Buy New
$64.53
Qty:1
  • List Price: $79.95
  • Save: $15.42 (19%)
In Stock.
Ships from and sold by Amazon.com.
Gift-wrap available.
Algebra (Graduate Texts i... has been added to your Cart
Trade in your item
Get a $28.50
Gift Card.
Have one to sell? Sell on Amazon
Flip to back Flip to front
Listen Playing... Paused   You're listening to a sample of the Audible audio edition.
Learn more
See all 2 images

Algebra (Graduate Texts in Mathematics) Hardcover – September 19, 2005

ISBN-13: 978-0387953854 ISBN-10: 038795385X Edition: 3rd

Buy New
Price: $64.53
34 New from $59.88 24 Used from $50.00
Amazon Price New from Used from
Hardcover
"Please retry"
$64.53
$59.88 $50.00
Free%20Two-Day%20Shipping%20for%20College%20Students%20with%20Amazon%20Student

$64.53 FREE Shipping. In Stock. Ships from and sold by Amazon.com. Gift-wrap available.

Frequently Bought Together

Algebra (Graduate Texts in Mathematics) + Abstract Algebra, 3rd Edition + Algebraic Topology
Price for all three: $206.80

Buy the selected items together

Customers Who Bought This Item Also Bought

NO_CONTENT_IN_FEATURE

Up to 50% Off Select Medical Titles
For a limited time, enjoy special savings on select medical books from Springer. Learn more

Product Details

  • Series: Graduate Texts in Mathematics (Book 211)
  • Hardcover: 917 pages
  • Publisher: Springer; 3rd edition (September 19, 2005)
  • Language: English
  • ISBN-10: 038795385X
  • ISBN-13: 978-0387953854
  • Product Dimensions: 9.3 x 6.5 x 2.3 inches
  • Shipping Weight: 3.2 pounds (View shipping rates and policies)
  • Average Customer Review: 4.0 out of 5 stars  See all reviews (19 customer reviews)
  • Amazon Best Sellers Rank: #97,748 in Books (See Top 100 in Books)

Editorial Reviews

Review

S. Lang

Algebra

"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

From the reviews of the third edition:

"The current third edition has grown again … dealing with topics close to the author’s heart from number theory, function theory and algebraic geometry. For the math graduate who wants to broaden his education this is an excellent account; apart from standard topics it picks out many items from other fields … . This makes it a fascinating book to read … . a very readable treatment of many modern mainline topics as well as some interesting out-of-the-way items." (Paul M. Cohn, Zentralblatt MATH, Vol. 984, 2003)

"Lang’s Algebra … has gained an iconic status, due both to the comprehensiveness of its coverage and its ability to be authoritative and lively at the same time. … a revolutionary work, changing the way in which graduate algebra was taught. … the author describes the book as ‘very stable’, indicating that there is little that he has wished to change. This confidence is reflected in the wider mathematical community, and ... this new printing deserves a place in every university departmental library." (Gerry Leversha, The Mathematical Gazette, Vol. 87 (509), 2003)

From the Back Cover

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.

Comments on Serge Lang's Algebra:
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.
April 1999 Notices of the AMS, announcing that the author was awarded the Leroy P. Steele Prize for Mathematical Exposition for his many mathematics books.

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.
MathSciNet's review of the first edition

Customer Reviews

This is among the finest references for Algebra I have ever seen.
GaloisGuy
I found this to be a problem in Galois theory in particular, where Lang's exposition is completely clear and easy to understand, but seemingly pointless.
Cloudy Skies
This is one of those books that becomes a must-read once have already read 25 or so other serious math books.
Alexander C. Zorach

Most Helpful Customer Reviews

95 of 100 people found the following review helpful By mathwonk on April 4, 2006
Format: Hardcover
As others have said, this is not a book to begin learning algebra, but is a necessary book for most students to have on their shelves. Why is that? Basic topics are discussed from scratch in this book from the most advanced possible viewpoint. Hence few can learn them here for the first time, but no one can graduate to professional status without eventually arriving at this perspective.

In particular the categorical point of view is simply essential to a research mathematician to acquire at some point, and Lang uses it here from the beginning, while Dummitt and Foote place it in appendix II, after page 800. So Lang's goal seems not to introduce basic algebra, but to provide essential algebraic facts not found elsewhere, and to give them all from a professional's perspective.

This is probably a third book on algebra in today's world, and that is assuming the student is pretty good. The only current book I know of out there that is really aimed at students and also written by a top professional is Artin. If you can, begin with Artin, then read Dummitt and Foote for topics Artin omits, then read Lang to see how you should view the same material and find things Dummitt and Foote left out.

Then you are ready to do research with these tools. For instance one of our research professors tells his students the prerecquisite for working in algebraic number theory is to become comfortable with algebra at the level of Lang. But our course in PhD prelim preparation for algebra will probably use Dummitt and Foote, just because it is a more feasible book for the students to read at that stage. Attempts to use Lang in trhe past have been disastrous.
Read more ›
Comment Was this review helpful to you? Yes No Sending feedback...
Thank you for your feedback. If this review is inappropriate, please let us know.
Sorry, we failed to record your vote. Please try again
58 of 63 people found the following review helpful By Jason Schorn on July 24, 2003
Format: Hardcover
I must concur with my fellow readers that in fact Langs Algebra text is extremely dry, the examples are sparse (as compared with, say, Hungerfords Graduate text), readers are left to fill in the gaps which exist within the majority of proofs and, finally, about the exercises; for the most part the exercises abound, they are challenging, non-trivial and in general are extensions of the material, which for whatever reason, have been relegated to the status of mere exercise. But for those who have a 'Solid' foundation in Algebra, preferably at the level of a Junior-Senior undergraduate who has completed courses in Linear Algebra, Modern/Abstract Algebra, then this text is worth its weight in gold. For those individuals who have either chosen to make Mathematics their career or those who are Mathematically gifted, a text of this stature must be appreciated for exactly those reasons I used to 'negatively' criticize this text. For example, when doing research at any level above that of advanced undergraduate, the researcher should have the confidence, temperance, skill and desire to fill in missing gaps within proofs since the ability to do so is an excellent gauge of how well one actually understands the given material. It would seem to logically follow from this that the researcher would then benefit from choosing a text that contained exercises, which were not trivial calculations or the requirement of proving somthing that is either routine or standard. Instead, major rewards, in the form of confidence and a deeper understanding, are a result of struggling through difficult problems and, in general, problems which lead you toward self-discovery, i.e. those which are extensions of the given material. For these reasons I highly recommend this text to all members of the Mathematical community who desire more bang for their buck since this will serve them well, both as a text for further study and as a lifelong reference.
Comment Was this review helpful to you? Yes No Sending feedback...
Thank you for your feedback. If this review is inappropriate, please let us know.
Sorry, we failed to record your vote. Please try again
41 of 47 people found the following review helpful By A Customer on November 12, 2003
Format: Hardcover
Lang's algebra book is one of the best algebra books available today. I agree with what most other readers have said. Namely, this shouldn't be your first foray into the subject, the proofs are often terse and take a good amount of time to absorb and there is a conspicuous lack/obscurity of examples. To cite an example, he gives a non-singular projective group variety as an example of a certain group. I shall not give an example of a terse proof. Let's just say that it suffices to note that whenever he says something is 'obvious', the non-expert reader should be prepared to scribble on 4-5 sheets of paper if she wishes to understand why it's 'obvious'.
The core matter (groups, rings, fields, modules) is the same as that you'd find in any other book. As far as topics are concerned, there are just too many fascinating topics in Algebra to cover in one book - even in one like Lang. He covers a fairly wide assortment of topics though. For instance, he covers most of the commutative algebra one would find in Atiyah-Macdonald. He also has a chapter and half on Algebraic Geometry which provides a good preparation for a treatment of schemes like that in Hartshorne Chapter 2,3. His section on Galois theory is detailed and even gets into Galois Cohomology. His chapter on Valuations gets into the theory of Local Fields, but only just. The chapters on multilinear algebra and representation theory are fairly detailed. I talk about the section on Homological Algebra later.
Regarding category theory, Lang likes to phrase his definitions in the language of category theory for a reason. It's much much better this way. Category theory is an elegant way of describing some commonly occuring themes in Mathematics, particularly algebra.
Read more ›
2 Comments Was this review helpful to you? Yes No Sending feedback...
Thank you for your feedback. If this review is inappropriate, please let us know.
Sorry, we failed to record your vote. Please try again

Most Recent Customer Reviews


What Other Items Do Customers Buy After Viewing This Item?