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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.

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

Visual Group Theory

Visual Group Theory Author Nathan Carter
ISBN-10 088385757X
Release 2009-04-09
Pages 297
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Group theory is the branch of mathematics that studies symmetry, found in crystals, art, architecture, music and many other contexts. But its beauty is lost on students when it is taught in a technical style that is difficult to understand. Visual Group Theory assumes only a high school mathematics background and covers a typical undergraduate course in group theory from a thoroughly visual perspective. The more than 300 illustrations in Visual Group Theory bring groups, subgroups, homomorphisms, products, and quotients into clear view. Every topic and theorem is accompanied with a visual demonstration of its meaning and import, from the basics of groups and subgroups through advanced structural concepts such as semidirect products and Sylow 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.

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.

Linear Algebra

Linear Algebra Author Reg Allenby
ISBN-10 9780080571799
Release 1995-01-05
Pages 240
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As the basis of equations (and therefore problem-solving), linear algebra is the most widely taught sub-division of pure mathematics. Dr Allenby has used his experience of teaching linear algebra to write a lively book on the subject that includes historical information about the founders of the subject as well as giving a basic introduction to the mathematics undergraduate. The whole text has been written in a connected way with ideas introduced as they occur naturally. As with the other books in the series, there are many worked examples.

Modular Functions and Dirichlet Series in Number Theory

Modular Functions and Dirichlet Series in Number Theory Author Tom M. Apostol
ISBN-10 9781461209997
Release 2012-12-06
Pages 207
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A new edition of a classical treatment of elliptic and modular functions with some of their number-theoretic applications, this text offers an updated bibliography and an alternative treatment of the transformation formula for the Dedekind eta function. It covers many topics, such as Hecke’s theory of entire forms with multiplicative Fourier coefficients, and the last chapter recounts Bohr’s theory of equivalence of general Dirichlet series.

Representations of Groups

Representations of Groups Author Klaus Lux
ISBN-10 9781139489188
Release 2010-07-01
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The representation theory of finite groups has seen rapid growth in recent years with the development of efficient algorithms and computer algebra systems. This is the first book to provide an introduction to the ordinary and modular representation theory of finite groups with special emphasis on the computational aspects of the subject. Evolving from courses taught at Aachen University, this well-paced text is ideal for graduate-level study. The authors provide over 200 exercises, both theoretical and computational, and include worked examples using the computer algebra system GAP. These make the abstract theory tangible and engage students in real hands-on work. GAP is freely available from and readers can download source code and solutions to selected exercises from the book's web page.

Moonshine of Finite Groups

 Moonshine  of Finite Groups Author Koichiro Harada
ISBN-10 3037190906
Release 2010
Pages 76
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Moonshine of Finite Groups has been writing in one form or another for most of life. You can find so many inspiration from Moonshine of Finite Groups also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Moonshine of Finite Groups book for free.

Character Theory of Finite Groups

Character Theory of Finite Groups Author Mark L. Lewis
ISBN-10 9780821848272
Release 2010-09-17
Pages 179
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This volume contains a collection of papers from the Conference on Character Theory of Finite Groups, held at the Universitat de Valencia, Spain, on June 3-5, 2009, in honor of I. Martin Isaacs. The topics include permutation groups, character theory, p-groups, and group rings. The research articles feature new results on large normal abelian subgroups of p-groups, construction of certain wreath products, computing idempotents in group algebras of finite groups, and using dual pairs to study representations of cross characteristic in classical groups. The expository articles present results on vertex subgroups, measuring theorems in permutation groups, the development of super character theory, and open problems in character theory.

Geometry In Advanced Pure Mathematics

Geometry In Advanced Pure Mathematics Author Bullett Shaun
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.

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

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.

Characters and Blocks of Finite Groups

Characters and Blocks of Finite Groups Author Gabriel Navarro
ISBN-10 0521595134
Release 1998-05-07
Pages 287
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This is a clear, accessible and up-to-date exposition of modular representation theory of finite groups from a character-theoretic viewpoint. After a short review of the necessary background material, the early chapters introduce Brauer characters and blocks and develop their basic properties. The next three chapters study and prove Brauer's first, second and third main theorems in turn. These results are then applied to prove a major application of finite groups, the Glauberman Z*-theorem. Later chapters examine Brauer characters in more detail. The relationship between blocks and normal subgroups is also explored and the modular characters and blocks in p-solvable groups are discussed. Finally, the character theory of groups with a Sylow p-subgroup of order p is studied. Each chapter concludes with a set of problems. The book is aimed at graduate students, with some previous knowledge of ordinary character theory, and researchers studying the representation theory of finite groups.

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.

Moonshine beyond the Monster

Moonshine beyond the Monster Author Terry Gannon
ISBN-10 1139457802
Release 2006-09-07
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This book was originally published in 2006. Moonshine forms a way of explaining the mysterious connection between the monster finite group and modular functions from classical number theory. The theory has evolved to describe the relationship between finite groups, modular forms and vertex operator algebras. Moonshine Beyond the Monster describes the general theory of Moonshine and its underlying concepts, emphasising the interconnections between mathematics and mathematical physics. Written in a clear and pedagogical style, this book is ideal for graduate students and researchers working in areas such as conformal field theory, string theory, algebra, number theory, geometry and functional analysis. Containing over a hundred exercises, it is also a suitable textbook for graduate courses on Moonshine and as supplementary reading for courses on conformal field theory and string theory.

Groups and Symmetry

Groups and Symmetry Author Mark A. Armstrong
ISBN-10 9781475740349
Release 2013-03-14
Pages 187
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This is a gentle introduction to the vocabulary and many of the highlights of elementary group theory. Written in an informal style, the material is divided into short sections, each of which deals with an important result or a new idea. Includes more than 300 exercises and approximately 60 illustrations.