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Wir schreiben das Die Welt steht uns offen. An Illustrated Theory of Numbers An Illustrated Theory of Numbers gives a comprehensive introduction to number theory, with complete proofs, worked examples, and exercises. Books By Language. Books in Spanish. Categories: Mathematics Number Theory.
An Illustrated Theory of Numbers. By author Martin H. Notify me. Description 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 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. 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, and to all mathematicians seeking a fresh perspective on an ancient subject. Product details Format Hardback pages Dimensions x x 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.
Review quote 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.
Its choice of topics, superb exposition and beautiful layout will appeal to professional mathematicians as well as to students at all levels. Ribet, University of California, Berkeley show more. About Martin H. Weissman Martin H. Rating details. Book ratings by Goodreads. Goodreads is the world's largest site for readers with over 50 million reviews.
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