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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There are contacts with many branches of mathematics and so it can serve as an alebra to nearly the whole of modern mathematics. The present edition represents a refinement of an already highly useful text. I quite like Etingof’s Introduction to representation theorywhich is available at his sitebut it maclne two chapters before it gets to the case of finite groups, which is usually what algebra professors focus on in a first graduate course. Some people mistakenly believe they cannot.

One of us would draft a chapter and the other would revise it.

But there is no dearth of good reference works in algebra, and in the reviewer’s opinion the present textbook will prove more useful than another encyclopedic treatise would have been. Garrett Birkhoff published more than papers and supervised more than 50 Ph.

Also,the author writes very well indeed. Wnd do not define a group as a groupoid with one object, at least not in an introductory course. Chapter VIImore field theory and linear algebra c. It is also worth noting Mac Lane does cover multilinear algebra pretty well, which is frequently forgotten. I think taking parts from Rotman’s An Introduction to Homological Algebra birkhff work in a similar vein, albeit with much more cutting. The idea is to birkhogf.

Certainly, one can survive it, but it is probably suboptimal for most. I am hard pressed to put a single book above the others, however. Rowen has been talked about a good bit, which is deserving for its extensive presentation on algebras and many applications, but I am not sure starting with modules is a good idea, for example.

Also, your review page is quite comprehensive! Garrett and I combined our preliminary notes to publish with MacMillan in our joint book, Survey of Modern Algebra. Thus there is a careful development of real numbers, such as Dedekind cuts, and such set-theoretic concepts as order, countability and cardinal number are discussed. We have also tried not to lose sight of the fact that, for many students, the value of algebra lies in its applications to other fields: Supplementing this with another book to get some coverage of representation theory and homological algebra is probably ideal.


Some material, especially that on linear algebra, has been rearranged in the light of experience.

Algebra – Saunders Mac Lane, Garrett Birkhoff – Google Books

There are other fairly popular graduate algebra texts that do not cover all the presumed topics, however. I had taught out of most of the extant books. Chapters 4 and 5 develop the basic algebraic properties of the bidkhoff and complex fields which are of such paramount importance for geometry and physics. Yet, I also think a course should start with basic material. Anr Your Answer Discard By clicking “Post Your Answer”, you acknowledge that you have read our updated terms of serviceprivacy policy and cookie policyand that your continued use of the website is subject to these policies.

They do not avoid using universal properties, and they do not always bother to give students something concrete to hold on. After teaching the course again the next year, I suggested that we co-author a book, usable by our colleagues, so that we wouldn’t have to alternate teaching it forever, and he agreed. Indeed, I find his writing quite agreeable. A section on bilinear forms and tensor products has been added alegbra the chapter 7 on vector spaces, while Chapter 11, now entitled “Boolean algebras and lattices”, birkhoft a new introduction to Boolean algebras, as aand as a section on the representation of such by sets.

Then the abstract definition appears simple, and the theoretical properties which are deduced from the definition exhibit the power of the concept.

Anyway, let me say a bit about my thinking for how this book would work for either audience. I am joking, if it is not clear.

Preliminary Thoughts

Theoretically, less-prepared students and more-prepared students would not only survive but also get from this something substantial. Also, I apologize for such a long response.

Terminology and notation which has become outmoded since the Revised Edition was published in have been brought up-to-date; material on Boolean algebra and lattices has been completely rewritten; an introduction to tensor products has been added; numerous problems have been replaced and many new ones added; and throughout the book are hundreds of minor revisions to keep the work in the forefront of modern algebra literature and pedagogy.

Maclae algebra textbooks are so concerned about the process of learning to prove things mqclane they communicate a sense of the subject as forbidding and stiff, dedicated to formalism and precision.

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I think such a book aogebra 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 nad professionals on standard works.

Getting across the rich motivation, ideas, analogies, history, and so forth should be an explicit goal, but it will not always be possible. I’ve already commented extensively on most of the standard algebra texts at my blog-you alhebra find the relevant post here: On the other hand, calculus has been pushed into high school, and introductory courses are substantially easier and less rigorous than in the days of Apostol, Courant, and Spivak.

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.

Only the last five chapters remain unchanged. Algebra was birhoff unheard of at the undergraduate level not too long ago, whereas now an undergraduate program would be remiss not to require students take at least an introductory course covering the basic theories of groups, rings, and fields. When I taught “modern algebra” in “Math 6” the first time, inI began with sets and ended with groups.

Vinberg seems similar but more intense, so I imagine it would work well, too. Young students can handle abstraction. There are still many overqualified students and many underqualified students, and I can provide a constructive proof of that fact. I should probably spend some time with it again, actually. maclahe

For undergraduates, we obviously need to ensure they see examples, learn the basic theory, be able to write proofs, etc. Sign up using Facebook.

Our collaboration involved some compromises. But they want to teach them algebra even more. The authors are to be congratulated on having improved an already excellent text.

A semester course on abstract algebra could deal with Chapters, abd, 13, and Although not enough to reconcile this problem, their exposition on categorical notions is quite clear, at least, albeit maybe not as good as some treatments that have since come.