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Mathematical Masterpieces

Further Chronicles by the Explorers

  • Textbook
  • © 2007

Overview

Authors:
  1. Arthur Knoebel
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  2. Jerry Lodder
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  3. Reinhard Laubenbacher
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  4. David Pengelley
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  • This text has been developed and class tested for over 15 years
  • Uses original sources to teach the history of mathematics
  • Heavily illustrated with line drawings and half-tones, and each chapter is accompanied by exercises
  • Each chapter is self-contained and could be used independently
  • Includes supplementary material: sn.pub/extras

Part of the book series: Undergraduate Texts in Mathematics (UTM)

Part of the book sub series: Readings in Mathematics (READINMATH)

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Table of contents (4 chapters)

  1. Front Matter

    Pages I-XII
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  2. The Bridge Between Continuous and Discrete

    • Arthur Knoebel, Jerry Lodder, Reinhard Laubenbacher, David Pengelley
    Pages 1-82
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  3. Solving Equations Numerically: Finding Our Roots

    • Arthur Knoebel, Jerry Lodder, Reinhard Laubenbacher, David Pengelley
    Pages 83-157
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  4. Curvature and the Notion of Space

    • Arthur Knoebel, Jerry Lodder, Reinhard Laubenbacher, David Pengelley
    Pages 159-227
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  5. Patterns in Prime Numbers: The Quadratic Reciprocity Law

    • Arthur Knoebel, Jerry Lodder, Reinhard Laubenbacher, David Pengelley
    Pages 229-322
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  6. Back Matter

    Pages 311-336
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Keywords

About this book

In introducing his essays on the study and understanding of nature and e- lution, biologist Stephen J. Gould writes: [W]e acquire a surprising source of rich and apparently limitless novelty from the primary documents of great thinkers throughout our history. But why should any nuggets, or even ?akes, be left for int- lectual miners in such terrain? Hasn’t the Origin of Species been read untold millions of times? Hasn’t every paragraph been subjected to overt scholarly scrutiny and exegesis? Letmeshareasecretrootedingeneralhumanfoibles. . . . Veryfew people, including authors willing to commit to paper, ever really read primary sources—certainly not in necessary depth and completion, and often not at all. . . . I can attest that all major documents of science remain cho- full of distinctive and illuminating novelty, if only people will study them—in full and in the original editions. Why would anyone not yearn to read these works; not hunger for the opportunity? [99, p. 6f] It is in the spirit of Gould’s insights on an approach to science based on p- mary texts that we o?er the present book of annotated mathematical sources, from which our undergraduate students have been learning for more than a decade. Although teaching and learning with primary historical sources require a commitment of study, the investment yields the rewards of a deeper understanding of the subject, an appreciation of its details, and a glimpse into the direction research has taken. Our students read sequences of primary sources.

Reviews

From the reviews:

"This book is closely related to courses of mathematics held for students at New Mexico State University … . An important aspect of the book is the numerous exercises, which should help students to gain a deeper insight into the presented material. Numerous references and well-organized indices make the book easy to use. It can be recommended for university libraries and students with an interest in the history of mathematics presented from a modern point of view." (EMS Newsletter, September, 2008)

"This book consists of four chapters, each of which presents a ‘sequence of selected primary sources’ leading up to a ‘masterpiece of mathematical achievement’. … Each chapter contains … lots of historical comments sketching the further development of the topic. There are also a lot of exercises. … This is a well written and entertaining book that can (and should) be used in seminars or reading courses." (Franz Lemmermeyer, Zentralblatt MATH, Vol. 1140, 2008)

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