The History of Mathematics

Roger L. Cooke 지음

Wiley 2012년 11월 08일 출간

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Praise for the Second Editionquot;An amazing assemblage of worldwide contributions in mathematics and, in addition to use as a course book, a valuable resource . . . essential.quot;m-CHOICEThis 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 contextSpecific parts of the history of mathematics presented as individual lessonsNew and revised exercises ranging between technical, factual, and integrativeIndividual 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

PREFACE xxiiiChanges from the Second Edition xxiiiElementary Texts on the History of Mathematics xxivPART I. WHAT IS MATHEMATICS?Contents of Part I 11. Mathematics and its History 31.1. Two Ways to Look at the History of Mathematics 31.2. The Origin of Mathematics 51.3. The Philosophy of Mathematics 81.4. Our Approach to the History of Mathematics 112. Proto-mathematics 142.1. Number 142.2. Shape 162.3. Symbols 182.4. Mathematical Reasoning 20PART II. THE MIDDLE EAST, 2000&n-1500 BCEContents of Part II 253. Overview of Mesopotamian Mathematics 273.1. A Sketch of Two Millennia of Mesopotamian History 273.2. Mathematical Cuneiform Tablets 293.3. Systems of Measuring and Counting 303.4. The Mesopotamian Numbering System 314. Computations in Ancient Mesopotamia 384.1. Arithmetic 384.2. Algebra 405. Geometry in Mesopotamia 465.1. The Pythagorean Theorem 465.2. Plane Figures 485.3. Volumes 495.4. Plimpton 322 496. Egyptian Numerals and Arithmetic 566.1. Sources 566.2. The Rhind Papyrus 586.3. Egyptian Arithmetic 586.4. Computation 597. Algebra and Geometry in Ancient Egypt 667.1. Algebra Problems in the Rhind Papyrus 667.2. Geometry 687.3. Areas 69PART III. GREEK MATHEMATICS FROM 500 BCE TO 500 CEContents of Part III 778. An Overview of Ancient Greek Mathematics 798.1. Sources 808.2. General Features of Greek Mathematics 828.3. Works and Authors 879. Greek Number Theory 919.1. The Euclidean Algorithm 929.2. The Arithmetica of Nicomachus 939.3. Euclid&'s Number Theory 979.4. The Arithmetica of

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저자(글) Roger L. Cooke

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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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