The History of Mathematics: A Brief Course

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John Wiley & Sons, Nov 8, 2012 - Mathematics - 648 pages
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Praise for the Second Edition

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

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

Aimed primarily at undergraduate students studying the historyof 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 ofmathematics involved at the time; and the integration of thisinformation into a coherent picture of the development ofmathematics. In addition, the book features carefully designedproblems that guide readers to a fuller understanding of therelevant mathematics and its social and historical context.Chapter-end exercises, numerous photographs, and a listing ofrelated websites are also included for readers who wish to pursue aspecialized topic in more depth. Additional features of TheHistory of Mathematics, Third Edition include:

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

In addition to being an ideal coursebook for undergraduatestudents, the book also serves as a fascinating reference formathematically inclined individuals who are interested in learningabout the history of mathematics.


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What is Mathematics?
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

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
Pappus andthe LaterCommentators 18 1 The Collection of Pappus
From the Vedas to Aryabhata I
Brahmagupta the Kuttaka and BhaskaraII
Chinese Mathematics
Special Topics
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
Name Index
Subject Index

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About the author (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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