An Introduction To The Theory Of Groups

Author : Joseph J. Rotman
Publisher : Springer Science & Business Media
Page : 447 pages
File Size : 50,9 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9781461245766

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An Introduction to Algebraic Topology by Joseph J. Rotman Pdf

A clear exposition, with exercises, of the basic ideas of algebraic topology. Suitable for a two-semester course at the beginning graduate level, it assumes a knowledge of point set topology and basic algebra. Although categories and functors are introduced early in the text, excessive generality is avoided, and the author explains the geometric or analytic origins of abstract concepts as they are introduced.

Author : Emmanuel Kowalski
Publisher : American Mathematical Society
Page : 442 pages
File Size : 55,9 Mb
Release : 2014-08-28
Category : Mathematics
ISBN : 9781470409661

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An Introduction to the Representation Theory of Groups by Emmanuel Kowalski Pdf

Representation theory is an important part of modern mathematics, not only as a subject in its own right but also as a tool for many applications. It provides a means for exploiting symmetry, making it particularly useful in number theory, algebraic geometry, and differential geometry, as well as classical and modern physics. The goal of this book is to present, in a motivated manner, the basic formalism of representation theory as well as some important applications. The style is intended to allow the reader to gain access to the insights and ideas of representation theory--not only to verify that a certain result is true, but also to explain why it is important and why the proof is natural. The presentation emphasizes the fact that the ideas of representation theory appear, sometimes in slightly different ways, in many contexts. Thus the book discusses in some detail the fundamental notions of representation theory for arbitrary groups. It then considers the special case of complex representations of finite groups and discusses the representations of compact groups, in both cases with some important applications. There is a short introduction to algebraic groups as well as an introduction to unitary representations of some noncompact groups. The text includes many exercises and examples.

Author : Derek J.S. Robinson
Publisher : Springer Science & Business Media
Page : 498 pages
File Size : 47,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468401288

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A Course in the Theory of Groups by Derek J.S. Robinson Pdf

" A group is defined by means of the laws of combinations of its symbols," according to a celebrated dictum of Cayley. And this is probably still as good a one-line explanation as any. The concept of a group is surely one of the central ideas of mathematics. Certainly there are a few branches of that science in which groups are not employed implicitly or explicitly. Nor is the use of groups confined to pure mathematics. Quantum theory, molecular and atomic structure, and crystallography are just a few of the areas of science in which the idea of a group as a measure of symmetry has played an important part. The theory of groups is the oldest branch of modern algebra. Its origins are to be found in the work of Joseph Louis Lagrange (1736-1813), Paulo Ruffini (1765-1822), and Evariste Galois (1811-1832) on the theory of algebraic equations. Their groups consisted of permutations of the variables or of the roots of polynomials, and indeed for much of the nineteenth century all groups were finite permutation groups. Nevertheless many of the fundamental ideas of group theory were introduced by these early workers and their successors, Augustin Louis Cauchy (1789-1857), Ludwig Sylow (1832-1918), Camille Jordan (1838-1922) among others. The concept of an abstract group is clearly recognizable in the work of Arthur Cayley (1821-1895) but it did not really win widespread acceptance until Walther von Dyck (1856-1934) introduced presentations of groups.

Author : Paul Alexandroff,Hazel Perfect,G. M. Petersen
Publisher : Courier Corporation
Page : 130 pages
File Size : 45,5 Mb
Release : 2012-01-01
Category : Mathematics
ISBN : 9780486488134

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An Introduction to the Theory of Groups by Paul Alexandroff,Hazel Perfect,G. M. Petersen Pdf

" This introductory exposition of group theory by an eminent Russian mathematician is particularly suited to undergraduates, developing material of fundamental importance in a clear and rigorous fashion. A wealth of simple examples, primarily geometrical, illustrate the primary concepts. Exercises at the end of each chapter provide additional reinforcement. 1959 edition"--

Author : Antonio Machì
Publisher : Springer Science & Business Media
Page : 385 pages
File Size : 43,9 Mb
Release : 2012-04-05
Category : Mathematics
ISBN : 9788847024212

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Groups by Antonio Machì Pdf

Groups are a means of classification, via the group action on a set, but also the object of a classification. How many groups of a given type are there, and how can they be described? Hölder’s program for attacking this problem in the case of finite groups is a sort of leitmotiv throughout the text. Infinite groups are also considered, with particular attention to logical and decision problems. Abelian, nilpotent and solvable groups are studied both in the finite and infinite case. Permutation groups and are treated in detail; their relationship with Galois theory is often taken into account. The last two chapters deal with the representation theory of finite group and the cohomology theory of groups; the latter with special emphasis on the extension problem. The sections are followed by exercises; hints to the solution are given, and for most of them a complete solution is provided.

Author : Robert D. Carmichael
Publisher : Unknown
Page : 0 pages
File Size : 50,9 Mb
Release : 1956
Category : Group theory
ISBN : OCLC:1071635609

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Introduction to the Theory of Groups of Finite Order by Robert D. Carmichael Pdf

Author : Nathan Carter
Publisher : American Mathematical Soc.
Page : 295 pages
File Size : 41,5 Mb
Release : 2021-06-08
Category : Education
ISBN : 9781470464332

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Visual Group Theory by Nathan Carter Pdf

Recipient of the Mathematical Association of America's Beckenbach Book Prize in 2012! 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.

Author : Jean A. Dieudonne
Publisher : CRC Press
Page : 286 pages
File Size : 43,6 Mb
Release : 2020-01-29
Category : Mathematics
ISBN : 9781000723311

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Introduction to the Theory of Formal Groups by Jean A. Dieudonne Pdf

The concept of formal Lie group was derived in a natural way from classical Lie theory by S. Bochner in 1946, for fields of characteristic 0. Its study over fields of characteristic p > 0 began in the early 1950’s, when it was realized, through the work of Chevalley, that the familiar “dictionary” between Lie groups and Lie algebras completely broke down for Lie algebras of algebraic groups over such a field. This volume, starts with the concept of C-group for any category C (with products and final object), but the author’s do not exploit it in its full generality. The book is meant to be introductory to the theory, and therefore the necessary background to its minimum possible level is minimised: no algebraic geometry and very little commutative algebra is required in chapters I to III, and the algebraic geometry used in chapter IV is limited to the Serre- Chevalley type (varieties over an algebraically closed field).

Author : John S. Rose
Publisher : Courier Corporation
Page : 320 pages
File Size : 44,5 Mb
Release : 2013-05-27
Category : Mathematics
ISBN : 9780486170664

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A Course on Group Theory by John S. Rose Pdf

Text for advanced courses in group theory focuses on finite groups, with emphasis on group actions. Explores normal and arithmetical structures of groups as well as applications. 679 exercises. 1978 edition.

Author : Hans Kurzweil,Bernd Stellmacher
Publisher : Springer Science & Business Media
Page : 390 pages
File Size : 50,8 Mb
Release : 2006-03-04
Category : Mathematics
ISBN : 9780387217680

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The Theory of Finite Groups by Hans Kurzweil,Bernd Stellmacher Pdf

From reviews of the German edition: "This is an exciting text and a refreshing contribution to an area in which challenges continue to flourish and to captivate the viewer. Even though representation theory and constructions of simple groups have been omitted, the text serves as a springboard for deeper study in many directions." Mathematical Reviews

Author : Yurii I. Lyubich
Publisher : Birkhäuser
Page : 231 pages
File Size : 47,8 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783034891691

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Introduction to the Theory of Banach Representations of Groups by Yurii I. Lyubich Pdf

The theory of group representations plays an important roie in modern mathematics and its applica~ions to natural sciences. In the compulsory university curriculum it is included as a branch of algebra, dealing with representations of finite groups (see, for example, the textbook of A. I. Kostrikin [25]). The representation theory for compact, locally compact Abelian, and Lie groups is co vered in graduate courses, concentrated around functional analysis. The author of the present boo~ has lectured for many years on functional analysis at Khar'kov University. He subsequently con tinued these lectures in the form of a graduate course on the theory of group representations, in which special attention was devoted to a retrospective exposition of operator theory and harmo nic analysis of functions from the standpoint of representation theory. In this approach it was natural to consider not only uni tary, but also Banach representations, and not only representations of groups, but also of semigroups.

Author : Peter Woit
Publisher : Springer
Page : 668 pages
File Size : 45,8 Mb
Release : 2017-11-01
Category : Science
ISBN : 9783319646121

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Quantum Theory, Groups and Representations by Peter Woit Pdf

This text systematically presents the basics of quantum mechanics, emphasizing the role of Lie groups, Lie algebras, and their unitary representations. The mathematical structure of the subject is brought to the fore, intentionally avoiding significant overlap with material from standard physics courses in quantum mechanics and quantum field theory. The level of presentation is attractive to mathematics students looking to learn about both quantum mechanics and representation theory, while also appealing to physics students who would like to know more about the mathematics underlying the subject. This text showcases the numerous differences between typical mathematical and physical treatments of the subject. The latter portions of the book focus on central mathematical objects that occur in the Standard Model of particle physics, underlining the deep and intimate connections between mathematics and the physical world. While an elementary physics course of some kind would be helpful to the reader, no specific background in physics is assumed, making this book accessible to students with a grounding in multivariable calculus and linear algebra. Many exercises are provided to develop the reader's understanding of and facility in quantum-theoretical concepts and calculations.

Author : Clara Löh
Publisher : Springer
Page : 389 pages
File Size : 51,5 Mb
Release : 2017-12-19
Category : Mathematics
ISBN : 9783319722542

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Geometric Group Theory by Clara Löh Pdf

Inspired by classical geometry, geometric group theory has in turn provided a variety of applications to geometry, topology, group theory, number theory and graph theory. This carefully written textbook provides a rigorous introduction to this rapidly evolving field whose methods have proven to be powerful tools in neighbouring fields such as geometric topology. Geometric group theory is the study of finitely generated groups via the geometry of their associated Cayley graphs. It turns out that the essence of the geometry of such groups is captured in the key notion of quasi-isometry, a large-scale version of isometry whose invariants include growth types, curvature conditions, boundary constructions, and amenability. This book covers the foundations of quasi-geometry of groups at an advanced undergraduate level. The subject is illustrated by many elementary examples, outlooks on applications, as well as an extensive collection of exercises.

Author : Gerald Burns
Publisher : Academic Press
Page : 446 pages
File Size : 40,5 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483191492

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Introduction to Group Theory with Applications by Gerald Burns Pdf

Introduction to Group Theory with Applications covers the basic principles, concepts, mathematical proofs, and applications of group theory. This book is divided into 13 chapters and begins with discussions of the elementary topics related to the subject, including symmetry operations and group concepts. The succeeding chapters deal with the properties of matrix representations of finite groups, the vibrations of molecular and crystals, vibrational wave function, selection rules, and molecular approximations. These topics are followed by reviews of the basic of quantum mechanics, crystal field theory, atomic physics, hybrid functions, and molecular orbital theory. The last chapters describe the symmetry of crystal lattices, the band theory of solids, and the full rotation group. This book will be of value to undergraduate mathematics and physics students.

Author : R. McWeeny
Publisher : Elsevier
Page : 263 pages
File Size : 48,6 Mb
Release : 2013-09-03
Category : Mathematics
ISBN : 9781483226248

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Symmetry by R. McWeeny Pdf

Symmetry: An Introduction to Group Theory and its Application is an eight-chapter text that covers the fundamental bases, the development of the theoretical and experimental aspects of the group theory. Chapter 1 deals with the elementary concepts and definitions, while Chapter 2 provides the necessary theory of vector spaces. Chapters 3 and 4 are devoted to an opportunity of actually working with groups and representations until the ideas already introduced are fully assimilated. Chapter 5 looks into the more formal theory of irreducible representations, while Chapter 6 is concerned largely with quadratic forms, illustrated by applications to crystal properties and to molecular vibrations. Chapter 7 surveys the symmetry properties of functions, with special emphasis on the eigenvalue equation in quantum mechanics. Chapter 8 covers more advanced applications, including the detailed analysis of tensor properties and tensor operators. This book is of great value to mathematicians, and math teachers and students.