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Science & Mathematics - An Illustrated Theory of Numbers

Description

Book Synopsis: 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.

Details

Discover the fascinating world of number theory with An Illustrated Theory of Numbers. Written by renowned author Marty Weissman, this comprehensive book offers a complete introduction to number theory, packed with proofs, examples, and exercises. With its cutting-edge approach and insightful geometric and dynamical arguments, it provides a rigorous yet accessible exploration of this ancient mathematical discipline.

What sets An Illustrated Theory of Numbers apart is its innovative use of almost 500 sharp illustrations to accompany elegant proofs. From prime decomposition to quadratic reciprocity, these visuals bring the concepts to life, making it easier for readers to grasp complex theories. No more endless algebraic manipulations – this book focuses on providing you with a visual understanding that will leave you with a fresh perspective on number theory.

But this book goes beyond just presenting the core concepts. In its final chapters, An Illustrated Theory of Numbers delves deep into binary quadratic forms, introducing Conway's topograph to solve quadratic Diophantine equations. It also explores topics like reduction, the finiteness of class numbers, and even touches on open questions and cutting-edge results in analytic number theory. Prepare to be fascinated by the Riemann hypothesis, the boundedness of prime gaps, and the class number 1 problem.

Whether you're a student looking for a first course in elementary number theory or a mathematician craving a fresh perspective on an ancient subject, An Illustrated Theory of Numbers is the perfect choice. With its concise and accessible explanations, this book requires only high school algebra and geometry as a prerequisite, making it suitable for a wide range of readers.

Don't miss out on the opportunity to explore the captivating world of number theory. Get your copy of An Illustrated Theory of Numbers today and uncover the beauty and elegance hidden within the numbers.

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