An Illustrated Theory Of Numbers
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An Illustrated Theory Of Numbers
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Author : Martin H. Weissman
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-09-15
An Illustrated Theory Of Numbers written by Martin H. Weissman and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-15 with Education categories.
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.
An Illustrated Theory Of Numbers
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Author : Martin H. Weissman
language : en
Publisher: American Mathematical Soc.
Release Date : 2017
An Illustrated Theory Of Numbers written by Martin H. Weissman and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with Mathematics categories.
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
Elements Of The Theory Of Numbers
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Author : Joseph B. Dence
language : en
Publisher: Academic Press
Release Date : 1999-01-20
Elements Of The Theory Of Numbers written by Joseph B. Dence and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-01-20 with Mathematics categories.
Elements of the Theory of Numbers teaches students how to develop, implement, and test numerical methods for standard mathematical problems. The authors have created a two-pronged pedagogical approach that integrates analysis and algebra with classical number theory. Making greater use of the language and concepts in algebra and analysis than is traditionally encountered in introductory courses, this pedagogical approach helps to instill in the minds of the students the idea of the unity of mathematics. Elements of the Theory of Numbers is a superb summary of classical material as well as allowing the reader to take a look at the exciting role of analysis and algebra in number theory. * In-depth coverage of classical number theory * Thorough discussion of the theory of groups and rings * Includes application of Taylor polynomials * Contains more advanced material than other texts * Illustrates the results of a theorem with an example * Excellent presentation of the standard computational exercises * Nearly 1000 problems--many are proof-oriented, several others require the writing of computer programs to complete the computations * Clear and well-motivated presentation * Provides historical references noting distinguished number theory luminaries such as Euclid, de Fermat, Hilbert, Brun, and Lehmer, to name a few * Annotated bibliographies appear at the end of all of the chapters
The Book Of Numbers
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Author : John H. Conway
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
The Book Of Numbers written by John H. Conway and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
"...the great feature of the book is that anyone can read it without excessive head scratching...You'll find plenty here to keep you occupied, amused, and informed. Buy, dip in, wallow." -IAN STEWART, NEW SCIENTIST "...a delightful look at numbers and their roles in everything from language to flowers to the imagination." -SCIENCE NEWS "...a fun and fascinating tour of numerical topics and concepts. It will have readers contemplating ideas they might never have thought were understandable or even possible." -WISCONSIN BOOKWATCH "This popularization of number theory looks like another classic." -LIBRARY JOURNAL
Introduction To The Theory Of Numbers
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Author : G. H. Hardy
language : en
Publisher:
Release Date : 1959
Introduction To The Theory Of Numbers written by G. H. Hardy and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1959 with Congruences and residues categories.
Number Theory
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Author : Róbert Freud
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-10-08
Number Theory written by Róbert Freud and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-08 with Education categories.
Number Theory is a newly translated and revised edition of the most popular introductory textbook on the subject in Hungary. The book covers the usual topics of introductory number theory: divisibility, primes, Diophantine equations, arithmetic functions, and so on. It also introduces several more advanced topics including congruences of higher degree, algebraic number theory, combinatorial number theory, primality testing, and cryptography. The development is carefully laid out with ample illustrative examples and a treasure trove of beautiful and challenging problems. The exposition is both clear and precise. The book is suitable for both graduate and undergraduate courses with enough material to fill two or more semesters and could be used as a source for independent study and capstone projects. Freud and Gyarmati are well-known mathematicians and mathematical educators in Hungary, and the Hungarian version of this book is legendary there. The authors' personal pedagogical style as a facet of the rich Hungarian tradition shines clearly through. It will inspire and exhilarate readers.
Excursions In Number Theory
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Author : Charles Stanley Ogilvy
language : en
Publisher: Courier Corporation
Release Date : 1988-01-01
Excursions In Number Theory written by Charles Stanley Ogilvy and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-01-01 with Mathematics categories.
Challenging, accessible mathematical adventures involving prime numbers, number patterns, irrationals and iterations, calculating prodigies, and more. No 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 And Geometry An Introduction To Arithmetic Geometry
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Author : Álvaro Lozano-Robledo
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-03-21
Number Theory And Geometry An Introduction To Arithmetic Geometry written by Álvaro Lozano-Robledo and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-03-21 with Arithmetical algebraic geometry categories.
Geometry and the theory of numbers are as old as some of the oldest historical records of humanity. Ever since antiquity, mathematicians have discovered many beautiful interactions between the two subjects and recorded them in such classical texts as Euclid's Elements and Diophantus's Arithmetica. Nowadays, the field of mathematics that studies the interactions between number theory and algebraic geometry is known as arithmetic geometry. This book is an introduction to number theory and arithmetic geometry, and the goal of the text is to use geometry as the motivation to prove the main theorems in the book. For example, the fundamental theorem of arithmetic is a consequence of the tools we develop in order to find all the integral points on a line in the plane. Similarly, Gauss's law of quadratic reciprocity and the theory of continued fractions naturally arise when we attempt to determine the integral points on a curve in the plane given by a quadratic polynomial equation. After an introduction to the theory of diophantine equations, the rest of the book is structured in three acts that correspond to the study of the integral and rational solutions of linear, quadratic, and cubic curves, respectively. This book describes many applications including modern applications in cryptography; it also presents some recent results in arithmetic geometry. With 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.
Elementary Theory Of Numbers
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Author : Hsiung
language : en
Publisher: Allied Publishers
Release Date : 1995
Elementary Theory Of Numbers written by Hsiung and has been published by Allied Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with categories.
Number Theory Revealed A Masterclass
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Author : Andrew Granville
language : en
Publisher: American Mathematical Society
Release Date : 2020-09-23
Number Theory Revealed A Masterclass written by Andrew Granville and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-23 with Mathematics categories.
Number Theory Revealed: A Masterclass acquaints enthusiastic students with the “Queen of Mathematics”. The text offers a fresh take on congruences, power residues, quadratic residues, primes, and Diophantine equations and presents hot topics like cryptography, factoring, and primality testing. Students are also introduced to beautiful enlightening questions like the structure of Pascal's triangle mod $p$ and modern twists on traditional questions like the values represented by binary quadratic forms, the anatomy of integers, and elliptic curves. This Masterclass edition contains many additional chapters and appendices not found in Number Theory Revealed: An Introduction, highlighting beautiful developments and inspiring other subjects in mathematics (like algebra). This allows instructors to tailor a course suited to their own (and their students') interests. There are new yet accessible topics like the curvature of circles in a tiling of a circle by circles, the latest discoveries on gaps between primes, a new proof of Mordell's Theorem for congruent elliptic curves, and a discussion of the $abc$-conjecture including its proof for polynomials. About the Author: Andrew Granville is the Canada Research Chair in Number Theory at the University of Montreal and professor of mathematics at University College London. He has won several international writing prizes for exposition in mathematics, including the 2008 Chauvenet Prize and the 2019 Halmos-Ford Prize, and is the author of Prime Suspects (Princeton University Press, 2019), a beautifully illustrated graphic novel murder mystery that explores surprising connections between the anatomies of integers and of permutations.