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Review of Algebra
Reviewed by gh-bigfoot, from Oregon,
USA
My first taste of algebra came from Lang's book (big mistake).
I then read Gallian's undergrad. book and tried Lang again,
it was still very difficult. I finally found Grove. This is
a great book. Very easy to read and understand. Although it
doesn't cover everything in Lang, it covers everything that
commonly comes up in a first year graduate class. The book's
only drawback is it's difficulty to find. If you're looking
for a good intro. to algebra text (and if you can find it) buy
it!
Reviewed by Todd Ebert, from Irvine,
Ca United States
This is one of my favorite beginning graduate texts. Although
it follows a very terse definition-example-theorem-proof style,
the proofs and examples seem very enlightening. Each Chapter
comeswith numerous exercises interleaved with the material,
as well asexercises at the end of the chapter. Groups, rings,
fields, and modules are covered in depth.
Review of Tae Algebra I
Editorial review
An abridged edition of the author's previous two-volume work,
Ring theory, which concentrates on essential material for a
general ring theory course while omitting much of the material
intended for ring theory specialists. Annotation copyright Book
News, Inc. Portland, Or.
Review of Algebra
Editorial review
This introduction to modern algebra emphasizes concrete mathematics
and features a strong linear algebra approach.
Reviewed by mikeu3, from Berkeley, CA,
USA
Pretty much any introductory abstract algebra book on the market
does a perfectly competent job of introducing the basic definitions
and proving the basic theorems that any math student has to
know. Artin's book is no exception, and I find his writing style
to be very appropriate for this purpose. What sets this book
apart is its treatment of topics beyond the basics--things like
matrix groups and group representations. I suppose many introductory
books shy away from much of the material on matrix groups in
Artin's book because it involves a little analysis (and likewise
for the section on Riemann surfaces in the chapter on field
theory). However, Artin correctly realizes that a reasonably
mathematically mature student--even one who doesn't know much
analysis--will be able to profit from and enjoy the relatively
informal treatments he gives these slightly more advanced topics.
Of course these topics can also be found in graduate-level texts,
but I for one would much rather be introduced to them via an
example-based approach such as that in Artin than through the
diagram-chasing obscurantism in more advanced books. I happened
upon this book a little late--in fact, only after I'd taken
a semester of graduate-level algebra and already felt like analysis
was the path I wanted to take--but I'm beginning to think I
would have been more keen on going into algebra if I'd first
learned it from a book like this one.
Reviewed by a reader, from Cambridge,
MA
This is the best undergraduate algebra text I've encountered.
It is written for students who are already fairly mathematically
mature. Artin's proofs contain just the right amount of detail
and the book rewards careful and attentive reading. Many people
are put off by the emphasis on linear groups and linear algebra.
But I think Artin's choice is the correct one. Students get
to use the tools of algebra on nontrivial groups from the very
beginning (for instance, the orbit-stabilizer theorem on SL_2(F_p)).
The exposition is beautiful and the exercises are both challenging
and interesting. Special points include Artin's inclusion of
a chapter on the classical linear groups and a brief introduction
to both Lie groups and a smattering of algebraic geometry.
Reviewed by wang@math.sc.edu, from COLUMBIA,
SC United States
I believe that the guys who favor this text book are those who
read group theorems only. As one of the best student, I have
to say, I believe you will encounter unbearable difficulties
if you read Ring and Field parts. I must read everything from
any other text book to understand clearly what Artin is saying
in his book. can you believe it? Few definition is described
clearly, few theorem is proved in a logic-clear, easy-to-undersatnd
way. The most important is that many useful properties of Ring
, field are not included in his book, but in the problems you
have to find all these totally by yourself in order to solve
the problems. Also, the textbook is NOT well- orginized. A typical
exmaple, Artin has not yet tell the reader basic informations
and properties of Ring Of Polynomial in one variable , but he
starts to describe the structure of Ring Of Polynomial in 2
or more variables. The reader's minds would be completely mixed
up if he doesn't not have an extremely high IQ. I believe ,
your knowlege of Ring and Filed will be very limited and very
unclear if you use Artin's book only. Abstract Algebra is a
hard topic. You should not use a book which is definitely not
a help for you but rather a trouble for you!!!. I hate this
book!!. Artin may be a famous mathematician, but he is not a
good educator. He doesn't not know to teach students in a good
manner.
Reviewed by nootropic@hotmail.com, from
a beautiful island
I don't like this book because it doesn't follow a clear definition/theorem/proof
format, like Rudin's Principles of Mathematical Analysis. In
Artin's efforts to clarify he actually ends up confusing. The
definitions and even some important concepts are haphazardly
introduced in a "conversational" style, in the middle
of long paragraphs (what are paragraphs doing in a math book?).
These "explanatory" paragraphs are meant to clarify
and add meaning, but although this style might sound helpful
it actually gets in your way and makes learning much, much harder
and more confusing. On the other hand, Rudin gets right to the
point, he formalizes and crystallizes everything, he presents
no pictures (and therefore forces you to make your own), he's
not your friend, and in fact helps you learn better than Artin.
There are plentiful examples, but Artin's obsession with the
rotation groups gets quite annoying; even if you're not interested
in the rotation groups, you have to study them in-depth in the
earlier chapters so that you can understand all the later examples,
many of which refer back to these (e.g., the examples in the
Group Representation chapter are almost entirely dependent on
the tetrahedral group!). The examples in a high-level introductory
book should be like those in Rudin's, throwing light on historically
and theoretically important problems.The exercises can range
from hard and interesting to routine, with a pleasantly surprising
number of the former. But Artin also seems to be obsessed with
linear algebra and rotation groups; this can be frustrating.
Also, some problems are just computationally hard--a consequence
of the linear algebra fetish; there shouldn't be so many computational,
almost-routine problems in a rigorous book.(To those who don't
know Rudin--I don't think he ever wrote an algebra text; I was
only comparing presentation styles. Rudin does analysis.)
Review of Intermediate Algebra for College Students (3rd Edition)
Editorial review
This textbook for a one-semester course in intermediate algebra
covers functions, systems of linear equations, polynomial factoring,
rational expressions, radical exponents, quadratic equations,
logarithms, conic sections, sequences, and series. The second
edition has been rewritten to make it more accessible, and adds
a separate chapter on inequalities.Book News, Inc.®, Portland,
OR
Reviewed by a reader, from Hollywood
CA
Blitzers' step by step is very helpful but does not always use
the best path to the solution. He could use more examples of
different types of the same problem, ie. What occurs when using
negetives on this problem? Great book, but with anything, could
be better.
Review of Intermediate Algebra (4th Edition)
Editorial review
Progresses from linear equations and polynomials through to
quadratic equations and exponential functions. Bright colors
and countless graphics will keep even nodding-off students up
to speed. The new edition focuses on real world math problems
and includes practice problems with solutions, application problems,
and chapter summaries presented in chart form. Book News, Inc.®,
Portland, OR --This text refers to the Paperback edition.
Reviewed by Theresa Froehlich, from Lynnwood,
WA
I am a mother who didn't do well in Algebra in high school.
I am now having to help my 8th grade daughter with her Algebra.
Having used Tobey & Slater's Basic College Math and Beginning
Algebra (whenever her textbook doesn't make sense to me or to
her), I am exceedingly impressed with their exceptional ability
to explain clearly yet simply the mathmatical concepts. My experience
with these books gave me the confidence to buy their Intermediate
Algebra (4th Edition 2002). This updated edition provides clear
explanations that make sense to someone who is not a math whiz.
It includes not only exercises, but also practice problems,
real-life applications, cumulative reviews, and writing exercises
to teach students to translate numbers into words. It is a very
comprehensive approach to empower the student to not just grasp
the concept but also to retain it.
Reviewed by a reader, from Somerville,
New Jersey USA
This textbook is extremely frustrating for the novice, who,
after all,will be using it! It omits critical steps in its examples,
and leaves the user confused. It is very difficult to succeed
in class with this book as a resource. I am online to purchase
a book which has a comprehensive format, to get me through the
course I'm taking!
Review of Introductory and Intermediate Algebra
Editorial review
Provides readers with a strong foundation in Algebra. Designed
to develop readers' critical thinking and problem-solving capabilities
and prepare readers for subsequent Algebra courses as well as
service math courses. Softcover.
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