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Book Reviews

Review of Algebra

Editorial review
"Lang's Algebra changed the way graduate algebra is taught, retaining classical topics but introducing language and ways of thinking from category theory and homological algebra. It has affected all subsequent graduate-level algebra books." - NOTICES OF THE AMS "The author has an impressive knack for presenting the important and interesting ideas of algebra in just the "right" way, and he never gets bogged down in the dry formalism which pervades some parts of algebra." - MATHEMATICAL REVIEWS This book is intended as a basic text for a one-year course in algebra at the graduate level, or as a useful reference for mathematicians and professionals who use higher-level algebra. It successfully addresses the basic concepts of algebra. For the revised third edition, the author has added exercises and made numerous corrections to the text.

Reviewed by gh-bigfoot, from Oregon, USA
After having struggled with this book for most of my first year algebra class I grew to hate it! I now find myself refering to this book time and time again. This book really has it all. If you already have a good background in algebra and want a great referance, this book is a must. If you are taking algebra for the first time I would avoid this book and look at another intro. to algebra text like Grove (one of my favorite math texts).

Reviewed by a reader, from Chicago, IL
Concise but comprehensive, Lang's book really has no peer as a reference text for algebra. Both Cohn's and Jacobson's books omit far too many topics. Jacobson's book, which I am more familiar with, follows a very linear structure, which I find limits its appeal both as a reference text and as bedtime reading. This book ought to be challenging for any undergraduate, and perhaps even for some graduate students, but much of the material is essential. The book, unfortunately, contains few examples. This is especially problematic in the section on homology theory, where the abstraction becomes nearly overwhealming. Working concrete examples such as Ext, Tor, or the (co)homology of groups into the text would have been helpful.

Reviewed by eltnjohn, from Tokyo, Japan
As always with Lang, this book is not user-friendly: it makes a pretty hard reading unless you already have a fair knowledge of algebra as covered by other good texts like Cohn (volumes 1 through 3). If you are looking for something as reference, you should turn to more comprehensive works like Bourbaki.

Reviewed by a reader, from NC
I purchased this text after completing my first course in abstract algebra. I took the class (MA407) through my high school (via a college release program) in 12th grade. For that class we used Gallian's text "Contemporary abstract algebra." I was not fully satisfied with the text's applied flavor so I used Artin's and Herstein's texts as supplements.Now I realize that my purchase of Lang's text was probably premature. It is a difficult text, and although I enjoy it, getting through any given chapter takes me a long time. I have not completed the text (as a matter of fact I am still in section I), but I feel that I can see the basic style of the text. Lang's text is well written (although I keep running into small errors), and probably should be in the library of any graduate student in the pure mathematics. As for me, I think I jumped at this book too soon and should go back to Artin and complete that text first. Lang's text is probably better suited for a second class in algebra at the graduate level (there are some other advanced tests such as Jacobson's, but I believe that Lang's text is the only well written text book in algebra which covers such a wide range of topics in proper detail).In fall 1999, my freshman year, I will take graduate algebra and graduate real analysis, I hope after those classes I will be able to tackle Lang's text in a more reasonable manner.

Review of Undergraduate Algebra (Undergraduate Texts in Math)

Editorial review
Splendid undergraduate text, intended to function as a companion to the distinguished author's Linear algebra and to provide young mathematicians with a secure command of the fundamentals of groups, rings, fields, and related structures. Ten chapters, many excellent problems, written with exemplary clarity and with exceptional sensitivity to what young readers might on first encounter consider to be "scary". Departs from the previous edition (1987) by the inclusion of some new material and exercises. The author has been very well served by the production people at Springer, who have produced a physically beautiful book at a reasonable price. (NW) Annotation copyright Book News, Inc. Portland, Or.

Reviewed by R. A. Williams, from Albuquerque, NM USA
The title is quite misleading. It sounds innocuous but conceals some pretty neat stuff. This book is an introduction into modern algebra that starts with group theory and continues into Galois theory. It is terse at times but contains all the essentials.This text should be required reading for all Computer Science majors who have an interest in cryptography or cryptanalysis.

Reviewed by duvvuri@hanover.edu, from Hanover, Indiana
I didn't enjoy this book at all. The author, as he states in the preface, has tried to strike a balance between rigour and brevity, while trying to set a standard for the American undergraduate algebra curriculum. The intentions are admirable; however, he doesn't quite pull it off. Most of the important topics are presented either in the text or in the problems. For that matter, they're well chosen, too. But quite often the presentation is either too brief, unclear, or devoid of motivation. Some definitions are ambiguous or imprecise, while the notation is sometimes clumsy. The only redeeming feature is the choice of problems. They vary in difficulty from section to section, but on an average are excellent(a factor that adds to their difficulty is that the material in the text is so skimpy). On the whole, I don't know what purpose this book serves. The average student is better off using Fraleigh or Gallian (or any of the host of easier books avalailable), while Herstein still has much to offer to the motivated one. Jacobson and Cohn(which I used a lot while taking my first Algebra course) are always available as outstanding references.

Review of Pre-Algebra: An Accelerated Course

Reviewed by musi215@aol.com, from The Nation's Capital (Washington, DC)
My 7th grade math class uses this as our text book. It's a really cool book. It explains things really well. Get this book if you need help with: INTRODUCTION TO ALGEBRA Using Variables, Finding SolutionsPOSITIVE AND NEGATIVE NUMBERS Sums and Differences, Products and QuocientsRATIONAL NUMBERS Number Theory and Fractions, Operations with FractionsSOLVING EQUATIONS Using Transformations, Word ProblemsGEOMETRIC FIGURES Basic Figures, Figures in the PlaneRATIO, PROPORTION, AND PERCENT Ratio and Proportion, PercentsPERCENTS AND PROBLEM SOLVING Buisness and Consumer Problems, Investment and Application ProblemsTHE COORDINATE PLANE Equations and the Coordinate Plane, Graphing Systems in the Coordinate PlaneAREAS AND VOLUMES Areas, Volumes and Areas of SolidsAPPLYING ALGEBRA TO RIGHT TRIANGLES Square Roots, Using Right TrianglesSTATISTICS AND PROBABILITY Analyzing Data, Probability

Review of Algebra 1: Explorations and Applications

Reviewed by a reader, from Caracas, Venezuela
An excellent textbook! Applications make algebra part of everyday's life... as it really is. The book ends with the concept that numbers are abstract things. I teach math & calculus, and I found it the best text in Algebra I I have ever used!!!

Review of Algebra: Introductory and Intermediate

Reviewed by Maureen C. Hamilton, from Natick, MA United States
I used this book to teach my community college algebra I and II courses.I found it to be so logical in its presentation, that Iquickly yanked my daughter out of her 7th grade math class (using the incredibly poor Connected Math Series -- see Mathematicallycorrect.com) and decided to home school her in math using this book. She is at the end of 8th grade and by following a program of 20 problems a night she is now completing 10th grade math. She now loves math and understands it thoroughly. There are enough problems to reinforce all concepts.

Reviewed by sequoian@bkis.net, from Visalia CA, USA
This text is well written and easy for students to follow. I would have given this book 5 stars except for a few proofreading errors. As of today, the solutions manual is not yet available, which would certainly support the text. This book can be used in consecutive classes for Into & Intermediate Algebra.

Review of Algebra Structure and Method Book 1

Reviewed by libroschico, from Akron, Ohio
When reading a textbook, it is essential that the student has a clear understanding of whatever the book is trying to teach, whether it's history, biology, or algebra. If the language in the book isn't concise and easy to understand, there is a good chance that the student will not grasp what the book is saying. Although I am an intelligent math student, I thought that "Algebra: Structure and Method: Book 1" was extremely difficult to interpret. This book was the text for my eighth grade Algebra I course; on days when I was absent from school and was forced to read the textbook to learn what I missed in class, I absolutely could not complete the homework without first having the teacher explain it to me. I believe that my experience in Algebra I reflects poorly on this book since it's only basic algebra, not rocket science -- if a teacher can explain it orally, a textbook should be able to teach the concepts as well. The main thing that is wrong with the lessons in this book is that the examples are not always clear; several steps are often combined without directions telling the student how the book arrived at the solution. In addition to that, new lessons are often introduced with only the bare minimum of information describing how to work the problems. My Geometry book from last year went into a great deal of explanation at the beginning of each lesson in order to describe the new information; my Algebra book did not. I understood the Geometry with out my teacher's help, but I could not understand the Algebra. If a student doesn't have an excellent Algebra teacher and gets stuck with this textbook, I know that it will be very hard for him or her to learn Algebra. Also, if a homeschooled student is using this book and his or her parent is not proficient in Algebra, chances are good that the student will be completely lost. For these reasons, I advise school districts and persons attempting to learn Algebra on their own to look for a textbook that is more comprehensible than this one. Use of this textbook is far from a guarantee of success. In fact, it is only a guarantee of one thing: a very frustrating experience in learning mathematics.

Reviewed by booket, from Istanbul, Turkey
My son says: "the book seems very exciting even for me who afraids of math" This must be important! My son will start to the 6th grade this year in a Turkish school in Istanbul. We bought this book for ... and when I see the actual price at ... I got really angry!!! Who gets the extra money? The school?But I like the book.

Reviewed by Matthew Dixon, from Waipahu, HI United States
This book was one of the best that I have ever used. Has very detailed instructions and will help you through algebra I.

Reviewed by a reader, from Idaho
I have been using this book for over a semester now, and I think it's pretty good. It does have some areas in which I think it needs more explanation, but otherwise, it's great!

Review of Algebra in Easy Steps

Editorial review
The theory of generalized inverses of real or complex matrices is a well-developed and well-documented subject. However, the wider subject of generalized inverses of matrices over rings has reached a state for a comprehensive treatment only recently. The author, who contributed to this development, provides a book for students of the subject. Mathematicians working in g-inverses of matrices, algebraists and control theorists will be interested in the results presented here. The book would also be suitable for graduate courses on G-inverses in algebra.

Review of Handbook of Algebra : Volume 1

Editorial review
The first volume of a multi-volume handbook intended to provide professional mathematicians with information on topics outside their own areas. The level is graduate and up; treatment of topics is too dense for use as a textbook. Articles in seven areas are to be published as they are received--rather than in volumes covering a single area--to avoid prolonged publishing delays. In addition to primary information, reference to relevant articles, books, and lecture notes guide the reader. Indexing is detailed. Volume 1 contains papers on linear (in)dependence; fields, Galois theory, and algebraic number theory; generalizations of fields and related objects; category theory; commutative rings and algebras; associative rings and algebras; and cohomology. Annotation c. by Book News, Inc., Portland, Or.

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