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Author : Kenneth S. Williams
Publisher : Cambridge University Press
Page : 307 pages
File Size : 48,7 Mb
Release : 2011
Category : Mathematics
ISBN : 9781107002531
A gentle introduction to Liouville's powerful method in elementary number theory. Suitable for advanced undergraduate and beginning graduate students.
Author : Bruce C. Berndt
Publisher : American Mathematical Soc.
Page : 210 pages
File Size : 46,9 Mb
Release : 2006
Category : Functions, Theta
ISBN : 9780821841785
Ramanujan is recognized as one of the great number theorists of the twentieth century. Here now is the first book to provide an introduction to his work in number theory. Most of Ramanujan's work in number theory arose out of $q$-series and theta functions. This book provides an introduction to these two important subjects and to some of the topics in number theory that are inextricably intertwined with them, including the theory of partitions, sums of squares and triangular numbers, and the Ramanujan tau function. The majority of the results discussed here are originally due to Ramanujan or were rediscovered by him. Ramanujan did not leave us proofs of the thousands of theorems he recorded in his notebooks, and so it cannot be claimed that many of the proofs given in this book are those found by Ramanujan. However, they are all in the spirit of his mathematics. The subjects examined in this book have a rich history dating back to Euler and Jacobi, and they continue to be focal points of contemporary mathematical research. Therefore, at the end of each of the seven chapters, Berndt discusses the results established in the chapter and places them in both historical and contemporary contexts. The book is suitable for advanced undergraduates and beginning graduate students interested in number theory.
Author : Giancarlo Travaglini
Publisher : Cambridge University Press
Page : 251 pages
File Size : 46,5 Mb
Release : 2014-06-12
Category : Mathematics
ISBN : 9781107044036
"The first part of this book is dedicated to the first goal. The reader will find some topics typically presented in introductory books on Number Theory: factorization, arithmetic functions and integer points, congruences and cryptography, quadratic reciprocity, and sums of two and four squares. Starting from the first few pages we introduce some simple and captivating findings, such as Chebyshev's theorem and the elementary results for the Gauss circle problem and for the Dirichlet divisor problem, which may lead the reader to a deeper study of Number Theory, particularly students who are interested in Calculus and Analysis"--
Author : George E. Andrews,Frank Garvan
Publisher : Springer
Page : 736 pages
File Size : 45,9 Mb
Release : 2018-02-01
Category : Mathematics
ISBN : 9783319683768
Gathered from the 2016 Gainesville Number Theory Conference honoring Krishna Alladi on his 60th birthday, these proceedings present recent research in number theory. Extensive and detailed, this volume features 40 articles by leading researchers on topics in analytic number theory, probabilistic number theory, irrationality and transcendence, Diophantine analysis, partitions, basic hypergeometric series, and modular forms. Readers will also find detailed discussions of several aspects of the path-breaking work of Srinivasa Ramanujan and its influence on current research. Many of the papers were motivated by Alladi's own research on partitions and q-series as well as his earlier work in number theory. Alladi is well known for his contributions in number theory and mathematics. His research interests include combinatorics, discrete mathematics, sieve methods, probabilistic and analytic number theory, Diophantine approximations, partitions and q-series identities. Graduate students and researchers will find this volume a valuable resource on new developments in various aspects of number theory.
Author : Markus Linckelmann
Publisher : Cambridge University Press
Page : 527 pages
File Size : 53,8 Mb
Release : 2018-05-24
Category : Mathematics
ISBN : 9781108425919
A comprehensive treatment of block theory, emphasising cornerstones of the area which have not appeared in any book before.
Author : Benjamin Klopsch,Nikolay Nikolov,Christopher Voll
Publisher : Cambridge University Press
Page : 128 pages
File Size : 48,7 Mb
Release : 2011-02-10
Category : Mathematics
ISBN : 9781139495653
In this book, three authors introduce readers to strong approximation methods, analytic pro-p groups and zeta functions of groups. Each chapter illustrates connections between infinite group theory, number theory and Lie theory. The first introduces the theory of compact p-adic Lie groups. The second explains how methods from linear algebraic groups can be utilised to study the finite images of linear groups. The final chapter provides an overview of zeta functions associated to groups and rings. Derived from an LMS/EPSRC Short Course for graduate students, this book provides a concise introduction to a very active research area and assumes less prior knowledge than existing monographs or original research articles. Accessible to beginning graduate students in group theory, it will also appeal to researchers interested in infinite group theory and its interface with Lie theory and number theory.
Author : Julia E. Bergner
Publisher : Cambridge University Press
Page : 289 pages
File Size : 41,7 Mb
Release : 2018-03-15
Category : Mathematics
ISBN : 9781107101364
An introductory treatment to the homotopy theory of homotopical categories, presenting several models and comparisons between them.
Author : Simeon Ball
Publisher : Cambridge University Press
Page : 299 pages
File Size : 46,6 Mb
Release : 2015-07-02
Category : Mathematics
ISBN : 9781107107991
A graduate-level introduction to finite geometry and its applications to other areas of combinatorics.
Author : Adrian Constantin
Publisher : Cambridge University Press
Page : 368 pages
File Size : 41,7 Mb
Release : 2016-06-02
Category : Mathematics
ISBN : 9781107044104
A two-volume advanced text for graduate students. This first volume covers the theory of Fourier analysis.
Author : Hansjörg Geiges
Publisher : Cambridge University Press
Page : 241 pages
File Size : 42,6 Mb
Release : 2016-03-24
Category : Mathematics
ISBN : 9781107125407
A first course in celestial mechanics emphasising the variety of geometric ideas that have shaped the subject.
Author : Michael Krivelevich,Konstantinos Panagiotou,Mathew Penrose
Publisher : Cambridge University Press
Page : 129 pages
File Size : 43,7 Mb
Release : 2016-04-25
Category : Mathematics
ISBN : 9781107136571
A concise introduction, aimed at young researchers, to recent developments of a geometric and topological nature in random graphs.
Author : Renzo Cavalieri,Eric Miles
Publisher : Cambridge University Press
Page : 197 pages
File Size : 46,9 Mb
Release : 2016-09-26
Category : Mathematics
ISBN : 9781107149243
Classroom-tested and featuring over 100 exercises, this text introduces the key algebraic geometry field of Hurwitz theory.
Author : M. Burak Erdoğan,Nikolaos Tzirakis
Publisher : Cambridge University Press
Page : 203 pages
File Size : 48,6 Mb
Release : 2016-05-12
Category : Mathematics
ISBN : 9781107149045
Introduces nonlinear dispersive partial differential equations in a detailed yet elementary way without compromising the depth and richness of the subject.
Author : D. J. H. Garling
Publisher : Cambridge University Press
Page : 209 pages
File Size : 55,6 Mb
Release : 2011-06-23
Category : Mathematics
ISBN : 9781107096387
A straightforward introduction to Clifford algebras, providing the necessary background material and many applications in mathematics and physics.
Author : Derek F. Holt,Sarah Rees,Claas E. Röver
Publisher : Cambridge University Press
Page : 307 pages
File Size : 46,8 Mb
Release : 2017-02-23
Category : Mathematics
ISBN : 9781107152359
A reference book discussing applications of formal language theory to group theory, particularly geometric and computational group theory.