Product Description
Concrete Abstract Algebra develops the theory of abstract algebra from numbers to Gr"obner bases, while takin in all the usual material of a traditional introductory course.In addition, there is a rich supply of topics such as cryptography, factoring algorithms for integers, quadratic residues, finite fields, factoring algorithms for polynomials, and systems of non-linear equations.A special feature is that Gr"obner bases do not appear as an isolated example.They are fully integrated as a subject that can be successfully taught in an undergraduate context. Lauritzen's approach to teaching abstract algebra is based on an extensive use of examples, applications, and exercises.The basic philosophy is that inspiring, non-trivial applications, and exercises.The basic philosophy is that inspiring, non-trivial applications and examples give motivation and ease the learning of abstract concepts.This book is built on several years of experienced teaching introductory abstract algebra at Aarhus, where the emphasis on concrete and inspiring examples has improved student performance significantly. ... Read more

Customer Reviews (1)

Very suitable textbook for courses in abstract algebra
The subject matter of a first course in abstract algebra is almost universally the same to all people. It begins with some fundamental background in number theory, relations, functions and a survey of notation. After this, it is groups, rings, fields in their various incarnations. Within these categories, the coverage is also generally the same, the pedagogical examples are well known and they are used in all books. Therefore, when making a choice concerning what book to adopt for a class, the decision is based largely on the clarity of the explanations and how one reacts to it on an emotional level.
The quality of the exposition in this book is excellent; it is easy to follow the explanations and proofs from start to finish. A large number, generally over 50, of exercises are included at the end of each chapter. If and when I teach abstract algebra again, this book will be given the most serious consideration for adoption.
... Read more

Product Description
Most students in abstract algebra classes have great difficulty making sense of what the instructor is saying. Moreover, this seems to remain true almost independently of the quality of the lecture.

This book is based on the constructivist belief that, before students can make sense of any presentation of abstract mathematics, they need to be engaged in mental activities which will establish an experiential base for any future verbal explanation. No less, they need to have the opportunity to reflect on their activities. This approach is based on extensive theoretical and empirical studies as well as on the substantial experience of the authors in teaching astract algebra.

The main source of activities in this course is computer constructions, specifically, small programs written in the mathlike programming language ISETL; the main tool for reflections is work in teams of 2-4 students, where the activities are discussed and debated. Because of the similarity of ISETL expressions to standard written mathematics, there is very little programming overhead: learning to program is inseparable from learning the mathematics.

Each topic is first introduced through computer activities, which are then followed by a text section and exercises. This text section is written in an informed, discusive style, closely relating definitions and proofs to the constructions in the activities. Notions such as cosets and quotient groups become much more meaningful to the students than when they are presented in a lecture. ... Read more

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This book is appropriate for second to fourth year undergraduates. In addition to the material traditionally taught at this level, the book contains several applications: Polya-Burnside Enumeration, Mutually Orthogonal Latin Squares, Error-Correcting Codes and a classification of the finite groups of isometries of the plane and the finite rotation groups in Euclidean 3-space. It is hoped that these applications will help the reader achieve a better grasp of the rather abstract ideas presented and convince him/her that pure mathematics, in addition to having an austere beauty of its own, can be applied to solving practical problems. An entire chapter is devoted to studying the algebraic system of the integers mod n under the usual operations of addition and multiplication. The reader is thus introduced - via congruence classes - to the idea of cosets and factor groups. This enables the transition to cosets and factor objects in a more abstract setting to be relatively painless. The chapters dealing with applications help to reinforce the concepts and methods developed in the context of more down-to earth problems.Most introductory texts in abstract algebra either avoid cosets, factor objects and homomorphisms completely or introduce them towards the end of the book. In this book, these topics are dealt with early on so that the reader has at his/her disposal the tools required to give elegant proofs of the fundamental theorems. Moreover, homomorphisms play such a prominent role in algebra that they are used in this text wherever possible, even if there are alternative methods of proof. ... Read more

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Combinatorial commutative algebra is an active area of research with thriving connections to other fields of pure and applied mathematics. This book provides a self-contained introduction to the subject, with an emphasis on combinatorial techniques for multigraded polynomial rings, semigroup algebras, and determinantal rings. The eighteen chapters cover a broad spectrum of topics, ranging from homological invariants of monomial ideals and their polyhedral resolutions, to hands-on tools for studying algebraic varieties with group actions, such as toric varieties, flag varieties, quiver loci, and Hilbert schemes. Over 100 figures, 250 exercises, and pointers to the literature make this book appealing to both graduate students and researchers.

Customer Reviews (1)

Coherent and Useful
This book does a good job at introducing some of the most interesting combinatorial problems in monomial resolutions.Although their chapter on toric varieties is somewhat weak, most of the other chapters (square-free monomial ideals, Borel-fixed ideals, staircases associated to monomial ideals in three variables, etc.) are very well written with challenging and revealing exercises at the end. ... Read more

Product Description
This book provides thorough coverage of the main topics of abstract algebra while offering nearly 100 pages of applications. A repetition and examples first approach introduces learners to mathematical rigor and abstraction while teaching them the basic notions and results of modern algebra.Chapter topics include group theory, direct products and Abelian groups, rings and fields, geometric constructions, historical notes, symmetries, and coding theory.For future teachers of algebra and geometry at the high school level. ... Read more

Customer Reviews (2)

it's in good quality
I forget when it comes, but i know that it didn't pass my deadline, so within 2 weeks. And it's in very good condition, exactly the thing that i want. Also fair price.

Perfect for Beginning Algebra Students
I used this as a textbook for an Abstract algebra course I took recently.It was surprisingly readable, and more importantly, there are plenty of examples that illustrate the definitions and theorems they've given.

Just a single complaint:There are times when important definitions are introduced in sections that are marked as examples, so it's not really safe to skip over the examples.This can be a little frustrating until you catch on, but it's not a big problem. ... Read more

Product Description
The first and second editions of this successful textbook have been highly praised for their lucid and detailed coverage of abstract algebra. In this third edition, the author has carefully revised and extended his treatment, particularly the material on rings and fields, to provide an even more satisfying first course in abstract algebra. ... Read more

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Realizing the specific needs of first-year graduate students, this reference allows readers to grasp and master fundamental concepts in abstract algebra—establishing a clear understanding of basic linear algebra and number, group, and commutative ring theory and progressing to sophisticated discussions on Galois and Sylow theory, the structure of abelian groups, the Jordan canonical form, and linear transformations and their matrix representations. ... Read more

Customer Reviews (1)

concrete, concise, easygoing
I was surprised how good the book was given its brevity. It's quite readable and the exercise reinforce and enhance the main outline of the book quite well. ... Read more

Product Description
This textbook offers a thorough, modern introduction into commutative algebra. It is intented mainly to serve as a guide for a course of one or two semesters, or for self-study. The carefully selected subject matter concentrates on the concepts and results at the center of the field. The book maintains a constant view on the natural geometric context, enabling the reader to gain a deeper understanding of the material. Although it emphasizes theory, three chapters are devoted to computational aspects. Many illustrative examples and exercises enrich the text. ... Read more

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Your hands-on guide to real-world applications of linear algebra

Does linear algebra leave you feeling lost? No worries —this easy-to-follow guide explains the how and the why of solving linear algebra problems in plain English. From matrices to vector spaces to linear transformations, you'll understand the key concepts and see how they relate to everything from genetics to nutrition to spotted owl extinction.

• Line up the basics — discover several different approaches to organizing numbers and equations, and solve systems of equations algebraically or with matrices

• Relate vectors and linear transformations — link vectors and matrices with linear combinations and seek solutions of homogeneous systems

• Evaluate determinants — see how to perform the determinant function on different sizes of matrices and take advantage of Cramer's rule

• Hone your skills with vector spaces — determine the properties of vector spaces and their subspaces and see linear transformation in action

• Tackle eigenvalues and eigenvectors — define and solve for eigenvalues and eigenvectors and understand how they interact with specific matrices

Open the book and find:

• Theoretical and practical ways of solving linear algebra problems

• Definitions of terms throughout and in the glossary

• New ways of looking at operations

• How linear algebra ties together vectors, matrices, determinants, and linear transformations

• Ten common mathematical representations of Greek letters

• Real-world applications of matrices and determinants

Customer Reviews (6)

not perfect but useful
you might notice a few typos every 20 pages. I can let that go cause I've never been exposed to this subject.

The typos are a tremendous shame
I just finished the text. It is a nice easy review. The amount of theory and proofs is kept to a minimum which should please those who are less gifted mathematically. The major issues as stated elsewhere are the number of typos and errors which were not caught in the editing process. Many are obvious and easy to fix. I would encourage the editors of this series to be more careful in the proofing. Perhaps it is too expensive given the low purchase price of the texts. Maybe we should all send in a list of errata and they could print a new edition.

be smarter than the book!
I really like the approach of this book, as it uses good analogies, examples, graphs, and figures that appeal to your intuition to give deeper meaning to the subtleties of linear algebra.But it is a shame there are typos and mistakes.One in particular blew my mind - on p. 51 she states " A square matrix is singular if it has a multiplicative inverse; a matrix is non-singular if it does not have a multiplicative inverse."This is exactly opposite of how everyone else defines "singular", but she uses this definition consistently throughout the book, so either it's a mistake or she has decided to rewrite the rules of linear algebra.Either way, it's not helpful!!!

I hate having to make corrections on a book I just paid for, but for the price, what can you expect?Most textbooks on the subject are between two and ten times more expensive, and they have mistakes too.But the other books are dense, dry, and boring.At least this book attempts to make linear algebra interesting, if not fun.

useful to me
College was a long time ago - I needed a refresher to do my job; this provided it.

Linear Algebra for Dummies
Good explanations, but a disappointing number of substantive typos that make the examples confusing.

I would recommend this book, particularly as a review for those of us who had the subject in college but have forgotten most of it.Just be careful of those typos and keep a pencil handy to make corrections while the details are fresh in your mind. ... Read more

Product Description
For use in your advanced abstract algebra course, Fundamentals of Abstract Algebra takes a blended theory and applications approach. Each chapter consists of definitions, theorems, proofs, and corollaries. Throughout the text you will find numerous examples that illustrate the concepts, historical background on the development of abstract algebra, and profiles of notable mathematicians. ... Read more

Customer Reviews (1)

Concrete Examples!
As one studies algebra, there is a common situation that the theorems get obscurity, immediately if you do not follow them on some concrete examples. And also a very common thing with the presentations is that the theorems follow without any motivation. This book provides lots of examples andmotivations which make one understand the concepts clearly. ... Read more

Product Description
This is the classic text for the first undergraduate course in abstract algebra; it follows the “rings before groups” philosophy that relies on the student's familiarity with the ring of integers to make the abstract axioms feel more concrete.The text and exercises are coordinated to help the student learn to read and write mathematical proofs.To achieve an understanding of the methods of proof, the unique factorization theorems are presented several times in different contexts.The integers are covered first, then polynomial rings over a field and, in the final chapter, factorization in principal ideal domains.Results on finite fields up through existence and uniqueness are proved without the use of linear algebra.The material on groups is studied in three chapters, the first giving definitions and examples, including permutation groups; the second gives the classification of finite abelian groups; the third discusses groups acting on sets and gives the proofs of the Sylow theorems.There are many worked examples and a large number of exercises of varying levels of difficulty.By carefully selecting sections to be covered in class lectures, an instructor will find this text suitable for almost any syllabus giving an introduction to abstract algebra. ... Read more

Customer Reviews (1)

Atrocious....Avoid at ALL COSTS
This is an atrocious book.If you can avoid it, do not buy.My complaints can be summarized into three points;

1. The concepts are incoherently presented and the exercises require knowledge that was not presented in the tutorial portion of the chapter.

2. There's a lot more to undergraduate level abstract algebra than what this book shows you.

3.The authors presented the material like how a number theorists would present the material,with too much emphasis on proving number theory topics.

I recommend the book by Hungerford, or, if you are mathematically mature enough, Dummit & Foote or Artin.You will see the difference. ... Read more

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Customer Reviews (1)

Stay away.Stay far away.
I wish I could offers some nice comments here, but the truth is I really, really don't like this book.You can get it for free at the author's website, but it's not worth the download.If your professor uses this as a class text, I suggest you switch sections.The title says "Introductory" but I'd wager few students for whom this book is intended could wade through it.I've had two semesters of 400-level Algebra and I find parts of this book unreadable. The proofs are sketchy and the examples are few and far between.When I read a math book I like to understand every little thing.Sometimes it takes me 20 minutes to get through a paragraph of this book because I'm constantly wondering where things came from.It seems at times as though the author wrote a beautiful 600-page Algebra book and the publisher decided to randomly chop it down to a couple hundred pages.I give it one star, but only because it included semi-direct products.

It's currently out of print, and for good reason. ... Read more

Product Description
Eliminating the need for heavy number-crunching, sophisticated mathematical software packages open the door to areas like cryptography, coding theory, and combinatorics that are dependent on abstract algebra. Applications of Abstract Algebra with Maple and MATLAB®, Second Edition explores these topics and shows how to apply the software programs to abstract algebra and its related fields.

Carefully integrating Maple™ and MATLAB®, this book provides an in-depth introduction to real-world abstract algebraic problems. The first chapter offers a concise and comprehensive review of prerequisite advanced mathematics. The next several chapters examine block designs, coding theory, and cryptography while the final chapters cover counting techniques, including Pólya's and Burnside's theorems. Other topics discussed include the Rivest, Shamir, and Adleman (RSA) cryptosystem, digital signatures, primes for security, and elliptic curve cryptosystems.

New to the Second Edition

Customer Reviews (1)

Great Condition, Arrived Quickly
I ordered this book for a class and it arrived on time in perfect condition.It's a great resource for abstract algebra. ... Read more

Product Description
A revision of McCoy's classic text, Introductory Abstract Algebra, Sixth Edition, retains the goals of earlier editions by providing the key information for a first course in abstract algebra in an easily understood, digestible manner. The material in the sixth edition is kept at approximately the same level as that in the previous editions with a number of comments, remarks, and exercises that point students toward more advanced topics. Rings are presented before groups because the ring of integers is already known to students and easily serves as a source of examples.

* Simple, clear, motivating style
* Many examples to illustrate concepts and theories

... Read more

Customer Reviews (1)

Abstract Algebra 6th edition
Very clear and concise book for beginners interested in a little of rigor. This book proves understandably essential proofs such as that of the Fundamental Theorem of Arithmitic,and the Division/Euclidean Algorithm, among others. But it lacks few basic spell out proofs that could be used to prove major results. This books is independent of Linear Algebra. I think that the first three chapters of the following book is a great complement because of its basic proven and spelled out results : "Beginning Number Theory, 2nd edition" by Neville Robbins. ... Read more

Product Description
The style and structure of Concepts in Abstract Algebra are designed to help students learn the core concepts and associated techniques in algebra deeply and well. Providing a fuller and richer account of material than time allows in a lecture, this text presents interesting examples of sufficient complexity so that students can see the concepts and results used in a nontrivial setting. Charles Lanski gives students the opportunity to practice by offering many exercises that require the use and synthesis of the techniques and results. Both readable and mathematically interesting, the text also helps students learn the art of constructing mathematical arguments. Overall, students discover how mathematics proceeds and how to use techniques that mathematicians actually employ. ... Read more