An Introduction To The Theory Of Groups PDF Download
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Author | : Joseph J. Rotman |
Publisher | : Springer Science & Business Media |
Total Pages | : 447 |
Release | : 2013-11-11 |
Genre | : Mathematics |
ISBN | : 1461245761 |
Download An Introduction to Algebraic Topology Book in PDF, ePub and Kindle
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 |
Total Pages | : 442 |
Release | : 2014-08-28 |
Genre | : Mathematics |
ISBN | : 1470409666 |
Download An Introduction to the Representation Theory of Groups Book in PDF, ePub and Kindle
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 |
Total Pages | : 498 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1468401289 |
Download A Course in the Theory of Groups Book in PDF, ePub and Kindle
" 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 | : Joseph J. Rotman |
Publisher | : Springer Science & Business Media |
Total Pages | : 533 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461241766 |
Download An Introduction to the Theory of Groups Book in PDF, ePub and Kindle
Anyone who has studied abstract algebra and linear algebra as an undergraduate can understand this book. The first six chapters provide material for a first course, while the rest of the book covers more advanced topics. This revised edition retains the clarity of presentation that was the hallmark of the previous editions. From the reviews: "Rotman has given us a very readable and valuable text, and has shown us many beautiful vistas along his chosen route." --MATHEMATICAL REVIEWS
Author | : R. McWeeny |
Publisher | : Elsevier |
Total Pages | : 263 |
Release | : 2013-09-03 |
Genre | : Mathematics |
ISBN | : 1483226247 |
Download Symmetry Book in PDF, ePub and Kindle
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.
Author | : Paul Alexandroff |
Publisher | : Courier Corporation |
Total Pages | : 130 |
Release | : 2012-01-01 |
Genre | : Mathematics |
ISBN | : 0486488136 |
Download An Introduction to the Theory of Groups Book in PDF, ePub and Kindle
" 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 | : Hermann Weyl |
Publisher | : Courier Corporation |
Total Pages | : 468 |
Release | : 1950-01-01 |
Genre | : Mathematics |
ISBN | : 9780486602691 |
Download The Theory of Groups and Quantum Mechanics Book in PDF, ePub and Kindle
This landmark among mathematics texts applies group theory to quantum mechanics, first covering unitary geometry, quantum theory, groups and their representations, then applications themselves — rotation, Lorentz, permutation groups, symmetric permutation groups, and the algebra of symmetric transformations.
Author | : John S. Rose |
Publisher | : Courier Corporation |
Total Pages | : 322 |
Release | : 2013-05-27 |
Genre | : Mathematics |
ISBN | : 0486170667 |
Download A Course on Group Theory Book in PDF, ePub and Kindle
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 | : Steven Roman |
Publisher | : Springer Science & Business Media |
Total Pages | : 385 |
Release | : 2011-10-26 |
Genre | : Mathematics |
ISBN | : 0817683011 |
Download Fundamentals of Group Theory Book in PDF, ePub and Kindle
Fundamentals of Group Theory provides a comprehensive account of the basic theory of groups. Both classic and unique topics in the field are covered, such as an historical look at how Galois viewed groups, a discussion of commutator and Sylow subgroups, and a presentation of Birkhoff’s theorem. Written in a clear and accessible style, the work presents a solid introduction for students wishing to learn more about this widely applicable subject area. This book will be suitable for graduate courses in group theory and abstract algebra, and will also have appeal to advanced undergraduates. In addition it will serve as a valuable resource for those pursuing independent study. Group Theory is a timely and fundamental addition to literature in the study of groups.
Author | : Hans Kurzweil |
Publisher | : Springer Science & Business Media |
Total Pages | : 389 |
Release | : 2003-11-06 |
Genre | : Mathematics |
ISBN | : 0387405100 |
Download The Theory of Finite Groups Book in PDF, ePub and Kindle
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