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Groups Modular Mathematics Series

Groups   Modular Mathematics Series Author Camilla Jordan
ISBN-10 9780080571652
Release 1994-07-01
Pages 224
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This text provides an introduction to group theory with an emphasis on clear examples. The authors present groups as naturally occurring structures arising from symmetry in geometrical figures and other mathematical objects. Written in a 'user-friendly' style, where new ideas are always motivated before being fully introduced, the text will help readers to gain confidence and skill in handling group theory notation before progressing on to applying it in complex situations. An ideal companion to any first or second year course on the topic.



Groups

Groups Author Camilla R. Jordan
ISBN-10 9780340610459
Release 1994-01
Pages 207
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Introduction to mathematical groups



Groups Rings and Fields

Groups  Rings and Fields Author David A.R. Wallace
ISBN-10 9781447104254
Release 2012-12-06
Pages 248
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This is a basic introduction to modern algebra, providing a solid understanding of the axiomatic treatment of groups and then rings, aiming to promote a feeling for the evolutionary and historical development of the subject. It includes problems and fully worked solutions, enabling readers to master the subject rather than simply observing it.



Modular Functions and Dirichlet Series in Number Theory

Modular Functions and Dirichlet Series in Number Theory Author Tom M. Apostol
ISBN-10 9781468499100
Release 2012-12-06
Pages 198
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This is the second volume of a 2-volume textbook* which evolved from a course (Mathematics 160) offered at the California Institute of Technology du ring the last 25 years. The second volume presupposes a background in number theory com parable to that provided in the first volume, together with a knowledge of the basic concepts of complex analysis. Most of the present volume is devoted to elliptic functions and modular functions with some of their number-theoretic applications. Among the major topics treated are Rademacher's convergent series for the partition function, Lehner's congruences for the Fourier coefficients of the modular functionj( r), and Hecke's theory of entire forms with multiplicative Fourier coefficients. The last chapter gives an account of Bohr's theory of equivalence of general Dirichlet series. Both volumes of this work emphasize classical aspects of a subject wh ich in recent years has undergone a great deal of modern development. It is hoped that these volumes will help the nonspecialist become acquainted with an important and fascinating part of mathematics and, at the same time, will provide some of the background that belongs to the repertory of every specialist in the field. This volume, like the first, is dedicated to the students who have taken this course and have gone on to make notable contributions to number theory and other parts of mathematics. T. M. A. January, 1976 * The first volume is in the Springer-Verlag series Undergraduate Texts in Mathematics under the title Introduction to Analytic Number Theory.



Geometry in Advanced Pure Mathematics

Geometry in Advanced Pure Mathematics Author Shaun Bullett
ISBN-10 9781786341099
Release 2017-03-07
Pages 236
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This book leads readers from a basic foundation to an advanced level understanding of geometry in advanced pure mathematics. Chapter by chapter, readers will be led from a foundation level understanding to advanced level understanding. This is the perfect text for graduate or PhD mathematical-science students looking for support in algebraic geometry, geometric group theory, modular group, holomorphic dynamics and hyperbolic geometry, syzygies and minimal resolutions, and minimal surfaces. Geometry in Advanced Pure Mathematics is the fourth volume of the LTCC Advanced Mathematics Series. This series is the first to provide advanced introductions to mathematical science topics to advanced students of mathematics. Editor the three joint heads of the London Taught Course Centre for PhD Students in the Mathematical Sciences (LTCC), each book supports readers in broadening their mathematical knowledge outside of their immediate research disciplines while also covering specialized key areas.



Character Theory of Finite Groups

Character Theory of Finite Groups Author I. Martin Isaacs
ISBN-10 0486680142
Release 1994
Pages 303
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"The book is a pleasure to read. There is no question but that it will become, and deserves to be, a widely used textbook and reference." — Bulletin of the American Mathematical Society. Character theory provides a powerful tool for proving theorems about finite groups. In addition to dealing with techniques for applying characters to "pure" group theory, a large part of this book is devoted to the properties of the characters themselves and how these properties reflect and are reflected in the structure of the group. Chapter I consists of ring theoretic preliminaries. Chapters 2 to 6 and 8 contain the basic material of character theory, while Chapter 7 treats an important technique for the application of characters to group theory. Chapter 9 considers irreducible representations over arbitrary fields, leading to a focus on subfields of the complex numbers in Chapter 10. In Chapter 15 the author introduces Brauer’s theory of blocks and "modular characters." Remaining chapters deal with more specialized topics, such as the connections between the set of degrees of the irreducible characters and structure of a group. Following each chapter is a selection of carefully thought out problems, including exercises, examples, further results and extensions and variations of theorems in the text. Prerequisites for this book are some basic finite group theory: the Sylow theorems, elementary properties of permutation groups and solvable and nilpotent groups. Also useful would be some familiarity with rings and Galois theory. In short, the contents of a first-year graduate algebra course should be sufficient preparation.



Problems in the Theory of Modular Forms

Problems in the Theory of Modular Forms Author M. Ram Murty
ISBN-10 9789811026515
Release 2016-11-25
Pages 291
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This book introduces the reader to the fascinating world of modular forms through a problem-solving approach. As such, besides researchers, the book can be used by the undergraduate and graduate students for self-instruction. The topics covered include q-series, the modular group, the upper half-plane, modular forms of level one and higher level, the Ramanujan τ-function, the Petersson inner product, Hecke operators, Dirichlet series attached to modular forms and further special topics. It can be viewed as a gentle introduction for a deeper study of the subject. Thus, it is ideal for non-experts seeking an entry into the field.



Representation Theory of Finite Groups

Representation Theory of Finite Groups Author Martin Burrow
ISBN-10 9780486145075
Release 2014-05-05
Pages 208
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DIVConcise, graduate-level exposition covers representation theory of rings with identity, representation theory of finite groups, more. Exercises. Appendix. 1965 edition. /div



Cohomology of Groups

Cohomology of Groups Author Kenneth S. Brown
ISBN-10 9781468493276
Release 2012-12-06
Pages 306
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Aimed at second year graduate students, this text introduces them to cohomology theory (involving a rich interplay between algebra and topology) with a minimum of prerequisites. No homological algebra is assumed beyond what is normally learned in a first course in algebraic topology, and the basics of the subject, as well as exercises, are given prior to discussion of more specialized topics.



Fuchsian Groups

Fuchsian Groups Author Svetlana Katok
ISBN-10 0226425827
Release 1992-08-01
Pages 175
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This introductory text provides a thoroughly modern treatment of Fuchsian groups that addresses both the classical material and recent developments in the field. A basic example of lattices in semisimple groups, Fuchsian groups have extensive connections to the theory of a single complex variable, number theory, algebraic and differential geometry, topology, Lie theory, representation theory, and group theory.



Modular Representations of Finite Groups of Lie Type

Modular Representations of Finite Groups of Lie Type Author James E. Humphreys
ISBN-10 0521674549
Release 2006-01
Pages 233
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Comprehensive treatment of the representation theory of finite groups of Lie type over a field of the defining prime characteristic.



Local Representation Theory

Local Representation Theory Author J. L. Alperin
ISBN-10 052144926X
Release 1993-09-24
Pages 178
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The aim of this text is to present some of the key results in the representation theory of finite groups. In order to keep the account reasonably elementary, so that it can be used for graduate-level courses, Professor Alperin has concentrated on local representation theory, emphasising module theory throughout. In this way many deep results can be obtained rather quickly. After two introductory chapters, the basic results of Green are proved, which in turn lead in due course to Brauer's First Main Theorem. A proof of the module form of Brauer's Second Main Theorem is then presented, followed by a discussion of Feit's work connecting maps and the Green correspondence. The work concludes with a treatment, new in part, of the Brauer-Dade theory. As a text, this book contains ample material for a one semester course. Exercises are provided at the end of most sections; the results of some are used later in the text. Representation theory is applied in number theory, combinatorics and in many areas of algebra. This book will serve as an excellent introduction to those interested in the subject itself or its applications.



Indra s Pearls

Indra s Pearls Author David Mumford
ISBN-10 0521352533
Release 2002-04-25
Pages 395
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Highly illustrated realization of infinitely reflected images related to fractals, chaos and symmetry.



Linear and Projective Representations of Symmetric Groups

Linear and Projective Representations of Symmetric Groups Author Alexander Kleshchev
ISBN-10 1139444069
Release 2005-06-30
Pages
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The representation theory of symmetric groups is one of the most beautiful, popular and important parts of algebra, with many deep relations to other areas of mathematics such as combinatories, Lie theory and algebraic geometry. Kleshchev describes a new approach to the subject, based on the recent work of Lascoux, Leclerc, Thibon, Ariki, Grojnowski and Brundan, as well as his own. Much of this work has previously appeared only in the research literature. However to make it accessible to graduate students, the theory is developed from scratch, the only prerequisite being a standard course in abstract algebra. For the sake of transparency, Kleshchev concentrates on symmetric and spin-symmetric groups, though methods he develops are quite general and apply to a number of related objects. In sum, this unique book will be welcomed by graduate students and researchers as a modern account of the subject.



Formal Groups and Applications

Formal Groups and Applications Author Michiel Hazewinkel
ISBN-10 9780821853498
Release 2012
Pages 573
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This title provides a comprehensive treatment of the theory of formal groups and its numerous applications in several areas of mathematics. The seven chapters of the book present basics and main results of the theory, as well as very important applications in algebraic topology, number theory, and algebraic geometry.



Rings Fields and Groups

Rings  Fields and Groups Author R. B. J. T. Allenby
ISBN-10 0340544406
Release 1991
Pages 383
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Provides an introduction to the results, methods and ideas which are now commonly studied in abstract algebra courses



Representations and Cohomology Volume 1 Basic Representation Theory of Finite Groups and Associative Algebras

Representations and Cohomology  Volume 1  Basic Representation Theory of Finite Groups and Associative Algebras Author D. J. Benson
ISBN-10 0521636531
Release 1998-06-18
Pages 260
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This is the first of two volumes providing an introduction to modern developments in the representation theory of finite groups and associative algebras, which have transformed the subject into a study of categories of modules. Thus, Dr. Benson's unique perspective in this book incorporates homological algebra and the theory of representations of finite-dimensional algebras. This volume is primarily concerned with the exposition of the necessary background material, and the heart of the discussion is a lengthy introduction to the (Auslander-Reiten) representation theory of finite dimensional algebras, in which the techniques of quivers with relations and almost-split sequences are discussed in some detail.