Preface. Birkhoff & Mac Lane’s Algebra is a brilliant book. I should probably spend some time with it again, actually. Also, I apologize for such a. In Garrett Birkhoff and Saunders Mac Lane published A Survey of Modern Algebra. The book became a classic undergraduate text. Below we examine a. Garrett BirkhoffHarvard University Saunders Mac Lane The University of Chicago A SURVEY OF ern fourth.

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Adding in some applications may be good, too; I do not remember many being in Mac Lane. This independence is intended to make the book useful not only for a full-year course, assuming only high-school algebra, but also for various shorter courses. Moreover, it was written in a clear and enthusiastic style that conveyed to the reader an appreciation of the aesthetic character of the subject as well as its rigour and power.

I would certainly place it in the hands of an interested undergraduate wondering what algebra was all about, particularly one who had already taken linear algebra.

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. Again, ajd the agebra should be given this stuff to them. I have come to like Gallian quite a bit since first giving it algevra real chance to see what my school teaches. Interesting historical references appear in a number of places. His paper, “On the Structure of Abstract Algebras” founded a new branch of mathematics, universal algebra.

This approach, which crystallized earlier insights of Cayley, Frobenius, Kronecker, and Dedekind, blossomed in Germany in the s. Sign up using Facebook. A semester course on abstract algebra could deal with Chapters, 11, 13, and Saunders Mac Lane was the author or co-author of more than research papers and six books. Our Survey in presented an exciting mix of classical and conceptual ideas about algebra. We also hope it will give a solid introduction to this fascinating and rapidly growing subject, to those students interested in modern algebra for its own sake.

Our third edition, infinally included tensor products of vector spaces, while the fourth edition clarified the treatment of Boolean algebras and lattices. Although two or three biekhoff on the new algebra have already appeared in English, the present volume appears to the reviewer to be the best all-round introduction to the subject, unique in its clarity, balance, generality and inclusiveness.

Nowhere birkhofv teachers better catch today’s spirit of mathematics. I had taught algebra courses at Harvard when I was an instructor, and at Cornell I taught algebra out of the book by Bocher; at Chicago, out of a book, ‘Modern Higher Algebra’ by Albert; and at Harvard again out of my own notes.

Accordingly, we have tried throughout to express the conceptual background of the various definitions used. Or, maybe you have a truly prodigious bunch who have all seen algebra before or who are as mature as most incoming graduate students at good algebrw, in which case following the text more closely ough to work without much issue.

Yet, I also think a course should start with basic material. Adopting this as the main textbook for an undergraduate abstract algebra course would today be an eccentric move.

### A survey of modern algebra / by Garrett Birkhoff and Saunders MacLane – Details – Trove

I don’t think hitting students with category theory unless they’ve already had considerable exposure to algebra is a good idea. I do not believe students are significantly less capable today than they were several decades ago, as you seem to suggest. At both the graduate and undergraduate level, it seems there are books that are better in parts or in whole.

But the authors’ delight in what was then a new subject shines through their writing, and their willingness to be informal when necessary was a smart move. I also think there should probably be more commutative algebra. If you alter the presentation for your lectures to skew more toward examples and concrete proofs, ideally while still discussing the more abstract stuff a bit, then I think this book can work well.

Also, your review page is quite comprehensive! We hope that the present book will prove an adequate reference for those wishing to apply the basic concepts of modern algebra to other branches of mathematics, physics, and statistics. Post as a guest Name. Birkhpff Lane had had much more teaching experience than I, and I think the popularity of our book owes more to him than to me. Being able to handle abstraction does not mean students should not learn many concrete, basic examples, however, nor does it ad they should learn things at the most abstract possible level and be expected to figure out the less abstract consequences on their own.

Chapter IIIand some field and vector space theory c. Finally, the last three chapters provide an introduction to general commutative algebra and arithmetic: We aimed to combine the abstract ideas with suitable emphasis on examples and illustrations. Would like to hear feedback on this question. Our book, first published 50 years ago, was intended to present this exciting new view of algebra to American undergraduate and beginning graduate students.

Modern algebra also enables one to reinterpret the results of classical algebra, giving them far greater unity and generality. I’m working on such a book myself,but for low cost texts only. Some combination of the approaches of the above books ought to make an excellent undergraduate course.

I am joking, if it is not clear.

### Survey of Modern Algebra

I think such a book would have found a massive audience and I’d encourage ANYONE working on such a book to birkhof as we’d then have many different opinions for students and professionals on standard works.

It provided a synthesis formerly obtainable only after much more advanced work. A second course may cover a bit more group theory c.

Dual spaces and tensor products are also discussed, macalne generalizations to modules over rings are not considered. While I’m really enjoying the book,I’ve got a real dilemma gnawing at me. The selection of exercises is sufficient to allow an instructor to adapt the text to students of quite varied degrees of maturity, of undergraduate or first year graduate level.

This book also does not match a clear unorthodox vision of how the subject should be taught, unlike, say, Aluffi or Adkins.

## Preliminary Thoughts

There are contacts with many branches of mathematics and so it can serve as an introduction to nearly the whole of modern mathematics. Rotman’s Advanced Modern Algebra is pretty light on the Galois theory but he gets points for having a chapter on algebras. This book is distinguished by its procedure from the concrete to the abstract. A ‘Survey of Modern Algebra’ made it possible to teach an undergraduate course that reflected the richness, vigour, and unity of the subject as it is growing today.

This is followed in Chapter 12 by a brief discussion of transfinite numbers.