Schaum's Outline of Group Theory

Book Description

The theory of abstract groups comes into play in an astounding number of seemingly unconnected areas like crystallography and quantum mechanics, geometry and topology, analysis and algebra, physics, chemistry and even biology. Readers need only know high school mathematics, much of which is reviewed here, to grasp this important subject. Hundreds of problems with detailed solutions illustrate the text, making important points easy to understand and remember.

Customer Reviews:

A Classic Text.......2006-06-22

I had been studying group theory on my own independently using this book for the last seven months when I misplaced it while at work - along with the notebook which I had painstakingly and carefully created from my hundreds of hours of study in this book. To say the least, I've been absolutely devastated at losing my notes; but the Schaum Outline I can easily replace.

I had thought, after the book was lost, of trying another text. But most of the introductory textbooks on abstract algebra cover a lot of other things besides group theory. And as a result, they do not go very deeply into any one algebraic structure, but just scratch the surface. I wanted to focus on groups because, as stated in the Introduction of this book, this will bring me into the advanced areas of more quickly as a result of the narrowness of focus.

The notation in this book is initially peculiar. I was not used to seeing the notation xf for a function instead of f(x). The lack of parentheses was confusing, so when making my notes I simply added them, creating the notation (x)f. In fact this backward notation does seem to work better for abstract algebra, and after a while it becomes natural, and the standard notation f(x) becomes odd. So expect to see such things as this for automorphisms: (a*b)f = (a)f*(b)f.

Initially I did not want to use a Schaum outline to study groups. I wanted a hard-cover textbook. But I found this book irresistible in both its scope and its detailed discussion of group concepts. In summary, I would say that if you are truly serious about abstract algebra, you cannot afford to be without this fascinating, thorough, and inexpensive text.

Comprehensive but Dated.......2005-09-13

This is a reprint of a book that's been around since the sixties. It needs an update, especially the exercises, which are somewhat disorganized. The authors, like many mathematicians, have difficulty with the spoken language and do not adequately motivate the material, on an historical or intellectual basis. That said, this is still one of the best introductions to the subject available, at less than 20% the going cost of a textbook.

Outdated notation and very dull.......2004-06-04

I know maths books aren't meant to be fun to read, but this book is *extremely* boring. It's got, in my opinion, too much content, and its content could've been explained more efficiently.

Most of the notation used in this book (it was published 36 years ago) is out of date, which can be annoying as it makes the confusion subject of group theory even more confusing.

The good thing about this book is that it's great value for money. However, as said above, it might contain too much if you're an undergraduate student like myself who just wants to understand the basic stuff.

Good introduction to groups.......2000-06-05

This book is well organized and broad for a problem-solver, and has several useful features for beginners such as classification of groups up to order 15 and complete multiplication tables for A4 and S4 (no one would take the time to actually write and print these out, but they did in this book).

I also find the problems very well-selected and are frequently used later on, so you feel you didn't just go randomly solving problems.

The authors give many examples of groups and

groupoids, ranging from isometries to Moebius transformations, and a bit of free groups and group presentations are also covered.

Book Description

Introduction to Algebraic and Abelian Functions is a self-contained presentation of a fundamental subject in algebraic geometry and number theory. For this revised edition, the material on theta functions has been expanded, and the example of the Fermat curves is carried throughout the text. This volume is geared toward a second-year graduate course, but it leads naturally to the study of more advanced books listed in the bibliography.

Class Field Theory: From Theory to Practice

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Class Field Theory: From Theory to Practice
Georges Gras
Manufacturer: Springer
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Binding: Hardcover

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ASIN: 3540441336

Book Description

Global class field theory is a major achievement of algebraic number theory, based on the functorial properties of the reciprocity map and the existence theorem. The author works out the consequences and the practical use of these results by giving detailed studies and illustrations of classical subjects (classes, idèles, ray class fields, symbols, reciprocity laws, Hasse's principles, the Grunwald--Wang theorem, Hilbert's towers,...). He also proves some new or less-known results (reflection theorem, structure of the abelian closure of a number field) and lays emphasis on the invariant T_p, of abelian p-ramification, which is related to important Galois cohomology properties and p-adic conjectures. This book gives much material in an elementary way, and is suitable for students, researchers, and all who are fascinated by this theory.

In the corrected 2nd printing 2005, the author improves many details all along the book (e.g., he gives an interpretation of the Spiegelungssatz for the pth cyclotomic field regarding the Kummer--Vandiver conjecture in a probabilistic point of view).

Abelian l-adic Representations and Elliptic Curves (Research Notes in Mathematics (a K Peters), Vol 7)

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Serre is great
excellent

Abelian l-adic Representations and Elliptic Curves (Research Notes in Mathematics (a K Peters), Vol 7)
Jean Pierre Serre
Manufacturer: A K Peters Ltd
ProductGroup: Book
Binding: Hardcover

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ASIN: 1568810776

Customer Reviews:

Serre is great.......2003-03-17

This book, as all books by Serre, is very good. He writes with precision, always giving the reader the central ideas. I can only think of Milnor as an author to compare to him. Buy the book if you are interested at all in the material. I am buying all books I can get by Serre.

excellent.......2000-04-04

great reference if you are doing work in algebraic representations of geometric structures at the graduate level. There aren't very many exercises, but as a graduate reference text, exercises don't do a whole lot of good. great explanations, and clear proofs.

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Infinite Abelian Groups.
Irving, Kaplansky
Manufacturer: University of Michigan Press
ProductGroup: Book
Binding: Paperback
ASIN: 047208500X

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Introduction to Lambda Trees
Ian Chiswell
Manufacturer: World Scientific Publishing Company
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Binding: Hardcover

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ASIN: 9810243863

Fourier Analysis on Finite Groups with Applications in Signal Processing and System Design

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Fourier Analysis on Finite Groups with Applications in Signal Processing and System Design
Radomir S. Stankovic , Claudio Moraga , and Jaakko Astola
Manufacturer: Wiley-IEEE Press
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ASIN: 0471694630

Book Description

Discover applications of Fourier analysis on finite non-Abelian groups

The majority of publications in spectral techniques consider Fourier transform on Abelian groups. However, non-Abelian groups provide notable advantages in efficient implementations of spectral methods.

Fourier Analysis on Finite Groups with Applications in Signal Processing and System Design examines aspects of Fourier analysis on finite non-Abelian groups and discusses different methods used to determine compact representations for discrete functions providing for their efficient realizations and related applications. Switching functions are included as an example of discrete functions in engineering practice. Additionally, consideration is given to the polynomial expressions and decision diagrams defined in terms of Fourier transform on finite non-Abelian groups.

A solid foundation of this complex topic is provided by beginning with a review of signals and their mathematical models and Fourier analysis. Next, the book examines recent achievements and discoveries in:

Matrix interpretation of the fast Fourier transform
Optimization of decision diagrams
Functional expressions on quaternion groups
Gibbs derivatives on finite groups
Linear systems on finite non-Abelian groups
Hilbert transform on finite groups

Among the highlights is an in-depth coverage of applications of abstract harmonic analysis on finite non-Abelian groups in compact representations of discrete functions and related tasks in signal processing and system design, including logic design. All chapters are self-contained, each with a list of references to facilitate the development of specialized courses or self-study.

With nearly 100 illustrative figures and fifty tables, this is an excellent textbook for graduate-level students and researchers in signal processing, logic design, and system theory-as well as the more general topics of computer science and applied mathematics.

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This book examines applications of Fourier analysis on finite non-Abelian groups, and discusses different methods to determine compact representations for discrete functions providing for their efficient realizations and related applications. Switching functions are included as a particular example of discrete functions in engineering practice. Consideration is given to the polynomial expressions and decision diagrams defined in terms of Fourier transform on finite non-Abelain groups. The book demonstrates how transferring a problem from its original form into the spectral domain may provide major advantages, such as simplifying numerical calculation tasks.

Non-Abelian Harmonic Analysis Applications of SL(2, R) (Universitext)

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Non-Abelian Harmonic Analysis Applications of SL(2, R) (Universitext)
R. Howe , and E.C. Tan
Manufacturer: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
ProductGroup: Book
Binding: Paperback

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Book Description

This book discusses the representation theory of the group SL(2, R), and some applications of this theory. The emphasis is in fact on the applications, some of which are outside representation theory and some are to representation theory itself. The topics outside representation theory are mostly of substantial classical importance (Fourier analysis, Laplace equation, Huyghen's Principle, Ergodic theory), while those inside representation theory mostly concern themes that have been central to Harish-Chandra's development of harmonic analysis on semisimple groups. This mix of topics should appeal to non-specialists in representation theory by illustrating how the theory can offer new perspectives on familiar topics, and by offering some insight into some important themes in representation theory itself.

Oeuvres - Collected Papers: Volume 4: 1985 - 1998

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Oeuvres - Collected Papers: Volume 4: 1985 - 1998
Jean-Pierre Serre
Manufacturer: Springer
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Binding: Paperback

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ASIN: 3540435654

Book Description

From the reviews of Vol. IV:

"This is the fourth volume of J-P. Serre's Collected Papers covering the period 1985-1998. Items, numbered 133-173, contain "the essence'' of his work from that period and are devoted to number theory, algebraic geometry, and group theory. Half of them are articles and another half are summaries of his courses in those years and letters. Most courses have never been previously published, nor proofs of the announced results. The letters reproduced, however (in particular to K. Ribet and M.-F. Vignéras), provide indications of some of those proofs. Also included is an interview with J-P. Serre from 1986, revealing his views on mathematics (with the stress upon its integrity) and his own mathematical activity. The volume ends with Notes which complete the text by reporting recent progress and occasionally correct it.

The volume is an indispensable addition to previous ones and the whole set presents a fine piece of modern mathematics."

Zentralblatt MATH

In this softcover edition of volume IV, two recently published articles have been added, one on the life and works of Andrè Weil, the other one on Finite Subgroups of Lie Groups.

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