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. A typical first undergraduate course may cover group theory through the isomorphism theorems and the structure theorem bjrkhoff finite abelian groups,possibly including group actions and the Sylow theorems c.

The Mathemagician 2 6. We enjoyed teaching and writing algebra because it was clear, exciting, and fun to present.

Math Forum Discussions

I am hard pressed to put a single book above the others, however. Chapter VIImore field theory and linear algebra c. Young students can handle abstraction.

Potential Courses 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. Our third edition, infinally included tensor products of vector spaces, while the fourth edition clarified the treatment of Boolean algebras and lattices. 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.

Home Questions Tags Users Unanswered. 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. The ratio of definitions to theorems and exercises is kept low.

They do not avoid using universal properties, and they do not always bother to give students something concrete to hold on. Although some additions and rearrangements have been made for this edition, the content remains essentially the same [as the edition].

Preliminary Thoughts

I should probably spend some time with it again, actually. But, hey, at least there are lattices! The truth, though, is that undergraduates are fairly unlikely to read their textbook. I have come to like Gallian quite a bit since first giving it a real chance to see what my school teaches.


When I taught “modern algebra” in “Math 6” the first time, inI began with sets and ended with groups. 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. This exposition of the elements of modern algebra has been planned with great skill, and the plan has been carried through very successfully.

This book is distinguished also by the great clarity with which all details have been presented. Modern algebra also enables one to reinterpret the results of classical algebra, giving them far greater unity and generality. These responsibilities were in effect combined in our activity. The most impressive thing about Rowen is how up to date it is. This approach, which crystallized earlier insights of Cayley, Frobenius, Kronecker, and Dedekind, blossomed in Germany in the s.

The original comprehensive Survey has been reordered somewhat and augmented to the extent of approximately fifty pages. Lots of people cannot stand Lang’s writing, too.

You mention Herstein and Vinberg, which are good; Artin or Gallian also work, for example. It is a great supplementary text, however.

Certainly, one can survive it, but it is probably suboptimal for most. I am less sure what makes a really excellent graduate course in terms of extant texts. Birkhoff and Algebrw Lane’s book first appeared inand van der Waerden’s book first appeared in Interesting historical references appear in a number of places.

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 algebfa. I mentioned flaws of a few books in my answer.

In fact, they may be better when it comes to algebra. This is not to say Mac Lane and Birkhoff do this! 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. I knew how it should be done and so did Garrett. Surely, people appreciate the extant ones e.


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. Also, the mathematics department at Harvard both emphasized research and expected all faculty members to be steadily active in teaching undergraduates. Our collaboration involved some compromises. The authors are quick to indicate applications and careful to motivate and illustrate abstractions. Many algebra textbooks are so concerned about the process of learning to prove things that they communicate a sense of the subject as forbidding and stiff, dedicated to formalism and precision.

alyebra Our book, first published 50 years ago, was intended to birkhoff this exciting new view of algebra to American undergraduate and beginning graduate students. A semester course on abstract algebra could deal with Chapters, 11, 13, and Birkhoff and Mac Lane also want to teach their students to prove things, of course.

Vinberg seems similar but more intense, so I imagine it would work well, too. Garrett and I combined our preliminary notes to publish with MacMillan in our joint book, Survey of Modern Algebra. Those are perhaps worth substantial time, even if they are somewhat too odd for most courses. Anyway, let me say a bit about my thinking for how this book would work for either audience. The most important parts of each theory are included and that is all that can be asked of an introductory textbook.

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.

Although many of the basic results stem back to Kronecker, Dedekind and Steinitz, the present-day subject is largely algebr creation of the great woman mathematician, Emmy Noether.