An Illustrated Theory of Numbers
- ISBN-10
- 1470463717
- ISBN-13
- 9781470463717
- Category
- Education
- Pages
- 323
- Language
- English
- Published
- 2020-09-15
- Publisher
- American Mathematical Soc.
- Author
- Martin H. Weissman
Description
News about this title: — Author Marty Weissman has been awarded a Guggenheim Fellowship for 2020. (Learn more here.) — Selected as a 2018 CHOICE Outstanding Academic Title — 2018 PROSE Awards Honorable Mention 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.
Get the book
Other editions
Similar books
-
Excursions in Number Theory
By Charles Stanley Ogilvy, John Timothy AndersonNo special training is needed, just high school mathematics and an inquisitive mind. "A splendidly written, well selected and presented collection. I recommend the book unreservedly to all readers." — Martin Gardner.
-
Number Theory
By Róbert Freud, Edit GyarmatiFreud and Gyarmati are well-known mathematicians and mathematical educators in Hungary, and the Hungarian version of this book is legendary there.
-
Elementary Number Theory
By Gareth A. Jones, Josephine M. JonesExercises, together with their solutions are integrated into the text, and the first few chapters assume only basic school algebra.
-
Number Theory and Geometry: An Introduction to Arithmetic Geometry
By Álvaro Lozano-RobledoWith many exercises, this book can be used as a text for a first course in number theory or for a subsequent course on arithmetic (or diophantine) geometry at the junior-senior level.
-
Numbers and Infinity: A Historical Account of Mathematical Concepts
By E. H. Sondheimer, Alan RogersonThis fresh overview of numbers and infinity avoids tedium and controversy while maintaining historical accuracy and modern relevance. Perfect for undergraduate mathematics or science history courses. 1981 edition.
-
The Book of Numbers
By Richard Guy, John H. ConwayJohn H. Conway, Richard Guy. We quote from the Preface of the Borweins' ... H.-D. Ebbinghaus, H. Hermes, F. Hirzebruch, M. Koecher, K. Mainzer, J. Neukirch, A. Prestel & R. Remmert. Numbers, Springer-Verlag, Graduate ... Karl Menninger.
-
Number Theory Revealed: A Masterclass
By Andrew GranvilleTurtle power The only 3-by-3 (normal) magic square up to isomorphism 2 7 6 94 5 3 1 8 was given to mankind by a turtle from the river Lo, in the days of the legendary Emperor Yu of China (≈ 2200 B.C.). It is magic because it is a ...
-
Elements of Number Theory
By John StillwellSolutions of equations in integers is the central problem of number theory and is the focus of this book.
-
Illustrating Mathematics
By Diana DavisThis book is for anyone who wishes to illustrate their mathematical ideas, which in our experience means everyone.
-
Introduction to the Theory of Numbers
By G. H. Hardy, Edward Maitland WrightIntroduction to the Theory of Numbers