Download or read book The Sensual Quadratic Form written by John Horton Conway and published by Cambridge University Press. This book was released on 1997 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quadratic forms are presented in a pictorial way, elucidating many topics in algebra, number theory and geometry.
Download or read book The Sensual quadratic Form written by John Horton Conway and published by American Mathematical Soc.. This book was released on 1997-12-31 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: John Horton Conway's unique approach to quadratic forms was the subject of the Hedrick Lectures that he gave in August of 1991 at the Joint Meetings of the Mathematical Association of America and the American Mathematical Society in Orono, Maine. This book presents the substance of those lectures. The book should not be thought of as a serious textbook on the theory of quadratic forms. It consists rather of a number of essays on particular aspects of quadratic forms that have interested the author. The lectures are self-contained and will be accessible to the generally informed reader who has no particular background in quadratic form theory. The minor exceptions should not interrupt the flow of ideas. The afterthoughts to the lectures contain discussion of related matters that occasionally presuppose greater knowledge.
Download or read book The sensual quadratic form written by John H. Conway and published by . This book was released on 1997 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Sensual Quadratic Form written by John Horton Conway and published by Mathematical Association of America. This book was released on 1998-03-05 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: The distinguished mathematician John Conway presents quadratic forms in a pictorial way that enables the reader to understand them mathematically without proving theorems in the traditional fashion. One learns to sense their properties. In his customary enthusiastic style, Conway uses his theme to cast light on all manner of mathematical topics from algebra, number theory and geometry, including many new ideas and features.
Download or read book The Sensual Quadratic Form written by John Horton Conway and published by Mathematical Association of America. This book was released on 1997-01-01 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Download or read book Rational Quadratic Forms written by J. W. S. Cassels and published by Courier Dover Publications. This book was released on 2008-08-08 with total page 429 pages. Available in PDF, EPUB and Kindle. Book excerpt: Exploration of quadratic forms over rational numbers and rational integers offers elementary introduction. Covers quadratic forms over local fields, forms with integral coefficients, reduction theory for definite forms, more. 1968 edition.
Download or read book Quadratic Forms and Their Applications written by Eva Bayer-Fluckiger and published by American Mathematical Soc.. This book was released on 2000 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume outlines the proceedings of the conference on "Quadratic Forms and Their Applications" held at University College Dublin. It includes survey articles and research papers ranging from applications in topology and geometry to the algebraic theory of quadratic forms and its history. Various aspects of the use of quadratic forms in algebra, analysis, topology, geometry, and number theory are addressed. Special features include the first published proof of the Conway-Schneeberger Fifteen Theorem on integer-valued quadratic forms and the first English-language biography of Ernst Witt, founder of the theory of quadratic forms.
Download or read book Basic Quadratic Forms written by Larry J. Gerstein and published by American Mathematical Soc.. This book was released on 2008 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: The arithmetic theory of quadratic forms is a rich branch of number theory that has had important applications to several areas of pure mathematics--particularly group theory and topology--as well as to cryptography and coding theory. This book is a self-contained introduction to quadratic forms that is based on graduate courses the author has taught many times. It leads the reader from foundation material up to topics of current research interest--with special attention to the theory over the integers and over polynomial rings in one variable over a field--and requires only a basic background in linear and abstract algebra as a prerequisite. Whenever possible, concrete constructions are chosen over more abstract arguments. The book includes many exercises and explicit examples, and it is appropriate as a textbook for graduate courses or for independent study. To facilitate further study, a guide to the extensive literature on quadratic forms is provided.
Download or read book Integral Quadratic Forms and Lattices written by Myung-Hwan Kim and published by American Mathematical Soc.. This book was released on 1999 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the proceedings of an international conference held at Seoul National University (Korea). Talks covered recent developments in diverse areas related to the theory of integral quadratic forms and hermitian forms, local densities, linear relations and congruences of theta series, zeta functions of prehomogeneous vector spaces, lattices with maximal finite matrix groups, globally irreducible lattices, Mordell-Weil lattices, and more. Articles in the volume represent expository lectures by leading experts on recent developments in the field. The book offers a comprehensive introduction to the current state of knowledge in the arithmetic theory of quadratic forms and provides active directions of research with new results. Topics addressed in the volume emphasize connections with related fields, such as group theory, arithmetic geometry, analytic number theory, and modular forms. The book is an excellent introductory guide for students as well as a rich reference source for researchers.
Download or read book Introduction to Quadratic Forms over Fields written by T.Y. Lam and published by American Mathematical Soc.. This book was released on with total page 578 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new version of the author's prizewinning book, Algebraic Theory of Quadratic Forms (W. A. Benjamin, Inc., 1973), gives a modern and self-contained introduction to the theory of quadratic forms over fields of characteristic different from two. Starting with few prerequisites beyond linear algebra, the author charts an expert course from Witt's classical theory of quadratic forms, quaternion and Clifford algebras, Artin-Schreier theory of formally real fields, and structural theorems on Witt rings, to the theory of Pfister forms, function fields, and field invariants. These main developments are seamlessly interwoven with excursions into Brauer-Wall groups, local and global fields, trace forms, Galois theory, and elementary algebraic K-theory, to create a uniquely original treatment of quadratic form theory over fields. Two new chapters totaling more than 100 pages have been added to the earlier incarnation of this book to take into account some of the newer results and more recent viewpoints in the area. As is characteristic of this author's expository style, the presentation of the main material in this book is interspersed with a copious number of carefully chosen examples to illustrate the general theory. This feature, together with a rich stock of some 280 exercises for the thirteen chapters, greatly enhances the pedagogical value of this book, both as a graduate text and as a reference work for researchers in algebra, number theory, algebraic geometry, algebraic topology, and geometric topology.
Download or read book Elementary Number Theory Primes Congruences and Secrets written by William Stein and published by Springer Science & Business Media. This book was released on 2008-10-28 with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a book about prime numbers, congruences, secret messages, and elliptic curves that you can read cover to cover. It grew out of undergr- uate courses that the author taught at Harvard, UC San Diego, and the University of Washington. The systematic study of number theory was initiated around 300B. C. when Euclid proved that there are in?nitely many prime numbers, and also cleverly deduced the fundamental theorem of arithmetic, which asserts that every positive integer factors uniquely as a product of primes. Over a thousand years later (around 972A. D. ) Arab mathematicians formulated the congruent number problem that asks for a way to decide whether or not a given positive integer n is the area of a right triangle, all three of whose sides are rational numbers. Then another thousand years later (in 1976), Di?e and Hellman introduced the ?rst ever public-key cryptosystem, which enabled two people to communicate secretely over a public communications channel with no predetermined secret; this invention and the ones that followed it revolutionized the world of digital communication. In the 1980s and 1990s, elliptic curves revolutionized number theory, providing striking new insights into the congruent number problem, primality testing, publ- key cryptography, attacks on public-key systems, and playing a central role in Andrew Wiles’ resolution of Fermat’s Last Theorem.
Download or read book Introduction to Quadratic Forms written by Onorato Timothy O’Meara and published by Springer. This book was released on 2013-12-01 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Tale of Two Fractals written by A.A. Kirillov and published by Springer Science & Business Media. This book was released on 2013-04-23 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since Benoit Mandelbrot's pioneering work in the late 1970s, scores of research articles and books have been published on the topic of fractals. Despite the volume of literature in the field, the general level of theoretical understanding has remained low; most work is aimed either at too mainstream an audience to achieve any depth or at too specialized a community to achieve widespread use. Written by celebrated mathematician and educator A.A. Kirillov, A Tale of Two Fractals is intended to help bridge this gap, providing an original treatment of fractals that is at once accessible to beginners and sufficiently rigorous for serious mathematicians. The work is designed to give young, non-specialist mathematicians a solid foundation in the theory of fractals, and, in the process, to equip them with exposure to a variety of geometric, analytical, and algebraic tools with applications across other areas.
Download or read book Binary Quadratic Forms written by Duncan A. Buell and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first coherent exposition of the theory of binary quadratic forms was given by Gauss in the Disqnisitiones Arithmeticae. During the nine teenth century, as the theory of ideals and the rudiments of algebraic number theory were developed, it became clear that this theory of bi nary quadratic forms, so elementary and computationally explicit, was indeed just a special case of a much more elega,nt and abstract theory which, unfortunately, is not computationally explicit. In recent years the original theory has been laid aside. Gauss's proofs, which involved brute force computations that can be done in what is essentially a two dimensional vector space, have been dropped in favor of n-dimensional arguments which prove the general theorems of algebraic number the ory. In consequence, this elegant, yet pleasantly simple, theory has been neglected even as some of its results have become extremely useful in certain computations. I find this neglect unfortunate, because binary quadratic forms have two distinct attractions. First, the subject involves explicit computa tion and many of the computer programs can be quite simple. The use of computers in experimenting with examples is both meaningful and enjoyable; one can actually discover interesting results by com puting examples, noticing patterns in the "data," and then proving that the patterns result from the conclusion of some provable theorem.
Download or read book Quadratic Forms with Applications to Algebraic Geometry and Topology written by Albrecht Pfister and published by Cambridge University Press. This book was released on 1995-09-28 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: A gem of a book bringing together 30 years worth of results that are certain to interest anyone whose research touches on quadratic forms.
Download or read book CRC Concise Encyclopedia of Mathematics written by Eric W. Weisstein and published by CRC Press. This book was released on 2002-12-12 with total page 3253 pages. Available in PDF, EPUB and Kindle. Book excerpt: Upon publication, the first edition of the CRC Concise Encyclopedia of Mathematics received overwhelming accolades for its unparalleled scope, readability, and utility. It soon took its place among the top selling books in the history of Chapman & Hall/CRC, and its popularity continues unabated. Yet also unabated has been the d
