Victor J. Katz

History of Mathematics, A (eBook, PDF)

Pearson New International Edition

• Format: PDF

Produktbeschreibung

A History of Mathematics, Third 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 book is ideal for a junior or senior level course in the history of mathematics for mathematics majors intending to become teachers.

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Produktdetails

• Verlag: Pearson HigherEducation
• Seitenzahl: 948
• Altersempfehlung: ab 18 Jahre
• Erscheinungstermin: 3. Oktober 2013
• Englisch
• ISBN-13: 9781292053783
• Artikelnr.: 41940537

Inhaltsangabe

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