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Number Theory Revealed An Introduction
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Book Synopsis Number Theory Revealed: A Masterclass by : Andrew Granville
Download or read book Number Theory Revealed: A Masterclass written by Andrew Granville and published by American Mathematical Society. This book was released on 2020-09-23 with total page 587 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Number Theory Revealed: An Introduction by : Andrew Granville
Download or read book Number Theory Revealed: An Introduction written by Andrew Granville and published by American Mathematical Soc.. This book was released on 2019-11-12 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: Number Theory Revealed: An Introduction acquaints undergraduates 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 p and modern twists on traditional questions like the values represented by binary quadratic forms and large solutions of equations. Each chapter includes an “elective appendix” with additional reading, projects, and references. An expanded edition, Number Theory Revealed: A Masterclass, offers a more comprehensive approach to these core topics and adds additional material in further chapters and appendices, allowing instructors to create an individualized course tailored to their own (and their students') interests.
Book Synopsis Introduction to Number Theory by : Daniel E. Flath
Download or read book Introduction to Number Theory written by Daniel E. Flath and published by American Mathematical Soc.. This book was released on 2018-09-27 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: Growing out of a course designed to teach Gauss's Disquisitiones Arithmeticae to honors-level undergraduates, Flath's Introduction to Number Theory focuses on Gauss's theory of binary quadratic forms. It is suitable for use as a textbook in a course or self-study by advanced undergraduates or graduate students who possess a basic familiarity with abstract algebra. The text treats a variety of topics from elementary number theory including the distribution of primes, sums of squares, continued factions, the Legendre, Jacobi and Kronecker symbols, the class group and genera. But the focus is on quadratic reciprocity (several proofs are given including one that highlights the p−q symmetry) and binary quadratic forms. The reader will come away with a good understanding of what Gauss intended in the Disquisitiones and Dirichlet in his Vorlesungen. The text also includes a lovely appendix by J. P. Serre titled Δ=b2−4ac. The clarity of the author's vision is matched by the clarity of his exposition. This is a book that reveals the discovery of the quadratic core of algebraic number theory. It should be on the desk of every instructor of introductory number theory as a source of inspiration, motivation, examples, and historical insight.
Book Synopsis An Illustrated Theory of Numbers by : Martin H. Weissman
Download or read book An Illustrated Theory of Numbers written by Martin H. Weissman and published by American Mathematical Soc.. This book was released on 2020-09-15 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Introduction to the Theory of Numbers by : Harold N. Shapiro
Download or read book Introduction to the Theory of Numbers written by Harold N. Shapiro and published by Courier Corporation. This book was released on 2008-01-01 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: Starting with the fundamentals of number theory, this text advances to an intermediate level. Author Harold N. Shapiro, Professor Emeritus of Mathematics at New York University's Courant Institute, addresses this treatment toward advanced undergraduates and graduate students. Selected chapters, sections, and exercises are appropriate for undergraduate courses. The first five chapters focus on the basic material of number theory, employing special problems, some of which are of historical interest. Succeeding chapters explore evolutions from the notion of congruence, examine a variety of applications related to counting problems, and develop the roots of number theory. Two "do-it-yourself" chapters offer readers the chance to carry out small-scale mathematical investigations that involve material covered in previous chapters.
Book Synopsis Fermat's Last Theorem by : Harold M. Edwards
Download or read book Fermat's Last Theorem written by Harold M. Edwards and published by Springer Science & Business Media. This book was released on 2000-01-14 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to algebraic number theory via the famous problem of "Fermats Last Theorem" follows its historical development, beginning with the work of Fermat and ending with Kummers theory of "ideal" factorization. The more elementary topics, such as Eulers proof of the impossibilty of x+y=z, are treated in an uncomplicated way, and new concepts and techniques are introduced only after having been motivated by specific problems. The book also covers in detail the application of Kummers theory to quadratic integers and relates this to Gauss'theory of binary quadratic forms, an interesting and important connection that is not explored in any other book.
Book Synopsis Introduction to Number Theory by : Anthony Vazzana
Download or read book Introduction to Number Theory written by Anthony Vazzana and published by CRC Press. This book was released on 2007-10-30 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the oldest branches of mathematics, number theory is a vast field devoted to studying the properties of whole numbers. Offering a flexible format for a one- or two-semester course, Introduction to Number Theory uses worked examples, numerous exercises, and two popular software packages to describe a diverse array of number theory topi
Download or read book Number Theory written by Robin Wilson and published by Oxford University Press, USA. This book was released on 2020 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: Number theory is the branch of mathematics primarily concerned with the counting numbers, especially primes. It dates back to the ancient Greeks, but today it has great practical importance in cryptography, from credit card security to national defence. This book introduces the main areas of number theory, and some of its most interesting problems.
Book Synopsis An Introduction to Number Theory by : Harold M. Stark
Download or read book An Introduction to Number Theory written by Harold M. Stark and published by . This book was released on 1978 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis An Introductory Course in Elementary Number Theory by : Wissam Raji
Download or read book An Introductory Course in Elementary Number Theory written by Wissam Raji and published by The Saylor Foundation. This book was released on 2013-05-09 with total page 171 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes serve as course notes for an undergraduate course in number theory. Most if not all universities worldwide offer introductory courses in number theory for math majors and in many cases as an elective course. The notes contain a useful introduction to important topics that need to be addressed in a course in number theory. Proofs of basic theorems are presented in an interesting and comprehensive way that can be read and understood even by non-majors with the exception in the last three chapters where a background in analysis, measure theory and abstract algebra is required. The exercises are carefully chosen to broaden the understanding of the concepts. Moreover, these notes shed light on analytic number theory, a subject that is rarely seen or approached by undergraduate students. One of the unique characteristics of these notes is the careful choice of topics and its importance in the theory of numbers. The freedom is given in the last two chapters because of the advanced nature of the topics that are presented.
Book Synopsis An introduction to the theory of numbers by : Ivan Niven
Download or read book An introduction to the theory of numbers written by Ivan Niven and published by . This book was released on 1993 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Fundamental Number Theory with Applications by : Richard A. Mollin
Download or read book Fundamental Number Theory with Applications written by Richard A. Mollin and published by CRC Press. This book was released on 1997-09-10 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: Beginning with the arithmetic of the rational integers and proceeding to an introduction of algebraic number theory via quadratic orders, Fundamental Number Theory with Applications reveals intriguing new applications of number theory. This text details aspects of computer science related to cryptography factoring primality testing complexity analysis computer arithmetic computational number theory Fundamental Number Theory with Applications also covers: Carmichael numbers Dirichlet products Jacobsthal sums Mersenne primes perfect numbers powerful numbers self-contained numbers Numerous exercises are included, testing the reader's knowledge of the concepts covered, introducing new and interesting topics, and providing a venue to learn background material. Written by a professor and author who is an accomplished scholar in this field, this book provides the material essential for an introduction to the fundamentals of number theory.
Book Synopsis Introduction to Analytic Number Theory by : A. G. Postnikov
Download or read book Introduction to Analytic Number Theory written by A. G. Postnikov and published by American Mathematical Soc.. This book was released on 1988-12-31 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aimed at a level between textbooks and the latest research monographs, this book is directed at researchers, teachers, and graduate students interested in number theory and its connections with other branches of science. Choosing to emphasize topics not sufficiently covered in the literature, the author has attempted to give as broad a picture as possible of the problems of analytic number theory.
Book Synopsis An Experimental Introduction to Number Theory by : Benjamin Hutz
Download or read book An Experimental Introduction to Number Theory written by Benjamin Hutz and published by American Mathematical Soc.. This book was released on 2018-04-17 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents material suitable for an undergraduate course in elementary number theory from a computational perspective. It seeks to not only introduce students to the standard topics in elementary number theory, such as prime factorization and modular arithmetic, but also to develop their ability to formulate and test precise conjectures from experimental data. Each topic is motivated by a question to be answered, followed by some experimental data, and, finally, the statement and proof of a theorem. There are numerous opportunities throughout the chapters and exercises for the students to engage in (guided) open-ended exploration. At the end of a course using this book, the students will understand how mathematics is developed from asking questions to gathering data to formulating and proving theorems. The mathematical prerequisites for this book are few. Early chapters contain topics such as integer divisibility, modular arithmetic, and applications to cryptography, while later chapters contain more specialized topics, such as Diophantine approximation, number theory of dynamical systems, and number theory with polynomials. Students of all levels will be drawn in by the patterns and relationships of number theory uncovered through data driven exploration.
Book Synopsis An Introduction to Number Theory by : G. Everest
Download or read book An Introduction to Number Theory written by G. Everest and published by Springer Science & Business Media. This book was released on 2007-05-21 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: Includes up-to-date material on recent developments and topics of significant interest, such as elliptic functions and the new primality test Selects material from both the algebraic and analytic disciplines, presenting several different proofs of a single result to illustrate the differing viewpoints and give good insight
Book Synopsis The Princeton Companion to Mathematics by : Timothy Gowers
Download or read book The Princeton Companion to Mathematics written by Timothy Gowers and published by Princeton University Press. This book was released on 2010-07-18 with total page 1057 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a one-of-a-kind reference for anyone with a serious interest in mathematics. Edited by Timothy Gowers, a recipient of the Fields Medal, it presents nearly two hundred entries, written especially for this book by some of the world's leading mathematicians, that introduce basic mathematical tools and vocabulary; trace the development of modern mathematics; explain essential terms and concepts; examine core ideas in major areas of mathematics; describe the achievements of scores of famous mathematicians; explore the impact of mathematics on other disciplines such as biology, finance, and music--and much, much more. Unparalleled in its depth of coverage, The Princeton Companion to Mathematics surveys the most active and exciting branches of pure mathematics. Accessible in style, this is an indispensable resource for undergraduate and graduate students in mathematics as well as for researchers and scholars seeking to understand areas outside their specialties. Features nearly 200 entries, organized thematically and written by an international team of distinguished contributors Presents major ideas and branches of pure mathematics in a clear, accessible style Defines and explains important mathematical concepts, methods, theorems, and open problems Introduces the language of mathematics and the goals of mathematical research Covers number theory, algebra, analysis, geometry, logic, probability, and more Traces the history and development of modern mathematics Profiles more than ninety-five mathematicians who influenced those working today Explores the influence of mathematics on other disciplines Includes bibliographies, cross-references, and a comprehensive index Contributors incude: Graham Allan, Noga Alon, George Andrews, Tom Archibald, Sir Michael Atiyah, David Aubin, Joan Bagaria, Keith Ball, June Barrow-Green, Alan Beardon, David D. Ben-Zvi, Vitaly Bergelson, Nicholas Bingham, Béla Bollobás, Henk Bos, Bodil Branner, Martin R. Bridson, John P. Burgess, Kevin Buzzard, Peter J. Cameron, Jean-Luc Chabert, Eugenia Cheng, Clifford C. Cocks, Alain Connes, Leo Corry, Wolfgang Coy, Tony Crilly, Serafina Cuomo, Mihalis Dafermos, Partha Dasgupta, Ingrid Daubechies, Joseph W. Dauben, John W. Dawson Jr., Francois de Gandt, Persi Diaconis, Jordan S. Ellenberg, Lawrence C. Evans, Florence Fasanelli, Anita Burdman Feferman, Solomon Feferman, Charles Fefferman, Della Fenster, José Ferreirós, David Fisher, Terry Gannon, A. Gardiner, Charles C. Gillispie, Oded Goldreich, Catherine Goldstein, Fernando Q. Gouvêa, Timothy Gowers, Andrew Granville, Ivor Grattan-Guinness, Jeremy Gray, Ben Green, Ian Grojnowski, Niccolò Guicciardini, Michael Harris, Ulf Hashagen, Nigel Higson, Andrew Hodges, F. E. A. Johnson, Mark Joshi, Kiran S. Kedlaya, Frank Kelly, Sergiu Klainerman, Jon Kleinberg, Israel Kleiner, Jacek Klinowski, Eberhard Knobloch, János Kollár, T. W. Körner, Michael Krivelevich, Peter D. Lax, Imre Leader, Jean-François Le Gall, W. B. R. Lickorish, Martin W. Liebeck, Jesper Lützen, Des MacHale, Alan L. Mackay, Shahn Majid, Lech Maligranda, David Marker, Jean Mawhin, Barry Mazur, Dusa McDuff, Colin McLarty, Bojan Mohar, Peter M. Neumann, Catherine Nolan, James Norris, Brian Osserman, Richard S. Palais, Marco Panza, Karen Hunger Parshall, Gabriel P. Paternain, Jeanne Peiffer, Carl Pomerance, Helmut Pulte, Bruce Reed, Michael C. Reed, Adrian Rice, Eleanor Robson, Igor Rodnianski, John Roe, Mark Ronan, Edward Sandifer, Tilman Sauer, Norbert Schappacher, Andrzej Schinzel, Erhard Scholz, Reinhard Siegmund-Schultze, Gordon Slade, David J. Spiegelhalter, Jacqueline Stedall, Arild Stubhaug, Madhu Sudan, Terence Tao, Jamie Tappenden, C. H. Taubes, Rüdiger Thiele, Burt Totaro, Lloyd N. Trefethen, Dirk van Dalen, Richard Weber, Dominic Welsh, Avi Wigderson, Herbert Wilf, David Wilkins, B. Yandell, Eric Zaslow, Doron Zeilberger
Book Synopsis Discrete Mathematics by : Oscar Levin
Download or read book Discrete Mathematics written by Oscar Levin and published by Createspace Independent Publishing Platform. This book was released on 2018-07-30 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: Note: This is a custom edition of Levin's full Discrete Mathematics text, arranged specifically for use in a discrete math course for future elementary and middle school teachers. (It is NOT a new and updated edition of the main text.)This gentle introduction to discrete mathematics is written for first and second year math majors, especially those who intend to teach. The text began as a set of lecture notes for the discrete mathematics course at the University of Northern Colorado. This course serves both as an introduction to topics in discrete math and as the "introduction to proof" course for math majors. The course is usually taught with a large amount of student inquiry, and this text is written to help facilitate this.Four main topics are covered: counting, sequences, logic, and graph theory. Along the way proofs are introduced, including proofs by contradiction, proofs by induction, and combinatorial proofs.While there are many fine discrete math textbooks available, this text has the following advantages: - It is written to be used in an inquiry rich course.- It is written to be used in a course for future math teachers.- It is open source, with low cost print editions and free electronic editions.
