) - Victor Katz

History of Mathematics, A (Classic Version)

(Autor)

Buch | Softcover
1000 Seiten
2017 | 3rd edition
Pearson (Verlag)
978-0-13-468952-4 (ISBN)
CHF 199,75 inkl. MwSt
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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.

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

Erscheinungsdatum
Reihe/Serie Pearson Modern Classics for Advanced Mathematics Series
Sprache englisch
Maße 203 x 231 mm
Gewicht 1440 g
Themenwelt Mathematik / Informatik Mathematik
ISBN-10 0-13-468952-6 / 0134689526
ISBN-13 978-0-13-468952-4 / 9780134689524
Zustand Neuware
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