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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 graduatelevel 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 oneyear course in algebra at the graduate level, or as
a useful reference for mathematicians and professionals who
use higherlevel 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 ghbigfoot, 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 userfriendly: 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 PreAlgebra: 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 welldeveloped and welldocumented 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
ginverses of matrices, algebraists and control theorists will
be interested in the results presented here. The book would
also be suitable for graduate courses on Ginverses in algebra.
Review of Handbook of Algebra : Volume 1
Editorial review
The first volume of a multivolume 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 receivedrather than
in volumes covering a single areato 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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