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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This book is distinguished also by the great clarity with which all details have been presented. Anyway, let me say a bit about my thinking for how this book would work for either audience. By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. The rejuvenation of algebra by the systematic use of the postulational method and the ideas and point of view of abstract group theory has been one of the crowning achievements of twentieth century mathematics.

Sign up or log in Sign up using Google. Linear algebra is first, because students have bjrkhoff best intuition there; ring theory is next, because the examples and applications are nicer there than in groups and the nirkhoff construction is easier.

The original comprehensive Survey has been reordered somewhat and augmented to the extent of approximately fifty pages. There are contacts with many branches of macalne and so it can serve as an introduction to nearly the whole of modern mathematics.

I had taught out of most of the extant books. Preliminary Thoughts In both undergraduate courses and graduate courses students’ abilities girkhoff background are quite variable; that much has not changed in the past few decades.

Preliminary Thoughts

In both undergraduate courses and graduate qnd students’ abilities and background are quite variable; that much has not changed in the past few decades. One of us would draft a chapter and the other would revise it. This reviewer can testify to its appeal to students. Artin 2e, not 1e is also good and emphasizes linear algebra and geometric intuition, which is good considering ane often students will need things from linear algebra and how often they will find themselves ignorant of those things.


A typical first undergraduate course may cover group theory through the isomorphism theorems and birkuoff structure theorem for finite abelian groups,possibly including group actions and the Sylow theorems c. Rotman may be a good primary text. 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 algebrq modules is a good idea, for example. 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.

Chapters 4 and 5 develop the basic algebraic properties of the real and complex fields which are of such paramount importance for geometry and physics. 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.

Supplementing this with another algsbra to get some coverage of representation theory and homological algebra is probably ideal.

The revised edition differs only in minor rearrangements and additions.

In addition the book is enlivened by striking applications of modern algebra to other branches of science and made eminently teachable by the inclusion of numerous excellent problems and exercises. Chapter IIIand some field and nirkhoff space theory c.

Modern algebra prospered mightily in the decadesfrom functional analysis to algebraic geometry – not to mention our own respective researches on lattices and on categories.

The authors express the belief that “for many students, the value of algebra lies in its algebraa to other fields: During the s, Birkhoff, along with his Harvard colleagues Marshall Stone and Saunders Mac Lane, substantially advanced American teaching and research in abstract algebra.

As Mac Lane did years ago, it is best to supplement algeebra text with something easier, something intended for undergraduates.


Math Forum Discussions

Chapter 11 includes a completely revised introduction to Boolean algebra and lattice theory. I understand from professors who were students at Harvard that MacLane himself would use the book-in all it’s versions,from the first mimeographed drafts in the early ‘s to the 3rd edition he used in his last teaching days in the mid’s-for both undergraduate and graduate courses in algebra depending on the strength of the students, which would vary enormously from class to class.

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.

It also introduces the student to modules, but it does not insist on working with modules instead of vector spaces whenever possible, which is probably good, because modules often serve to slightly confuse without adding anything more than a bit of generality.

Still other arrangements are possible. For the social scientist whose mathematical studies have reached through the calculus, this book can confidently be urged as the thing to study next.

Perhaps a lecture reviewing elementary set theoretical notions, then cover some linear algebra introducing basic category theory after seeing direct sumsthen cover some ring theory, then plenty of group theory, then modules and advanced linear algebra, followed by field and Galois theory, representation theory using algebras and specializing quickly to groupscommutative algebra including some applications to algebraic geometry and the likeand finally homological algebra, with some advanced or extra topics at the end, if possible e.