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An Illustrated Theory of Numbers


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Table of Contents

  • Seeing arithmetic
  • Foundations: The Euclidean algorithm
  • Prime factorization
  • Rational and constructible numbers
  • Gaussian and Eisenstein integers
  • Modular arithmetic: The modular worlds
  • Modular dynamics
  • Assembling the modular worlds
  • Quadratic residues
  • Quadratic forms: The topograph
  • Definite forms
  • Indefinite forms
  • Index of theorems
  • Index of terms
  • Index of names
  • Bibliography.

About the Author

Martin H. Weissman, University of California, Santa Cruz, CA.


This is a meticulously written and stunningly laid-out book influenced not only by the classical masters of number theory like Fermat, Euler, and Gauss, but also by the work of Edward Tufte on data visualization. Assuming little beyond basic high school mathematics, the author covers a tremendous amount of territory, including topics like Ford circles, Conway's topographs, and Zolotarev's lemma which are rarely seen in introductory courses. All of this is done with a visual and literary flair which very few math books even strive for, let alone accomplish"". - Matthew Baker, Georgia Institute of Technology

""Weissman's book represents a totally fresh approach to a venerable subject. Its choice of topics, superb exposition and beautiful layout will appeal to professional mathematicians as well as to students at all levels."" - Kenneth A. Ribet, University of California, Berkeley

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