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Number Theory
Undergraduate text uses combinatorial approach to accommodate both math majors and liberal arts students. Covers the basics of number theory, offers an outstanding introduction to partitions, plus chapters on multiplicativity-divisibility, quadratic congruences, additivity, and more.
100 Must-read Science Fiction Novels
"A reliable guide to what science fiction is" Christopher Priest, award-winning science fiction author "A really good introduction to the genre" SFX Magazine "Perceptive and glorious" Ian Watson, author of the screenplay for Steve Spielberg's A.I. Want to become a science fiction buff? Want to expand your reading in your favourite genre? This is a good place to start! From the publishers of the popular Good Reading Guide comes a rich selection of some of the finest SF novels ever published. With 100 of the best titles fully reviewed and a further 500 recommended, you'll quickly become an expert in the world of science fiction. The book is arranged by author and includes some thematic entries and special categories such as SF film adaptations, SF in rock music and Philip K. Dick in the mass media . It also includes a history of SF and a new definition of the genre, plus lists of award winners and book club recommendations. Foreword by Christopher Priest, the multiple award-winning SF author.
Number Theory
Written by a distinguished mathematician and teacher, this undergraduate text uses a combinatorial approach to accommodate both math majors and liberal arts students. In addition to covering the basics of number theory, it offers an outstanding introduction to partitions, plus chapters on multiplicativity-divisibility, quadratic congruences, additivity, and more.
An Introduction to q-analysis
Starting from simple generalizations of factorials and binomial coefficients, this book gives a friendly and accessible introduction to q q-analysis, a subject consisting primarily of identities between certain kinds of series and products. Many applications of these identities to combinatorics and number theory are developed in detail. There are numerous exercises to help students appreciate the beauty and power of the ideas, and the history of the subject is kept consistently in view. The book has few prerequisites beyond calculus. It is well suited to a capstone course, or for self-study in combinatorics or classical analysis. Ph.D. students and research mathematicians will also find it useful as a reference.
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Harmonic Maass Forms and Mock Modular Forms: Theory and Applications
Modular forms and Jacobi forms play a central role in many areas of mathematics. Over the last 10–15 years, this theory has been extended to certain non-holomorphic functions, the so-called “harmonic Maass forms”. The first glimpses of this theory appeared in Ramanujan's enigmatic last letter to G. H. Hardy written from his deathbed. Ramanujan discovered functions he called “mock theta functions” which over eighty years later were recognized as pieces of harmonic Maass forms. This book contains the essential features of the theory of harmonic Maass forms and mock modular forms, together with a wide variety of applications to algebraic number theory, combinatorics, elliptic curves, mathematical physics, quantum modular forms, and representation theory.
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