This volume is not part of this online collection.
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
“An Illustrated Theory of Numbers”
is a textbook like none other I know; and not just a textbook, but a
work of practical art. This book would be a delight to use in the
undergraduate classroom, to give to a high school student in search of
enlightenment, or to have on your coffee table, to give guests from
the world outside mathematics a visceral and visual sense of the
beauty of our subject.
—Jordan Ellenberg, University of
Wisconsin-Madison, author of “How Not to Be Wrong: the Power of
Mathematical Thinking”
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
An Illustrated Theory of Numbers gives a comprehensive
introduction to number theory, with complete proofs, worked examples,
and exercises. Its exposition reflects the most recent scholarship in
mathematics and its history.
Almost 500 sharp illustrations accompany elegant proofs, from prime
decomposition through quadratic reciprocity. Geometric and dynamical
arguments provide new insights, and allow for a rigorous approach with
less algebraic manipulation. The final chapters contain an extended
treatment of binary quadratic forms, using Conway's topograph to solve
quadratic Diophantine equations (e.g., Pell's equation) and to study
reduction and the finiteness of class numbers.
Data visualizations introduce the reader to open questions and
cutting-edge results in analytic number theory such as the Riemann
hypothesis, boundedness of prime gaps, and the class number 1
problem. Accompanying each chapter, historical notes curate primary
sources and secondary scholarship to trace the development of number
theory within and outside the Western tradition.
Requiring only high school algebra and geometry, this text is
recommended for a first course in elementary number theory. It is also
suitable for mathematicians seeking a fresh perspective on an ancient
subject.
Readership
Undergraduate and graduate students interested in
number theory.