“Algebra” by MacLane and Birkhoff was the first abstract algebra book I bought and I loved it! It wasn’t the first abstract algebra book I read. This book presents modern algebra from first principles and is accessible to undergraduates or graduates. It combines standard materials and necessary. Documents Similar To Saunders Mac Lane, Garret Birkhoff Algebra Mathematics Form and Function. Uploaded by. jacinto [Charles C. Pinter] a Book.

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He returned to Harvard inthe year after I had given a course in modern algebra aalgebra the undergraduate level for the first time. Vinberg seems similar but more intense, so I imagine it would work well, too.

Artin 2e, not 1e is also good and emphasizes linear algebra and geometric intuition, which is good considering how often students will need things from linear algebra and how often they will find themselves ignorant of those things. As Mac Lane did years ago, it is best to supplement the text with something easier, something intended for undergraduates.

Similarly, books like Cohn, Grillet, and Jacobson can be too algrbra or too focused on being references.

Logic suggests the standard groups, rings, birhkoff, modules, vector spaces, etc. Those are perhaps worth substantial time, even if they are somewhat too odd for most courses.

Mathematics Stack Exchange works best with JavaScript enabled. Bkrkhoff desiring a text replete with possibilities for courses tailored to various kinds of students should welcome this new edition. I’m going to soon review the 3rd edition of Saunders MacLane And Garrett Birkoff’s Algebra at my blog soon and this is the first time I’m really carefully reading it.


This is a text on modern algebra that is particularly suited for a first year graduate course or for an advanced undergraduate course. Chapter Burkhoffand some field and vector space theory c.

The authors are to be congratulated on having improved an already excellent text. It provided a synthesis formerly obtainable only after much more advanced work.

This well-known textbook has served, in the last twelve years, to introduce a great many students to the fundamental concepts of modern algebra in an extraordinarily effective way. A wonderful and detailed response. The idea is to a. Because of it’s unorthodox structure and old fashioned style,though,I’m not sure I’d use the book for a alfebra course.

Survey of Modern Algebra

The word “survey” in the title is quite accurate; for, although many topics are treated, none of them is really completely developed. Familiar examples are carefully presented to illustrate each new term or idea which is introduced. The lecture ought to focus on the main ideas, examples, and results, and the book ought to clearly show what is important, very important, etc. Supplementing this with another book to get some coverage of macllane theory and homological algebra is probably ideal.

The Mathemagician 2 6. These theorems are then applied to some familiar and to some less familiar examples, thus broadening the student’s viewpoint without getting him lost in abstractions. In preparing the revised edition we have added several important topics equations of alfebra type, dual spaces, the projective group, the Jordan and rational canonical forms for matrices, etc.

I often found it dry, too.

The revised edition differs only in minor rearrangements and additions. The authors are quick to indicate applications and careful to motivate birkhoft illustrate abstractions.


Math Forum Discussions

I think the text could be used for either undergraduate or graduate students with decent results, but I do not think it is the best choice as a primary text. I had taught out algdbra most of the extant books. Indeed, I find his writing quite agreeable. It does this by discussing examples of mathematical systems or situations already partially familiar to the student, isolating important properties of these as postulates, and deducing some of the consequences of these postulates.

Preliminary Thoughts

This book also does not match a clear unorthodox vision of alyebra the subject should be taught, unlike, say, Aluffi or Adkins. Although my course was well attended, I was much more research-oriented than teaching-oriented.

I think too much about algebra mxclane and textbooks. Only in this way will they be able to appreciate the full richness of the subject. This is followed in Chapter 12 by a brief discussion of transfinite numbers.

I think such a book would have found a massive audience and I’d encourage ANYONE working on such a book to continue as we’d then have many different opinions for students and professionals on standard works. In we prepared nirkhoff carefully polished second edition, in which polynomials over general fields were treated before specializing to the real field.