Product Description
Taking a slightly different approach from similar texts, Introduction to Abstract Algebra presents abstract algebra as the main tool underlying discrete mathematics and the digital world. It helps students fully understand groups, rings, semigroups, and monoids by rigorously building concepts from first principles.

A Quick Introduction to Algebra

The first three chapters of the book show how functional composition, cycle notation for permutations, and matrix notation for linear functions provide techniques for practical computation. The author also uses equivalence relations to introduce rational numbers and modular arithmetic as well as to present the first isomorphism theorem at the set level.

The Basics of Abstract Algebra for a First-Semester Course

Subsequent chapters cover orthogonal groups, stochastic matrices, Lagrange’s theorem, and groups of units of monoids. The text also deals with homomorphisms, which lead to Cayley’s theorem of reducing abstract groups to concrete groups of permutations. It then explores rings, integral domains, and fields.

Advanced Topics for a Second-Semester Course

The final, mostly self-contained chapters delve deeper into the theory of rings, fields, and groups. They discuss modules (such as vector spaces and abelian groups), group theory, and quasigroups. ... Read more

Customer Reviews (1)

Crisp and clean
This is one of those math books built from "first principles" onward.

It is also done very nicely.Very well formatted, very well organized, proofs short and very clear.

A wide variety of exercises at the end of each chapter.

It is what it says it is, an introduction to A.A, covering:
- Well ordering of numbers, euclidean algorithms
- abstract Function definitions, injective and surjective, isomorphisms, groups of permutations
- Uses monoids to help introduce groups
- Homomorphisms, Cayley's theorem
- Rings, Subrings, Polynomial Rings, Ring homomorphisms
- Fields, irreducible polynomials, LaGrange interpolation
- Factorization, roots of polynomials, Galois fields
- Modules, Vector spaces, Abelian groups
- Group actions, orbits, fixed points, alternating groups
- Quasigroups, latin squares, quasigroup homomorphisms
... Read more

Product Description
Beginning from scratch and developing the standard topics of Linear Algebra, this book is intended as a text for a first course on the subject. The goal to which this work leads is the Theorem of Hurwitz - that the only normed algebras over the real numbers are the real numbers, the complex numbers, the quaternions, and the octonions. Unique in presenting this material at an elementary level, the book stresses the complete logical development of the subject and will provide a bavuable reference for mathematicians in general. ... Read more

Customer Reviews (1)

An illuminated, highly concentrated review of Linear Algebra
From a physics undergrad: This is one of those wonderful, highly concentrated books that deliver extensive Wisdom in only a few pages of hardcore, to-the-point Theory, without simplifying. If you enjoy being told things in a frank manner and without excessive preambles, even if this means slower reading, this book is for you. The theory is built from scratch, but a lack of general abstract mathematical culture might prove problematic. Not recommended for the unprepared or those greedily seeking immediate applications. ... Read more

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Apply "Transferred to Digital Printing 2005" on copyright page ... Read more

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Product Description
An ambitious, comprehensive book covering subject matter typically taught over the course of two or three years, Abstract Algebra offers a self-contained presentation, detailed definitions, and excellent chapter-matched exercises to automatically smooth the trajectory of learning algebra from zero to one—and includes an original treatment of representation of finite groups that avoids the use of semisimple ring theory. ... Read more

Customer Reviews (1)

A Comprehensive Treatment
The textbook is exactly what it says it is, 'A Comprehensive Treatment'. It is 750 pages of algebra and covers more topics than any other Abstract Algebra text I've seen. It aims to start the reader from the beginning and requires no prerequisites. ... Read more

Product Description
This Third Edition of the acclaimed self-study text lets you learn abstract algebra at your own pace

The Third Edition of Introduction to Abstract Algebra continues to provide an accessible introduction to the basic structures of abstract algebra: groups, rings, and fields.The text's unique approach helps readers advance to abstract theory by presenting concrete examples of induction, number theory, integers modulo n, and permutations before the abstract structures are defined. Readers can immediately begin to perform computations using abstract concepts that are developed in greater detail later in the text.

As in the previous editions, the Third Edition offers many special features to help readers learn and apply their developing knowledge of abstract algebra:

• Historical notes and biographies of mathematicians provide context and perspective
• Some 500 worked examples help readers understand key concepts and their applications
• Almost 1,500 computational and theoretical exercises ranging from basic to complex challenge readers to apply their knowledge to solve problems. Many answers are provided in the text
• Applications to real-world problems in such areas as coding theory and combinatorics help readers grasp the topic's relevancy
• Special topics such as symmetric polynomials, nilpotent groups, semidirect products of groups, and the Wedderburn-Artin theorem for rings are included for more advanced study

This Third Edition includes thoroughly revised chapters and much new material, including new sections covering free, semisimple, and projective modules; modules over principal ideal domains; as well as semidirect products and the Wedderburn-Artin theorem. Two new appendices have been added on Zorn's lemma and the proof of the recursion theorem.

Numerous worked examples, exercises, and real-world applications make this text perfect for upper-level undergraduate and graduate courses. Moreover, with this book's self-contained chapters, students can learn at their own pace, and instructors can adapt the text to meet a variety of course objectives. ... Read more

Customer Reviews (3)

Great Seller
I received my item fast and in the condition it was described. Great Seller! A+++++++++++

Hard to read
As a new student that is new to proofs and Abstract algebra, I found this book hard to read and hard to follow. The language itself is very difficult and spares a lot of words.
Granted, if you are somewhat familiar with abstract algebra and the terminology the book might not be as difficult. However, I had to buy two other books in order to understand the material.

Although it's loaded with information and even covers the basic information, my other books expressed it in clearer language and walked me thorough the beginning proofs, much better than this book did.

If you are brand new to the subject, I don't recommend using this book.

In addition the glue/binding in the middle of the book starts to tear, so groups of pages will become lose if you are not careful. It happened to my book, as well as the books of my class mates even though we bought it from different sources.

Very good introductory text
The first time I took Abstract Algebra. I used Herstein's text the most cryptic text I have yet to use. I read the book cover to cover several times and still lacked a firm grasp on the material. Nicholson's book takes the time to present many examples and to thoroughly cover each topic. The examples of groups most frequently discussed are all placed at the beginning allowing the reader to have many examples to go on. While the book is not a terse reference it is a great introduction to the world of abstract algebra. It gives the undergraduate a chance to make that large step to this higher level of abstraction.However, the exercises are a little easy and the counterside to the above is that it is quite long. ... Read more

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New edition includes extensive revisions of the material on finite groups and Galois Theory. New problems added throughout. ... Read more

Customer Reviews (24)

great book, look for a cheaper copy
It helps to have a little maturity with sets and proofs when starting. The book has all the topics for undergrad and even 1st year grad (some schools). Lots of very good problems. Very well written. Look for used copies.

Easy to read, covers basic concepts
Topics is good for a first taste of Abstract Algebra.It seems very elementary to me, as I took a look at this after having gone through the book by Michael Artin.After Artin, the problems seem too easy, and the range of topics are minimal.However, unlike Artin, it seems to be much better at building a foundation.It is easy to read, and seems like a good how-to book on the subject.

Disadvantages, Advantages Depending on Reader's Needs
While this book may have deserved 5 stars when it first came out, as it is very well written, it has disadvantages for students today.As with any mathematics text, it does not serve the needs of all students, and it should be purchased only with this in mind.

A word of caution:I have used this book for group theory only, and have read only about half of Herstein's chapter on this subject.Still, it's my hope that my comments will be of use to buyers in my situation.

I purchased this book to help me prepare for a comprehensive algebra exam that covers all the standard undergraduate level topics in linear algebra, group, and ring theory.While the text had definite advantages, and I can see why it is viewed by many as a classic, I have found that it is not the best book for my purposes.

Some advantages:(1) The book is nicely structured. (2) The book is written from the perspective of a research mathematician.That is, the author takes many opportunities to motivate definitions and arguments, often in a historical sense.For example, in his section on normal subgroups and quotient groups, he comments that "It is a tribute to the genius of Galois that he recognized that those subgroups for which the left and right cosets coincide are distinguished ones.Very often in mathematics the crucial problem is to recognize and discover what are the relevant concepts..."Moreover, he manages to offer such insights without engaging in long digressions.(3)If you like your proofs to be detailed, you'll probably like the proofs in Herstein.

Some disadvantages:Math is always evolving, and it seems that the text might be a bit outdated.Notational choices aside, it seems that a number of results and definitions that may be considered standard today are relegated to the exercises.This may be a conscious choice on the part of the author, and I can certainly understand the value in discovering such results on one's own.However, for a student who is reviewing material independently, with a limited time in which to cover a lot of material, this situation is not ideal.

To summarize, I do not wish to disrespect the author or to claim that this book is not excellent in many ways.Based on my limited use of the book, however, it seems that the book may not be the best choice for a student who wants a comprehensive and time-efficient source for independent study.

Very nice book
This book is very nice. As an undergraduate I try to study this book to have a glimpse of abstract algebra. So far this is a pleasant experience. The proofs are clear and rigorous. The author makes good reason for new definitions to be made or new terms to come up. Some exercises are standard that they ask you to imitate the proof of some preceding theorems, or just to have some hand-on calculations. However, part of them are really tough, especially those starred ones.
One drawback is that it doesn't seem to mention anything about group actions, even amid the proof of Cayley's theorem nothing was defined. Also the names are not explicitly stated, like those three isomorphism theorems. In a nutshell this is a very good book and it is not easy as well.

Good Introduction, useful for self study
I am an engineer by training and a sales man by profession, with a a strong liking for mathematics.
I found this book to be an very readable introduction to a subject (abstract algebra), I had never been exposed to during my engineering math - other than matirx theory, which was obviously taught extensively.
The proofs are generally easy to understand, but certainly not trivial.
A pleasure to read ... Read more

Product Description
The Second Edition of this classic text maintains the clear exposition, logical organization, and accessible breadth of coverage that have been its hallmarks. It plunges directly into algebraic structures and incorporates an unusually large number of examples to clarify abstract concepts as they arise. Proofs of theorems do more than just prove the stated results; Saracino examines them so readers gain a better impression of where the proofs come from and why they proceed as they do. Most of the exercises range from easy to moderately difficult and ask for understanding of ideas rather than flashes of insight. The new edition introduces five new sections on field extensions and Galois theory, increasing its versatility by making it appropriate for a two-semester as well as a one-semester course. ... Read more

Customer Reviews (5)

Perfect Condition and fast shipping!
Great condition and super fast shipping the book arrived in a timely manner. Will purchase from again and happy to give a 5 star review!

A good book for a great class
I used this text for a one semester course on Group Theory in the spring of 2007. It's a great text for reference, but time is required to really grasp the concepts. I wouldn't recommend it as a book to teach yourself with, but with a good professor on your side it's a valuable asset. Another interesting (I'm not sure if I would consider it positive or negative) thing about this book is that problems are not merely examples of material covered in the text, but important theorems are also assigned for the students to prove on their own.

Excellent
This book had some great examples. The examples help me to understand abstract concepts. The proofs were very well constructed.

A wonderful text.
Concise and wonderfully coherent, this book isn't filled with "fluff" such as dumb examples and spoonfed advice.Clearly targeted for a mathematically inclined class of undergraduate modernalgebra students, you will find the immense amount of knowledge and theprice of this book to be absolutely pleasing.

okay
All the material here is very thorough, which leaves very little unclear about the material.I do have one hang-up with this text: the problems are uninteresting.Nearly all of the problems are trivial.The text to consult: "A Book of Abstract Algebra", Charles Pinter ... Read more

Product Description
'Rings, Fields and Groups' gives a stimulating and unusual introduction to the results, methods and ideas now commonly studied on abstract algebra courses at undergraduate level. The author provides a mixture of informal and formal material which help to stimulate the enthusiasm of the student, whilst still providing the essential theoretical concepts necessary for serious study.

Retaining the highly readable style of its predecessor, this second edition has also been thoroughly revised to include a new chapter on Galois theory plus hints and solutions to many of the 800 exercises featured. ... Read more

Customer Reviews (2)

Good for self-study
For the most part, this book is a clear and concise introduction to abstract algebra. The prose is lucid and the author's notes and remarks give some intuitive rationale behind several of the results. The exercises are well-thought out, and in some cases they expound on an idea touched on earlier in the chapter.

On the other hand, a few of the chapters went over my head. The Prologue, for example, cites the major contributions of the key figures in the historical development of algebra. Since I was still an algebra novice when I read the Prologue, I found it hard to follow. Moreover, Chapter 5 on Group Theory begins with an introduction that summarizes two methods of solving the cubic. I had a lot of trouble following this section as well. In his description of Tchirnhaus' method, he brings up a simultaneous equation involving a cubic and quadratic but skips over some calculations. I spent 2 days trying to fill in the gaps, only to throw my 20 pages of scribble into the wastebasket in frustration. If you are not as obsessive as I am, then you might be ok with skipping over topics or exercises that are too advanced.

Having done every exercise up to Chapter 5, I've found about 5-6 typos in the print, which is decent for a math text.Brief solutions for most problems are in the back, which makes this book ideal for self-study.

Algebra for advanced beginners
I used this book as a supplement to a course in algebra at master level.Allenby uses a simple step by step approach to the subject supplied withsimple examples and some exercises (not that simple).

What I realy likewith this book is the historical tour of algebra and the brief presentationof many of the worlds famoust mathematicians.

I think the simple approachand the historical elements is main reason for still using this book when Iam plying with the math. ... Read more

Product Description

Algebra, Second Edition, by Michael Artin, provides comprehensive coverage at the level of an honors-undergraduate or introductory-graduate course. The second edition of this classic text incorporates twenty years of feedback plus the author’s own teaching experience. This book discusses concrete topics of algebra in greater detail than others, preparing readers for the more abstract concepts; linear algebra is tightly integrated throughout.

Customer Reviews (34)

Excellent undergraduate algebra
Excellent undergraduate algebra, with emphasis on examples and interaction with other areas of mathematics, a mixture of simplicity and sophistication.For those studying the book I recommend to take a look at the beautifulon-line lectures of Benedict Gross(Harvard)-based on Artin's book [...]

Teaches instead of expounds
Not having the experience of listening to Artin lecture, one can only surmise that this man has to be a great teacher. The text does exaclty that -- it teaches and there are precious few that accomplish that objective as well, maybe none. Almost every theorem or proposition is placed in context and explained thoroughly with clear and concise examples and the themes are well articulated and consistent. There are many "surveys of modern algebra" that also have extensive scope but none touch the clarity of this text.

Why You Should Get This Book Instead of Dummite & Foote
Artin's Algebra is a great book.It covers a good deal of introductory Algebra, leaving out some stuff, but ultimately covering everything you need to be able to move on to the next level, like Lang's Algebra.While Dummit & Foote is longer and covers more material than Artin, it is not as good an introductory book as Artin, and it's not as good as Lang for higher-level stuff.

Here's what I'd suggest:Get Artin then Lang.

Incredibly insightful, deliberately disorganized text
I wish to first point out that several positive reviewers argue that the strength of the book is what it forces you to look for and that if you cannot find the missing puzzle pieces you must be mathematically weak or studying poorly. The argument seems to be that the book's strength lies in that which is omitted.

This is a silly argument, but it is telling of the pedagogical philosophy and communication bias in the book. The purpose of a text book is to communicate, but Artin's lazy stream-of-consciousness style will leave many out in the cold.

Indeed, the book does seem to be written for those who do not need it, an enormous sequence of casual asides to a lost conversation between students already versed in the field and a professor intent on communicating in fits and starts, short growls and nods.

As one reviewer noted, the text derives from Artin's lecture notes. This is not uncommon, but the book shows little evidence of any thought put into making the book useful as a reference. Rather it has many gaps both large and small. It is what one might expect from putting in the least amount of editorial work and hastily typesetting the notes for publication.

In terms of original content, Artin provides important insights. Still, while I can imagine thinking "what does Artin have to say about (blank)", I cannot imagine bothering to search a book so deliberately and thoroughly written to make the reader ask and answer their own questions.

A totally useless textbook.
The book by Artin was the most useless math textbook I have ever used.His proofs are impossible to understand, the exercises are frequently useless (either trivial results or monstrously tedious), and for the difficulty of the text to understand, the rigor of the presentation is astoundingly low (i.e. proving everything with matrices).His proving most of his statements with verbal exposition is also annoying as it makes it impossible to reference results in the book when solving problems.Also there are the times when an essential part of a problem is not even defined in the chapter but only in some other exercise.He also expects one to be able to compute character tables, but I had to look them up on mathworld to actually know how to do the computations.The book also tries to provide geometric examples, but does not explain them well or use them consistently.Also, there was a serious lack of diagrams, and when they existed they were unenlightening.I came into this class with a fairly strong background in Linear Algebra (Using Axler's Linear Algebra Done Right) and was highly annoyed by the topics that were left out (like tensors and duality) and the things that were overemphasized (rigid motions in the plane, change of basis).Another peeve is the statement that "most complex matrices are diagonalizable".What is the term "most" doing in a math textbook? ... Read more

Product Description
Contains an online laboratory manual for the computer algebra system GAP, with exercises tied to the book, and links on the author's website to true/false questions, flash cards, essays, software downloads, and other abstract algebra-related materials. ... Read more

Customer Reviews (1)

WASTE OF MONEY!
I purchased this product along with the text book because I thought I would need the extra help with the homework problems.COMPLETE waste of my money because EVERYTHING- I mean everything- in this book is located in the back of the text book.There's no new information, no help with any of the problems, or any additional supplementary information to the book.It is way overpriced and a very clear rip off. ... Read more

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Some remarkable connections between commutative algebra and combinatorics have been discovered in recent years. This book provides an overview of two of the main topics in this area. The first concerns the solutions of linear equations in nonnegative integers. Applications are given to the enumeration of integer stochastic matrices (or magic squares), the volume of polytopes, combinatorial reciprocity theorems, and related results. The second topic deals with the face ring of a simplicial complex, and includes a proof of the Upper Bound Conjecture for Spheres. An introductory chapter giving background information in algebra, combinatorics and topology broadens access to this material for non-specialists.

Customer Reviews (2)

great book
Great book - just be ready to get hold of some other books to fill in the details.If you're not entirely comfortable with the stuff in chapter 0 concerning modules (projectivity, injectivity), tor and ext, and homology from topology, maybe find a quick introduction to these elsewhere - while its certainly possible to learn about these things from chapter 0 of this book, it's not exactly the most painless way to do it.It was my first book on the subject, then I got Miller and Sturmfels: it would make more sense to reverse that order.Better still, get both simultaneously, and when the Stanley becomes a bit dense refer to M+S.I really loved this book, but it was damn hard at times!

This is a research monograph!
For those looking for a thorough introduction to the theory in this book, I would suggest a look at Miller and Sturmfels recent book on combinatorial commutative algebra or the book on Cohen-Macaulay rings by Bruns and Herzog. This is a great book, but I don't think it was intended as a beginners first book . Instead its style concentrates on presenting results found in research-articles ( prior to this book, there doesn't seem to have been any texts giving an overview of the theory ). It is great for looking up results, reading the needed prerequisites without going into details and finding important references. ... Read more

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This book explores the essential theories and techniques of modern algebra, including its problem-solving skills, basic proof techniques, many applications, and the interplay between algebra and geometry. It takes a concrete, example-oriented approach to the subject matter.

Customer Reviews (5)

For esoteric minds
Only on chapter 2, but I can see that the text jumps several steps in the equations.Need to fill them in for yourself.If you're a career changer like myself who is coming back to this level math after several years, search the internet for math examples or look up other texts that fill in the holes.

an excellent book for a student who will work hard
This is a very intelligent book, by a gifted expositor and teacher.The organization is based on thoughtful pedagogy rather than imitating other standard texts.E.g. it makes sense to begin with integers and polynomials and fields, instead of groups as most books do, because these are simpler and more familiar objects, and most people will find them more useful.

The abstract ideas that will occur in studying groups (and general rings) come up here in a more familiar setting.The author is always mindful of the interest of the material and gives significant applications as soon as they are feasible.

A particularly strong feature is the excellent sets of problems.Students should try all of them.The use of algebra to do some interesting projective geometry offers a fine glimpse of the more advanced use of the topic usually denied beginning students.

The book is written in a style suitable to a reader who has some mathematical sophistication, clear but not spoonfed.Shifrin never talks down to the student, and tends to present proofs in an articulate, but somewhat succint, rigorous, elegant style.A student with no experience at proofs will be challenged to understand some arguments, where parts are left for the student to fill in.

Thus reading this book is intended to be an active endeavor, pencil in hand, as it should always be.

The Worst Book of my Studies in Mathematics
This is the worst math book I have ever encountered.It is counterintuitative moving backwards compared to other text books teaching the same content.This book could have been so much more informative, however,there are little theorems that are missing.It could have had more pictures illustating the bigger ideas!There is no solutions to odd numbered exercises.I struggled to find other books to help me through this one, but no other book I found approaches the material in the same manner.

A clear and well organized book.
I took Ted Shifrin's Abstract Algebra course at UGA using the lecture notes that eventually became this book.Shifrin is one of the most decorated mathematics teachers around; his skill at presentation and hisconcern for student understanding come through in this book.

A coursetaught from this book will, of course, reflect its instructors abilitiesand compatibility with the text.As a book to read yourself this is anoutstanding text.The geometric flavor of the book works extremely wellfor the geometrically inclined.Because of its focus on clear instruction,its weakest role is as a reference book.

If they'd only release a secondedition fixing the books typos this would be more solid five star text. [...]

see below
I took a course which used this text, and I must say that that class was the least interesting class I have taken in my life.I think that looking at algebra from a geometric standpoint (and vice versa, an equivalent statement) ruins both algebra and geometry.Algebra is beautiful. Geometry is beautiful, but for a different reason.The intersection oftheir beauty (also, the beauty of their intersection) is the null set. ... Read more

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Never HIGHLIGHT a Book Again!Virtually all testable terms, concepts, persons, places, and events are included. Cram101 Textbook Outlines gives all of the outlines, highlights, notes for your textbook with optional online practice tests. Only Cram101 Out ... Read more

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-------------------Description--------------------Most abstract algebra texts begin with groups, then proceed to rings and fields. While groups are the logically simplest of the structures, the motivation for studying groups can be somewhat lost on students approaching abstract algebra for the first time. To engage and motivate them, starting with something students know and abstracting from there is more natural-and ultimately more effective.

Authors Anderson and Feil developed A First Course in Abstract Algebra: Rings, Groups and Fields based upon that conviction. The text begins with ring theory, building upon students' familiarity with integers and polynomials. Later, when students have become more experienced, it introduces groups. The last section of the book develops Galois Theory with the goal of showing the impossibility of solving the quintic with radicals.

Each section of the book ends with a "Section in a Nutshell" synopsis of important definitions and theorems. Each chapter includes "Quick Exercises" that reinforce the topic addressed and are designed to be worked as the text is read. Problem sets at the end of each chapter begin with "Warm-Up Exercises" that test fundamental comprehension, followed by regular exercises, both computational and "supply the proof" problems. A Hints and Answers section is provided at the end of the book.

As stated in the title, this book is designed for a first course--either one or two semesters in abstract algebra. It. requires only a typical calculus sequence as a prerequisite and does not assume any familiarity with linear algebra or complex numbers.---------------------Features---------------------· Provides sufficient material to design a one or two semester course · Builds on students' familiarity with integers and polynomials by studying rings first, then building up to groups · Motivates abstraction using concrete examples · Incorporates many exercises and problem sets throughout the text to provide immediate reinforcement of ideas and includes an unusually compete Hints and Solutions section· Incorporates historical remarks that engage students' interest in the subject· Includes a section on Galois theory---------------------Contents---------------------NUMBERS, POLYNOMIALS, AND FACTORINGThe Natural NumbersThe IntegersModular ArithmeticPolynomials with Rational CoefficientsFactorization of PolynomialsSection I in a Nutshell

RINGS, DOMAINS, AND FIELDSRingsSubrings and UnityIntegral Domains and FieldsPolynomials over a FieldSection II in a Nutshell

UNIQUE FACTORIZATIONAssociates and IrreduciblesFactorization and IdealsPrincipal Ideal DomainsPrimes and Unique FactorizationPolynomials with Integer CoefficientsEuclidean DomainsSection III in a Nutshell

RING HOMOMORPHISMS AND IDEALSRing HomomorphismsThe KernelRings of CosetsThe Isomorphism Theorem for RingsMaximal and Prime IdealsThe Chinese Remainder TheoremSection IV in a Nutshell

GROUPSSymmetries of Figures in the PlaneSymmetries of Figures in SpaceAbstract GroupsSubgroupsCyclic GroupsSection V in a Nutshell

GROUP HOMOMORPHISMS AND PERMUTATIONSGroup HomomorphismsGroup IsomorphismsPermutations and Cayley's TheoremMore About PermutationsCosets and Lagrange's TheoremGroups of CosetsThe Isomorphism Theorem for GroupsThe Alternating GroupsFundamental Theorem for Finite Abelian GroupsSolvable GroupsSection VI in a Nutshell

CONSTRUCTIBILITY PROBLEMSConstructions with Compass and StraightedgeConstructibility and Quadratic Field ExtensionsThe Impossibility of Certain ConstructionsSection VII in a Nutshell

VECTOR SPACES AND FIELD EXTENSIONSVector Spaces IVector Spaces IIField Extensions and Kronecker's TheoremAlgebraic Field ExtensionsFinite Extensions and Constructibility RevisitedSection VIII in a Nutshell

GALOIS THEORYThe Splitting FieldFinite FieldsGalois GroupsThe Fundamental Theorem of Galois TheorySolving Polynomials by RadicalsSection IX in a Nutshell

Hints and SolutionsGuide to NotationIndex ... Read more

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Low Price edition of A first course in Abstract Algebra. ... Read more

Product Description
Designed for an advanced undergraduate- or graduate-level course, Abstract Algebra provides an example-oriented, less heavily symbolic approach to abstract algebra. The text emphasizes specifics such as basic number theory, polynomials, finite fields, as well as linear and multilinear algebra. This classroom-tested, how-to manual takes a more narrative approach than the stiff formalism of many other textbooks, presenting coherent storylines to convey crucial ideas in a student-friendly, accessible manner. An unusual feature of the text is the systematic characterization of objects by universal mapping properties, rather than by constructions whose technical details are irrelevant.

Addresses Common Curricular Weaknesses
In addition to standard introductory material on the subject, such as Lagrange's and Sylow's theorems in group theory, the text provides important specific illustrations of general theory, discussing in detail finite fields, cyclotomic polynomials, and cyclotomic fields. The book also focuses on broader background, including brief but representative discussions of naive set theory and equivalents of the axiom of choice, quadratic reciprocity, Dirichlet's theorem on primes in arithmetic progressions, and some basic complex analysis. Numerous worked examples and exercises throughout facilitate a thorough understanding of the material. ... Read more