The History of Mathematics: A Brief Course

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John Wiley & Sons, 8 de nov. 2012 - 648 pàgines
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Praise for the Second Edition

"An amazing assemblage of worldwide contributions in mathematics and, in addition to use as a course book, a valuable resource . . . essential."
—CHOICE

This Third Edition of The History of Mathematics examines the elementary arithmetic, geometry, and algebra of numerous cultures, tracing their usage from Mesopotamia, Egypt, Greece, India, China, and Japan all the way to Europe during the Medieval and Renaissance periods where calculus was developed.

Aimed primarily at undergraduate students studying the history of mathematics for science, engineering, and secondary education, the book focuses on three main ideas: the facts of who, what, when, and where major advances in mathematics took place; the type of mathematics involved at the time; and the integration of this information into a coherent picture of the development of mathematics. In addition, the book features carefully designed problems that guide readers to a fuller understanding of the relevant mathematics and its social and historical context. Chapter-end exercises, numerous photographs, and a listing of related websites are also included for readers who wish to pursue a specialized topic in more depth. Additional features of The History of Mathematics, Third Edition include:

  • Material arranged in a chronological and cultural context
  • Specific parts of the history of mathematics presented as individual lessons
  • New and revised exercises ranging between technical, factual, and integrative
  • Individual PowerPoint presentations for each chapter and a bank of homework and test questions (in addition to the exercises in the book)
  • An emphasis on geography, culture, and mathematics

In addition to being an ideal coursebook for undergraduate students, the book also serves as a fascinating reference for mathematically inclined individuals who are interested in learning about the history of mathematics.

 

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Continguts

What is Mathematics?
Protomathematics
The Middle East 20001500
Computations in Ancient Mesopotamia
Geometry inMesopotamia 5 1 The Pythagorean Theorem 5 2 PlaneFigures
Egyptian Numerals and Arithmetic
Algebra and Geometry in Ancient Egypt
Greek Mathematics From 500
LaterChinese Algebra and Geometry 23 1 Algebra 23 2 Later Chinese
Traditional Japanese Mathematics
Contents of Part V
Islamic Geometry
European Mathematics 5001900
Medieval and Early Modern Europe
European Mathematics 12001500
RenaissanceArtandGeometry

Greek Number Theory
FifthCentury GreekGeometry 10 1 Pythagorean Geometry 10 2 Challenge No 1Unsolved Problems 10 3 Challenge No 2The Paradoxes ofZenoof Elea
Athenian Mathematics I The Classical
AthenianMathematics II Plato and Aristotle
Euclid of Alexandria
Archimedes of Syracuse
Apollonius ofPerga 15 1 History ofthe Conics
Hellenistic and Roman Geometry
Ptolemys Geography
Part
Pappus andthe LaterCommentators 18 1 The Collection of Pappus
AryabhataI
From the Vedas to Aryabhata I
Brahmagupta the Kuttaka and BhaskaraII
Chinese Mathematics
Chapter
Special Topics
Probability
Algebra from 1600 to 1850
Projective and Algebraic Geometry
Differential Geometry 39 1Plane Curves
NonEuclidean Geometry
Complex Analysis
Foundations of Real Analysis
Set Theory 44 1 Technical Background
Logic
Name Index
Subject Index
Copyright

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Quant a l’autor (2012)

ROGER L. COOKE, PhD, is Williams Professor of Mathematics at the University of Vermont. His research interests include the history of mathematics and Fourier analysis, and he has taught a general introduction to the history and development of mathematics for many years.

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