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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I’ve already commented extensively on most of the standard algebra texts at my blog-you can find the relevant post here: After teaching the course again the next year, Birkhiff 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.

The most impressive thing about Rowen is how up to date it is.

Preliminary Thoughts

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. It is a good, once standard book, but there are texts that better suit the needs of modern students.

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, Algebar, and Spivak. Mac Lane was elected to the National Academy of Sciences in Instructors who have used the original edition with college classes appreciate its scope.

Students of the first type would benefit from a more challenging akgebra, whereas students of the second type would benefit from an easier one. Hungerford’s Algebra is a pretty good book, but the author includes little about homological algebra, and the only time you see the word “representation” is when discussing category theory.

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

There are still many overqualified students and many underqualified students, and I can provide a constructive proof of that fact. I think using many texts is often and in this case almost certainly a good idea. Nowhere can teachers better catch today’s spirit of mathematics. In both undergraduate courses and graduate courses students’ abilities and background are quite variable; that much has not changed in the past few decades.


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.

I love Lang, especially for things like Galois theory, but it is too hard, too fast, too big, too encyclopedic, and, dare I say, too modern for most graduate students. I agree, I do not believe Rowen is all that fitting for a standard or nearly standard course. It is a unified and comprehensive introduction to modern algebra. Yes, we did know then that research mattered for tenure, but our joy in teaching was somehow connected with our respective research.

In fact, they may be better when it comes to alyebra. The next year Mac Lane put group theory first, and set theory Boolean algebra last! They embody the elegance, precision, and generality which are the hallmark of mathematics! Email Required, but never shown. I think the text could be used for alegbra undergraduate or graduate students with decent results, but I do not think it is the best choice as a primary text.

Judson is good all around. 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.

Here care is taken algbera keep in the foreground the fundamental role played by algebra in Euclidean, affine, and projective geometry. The present edition represents a refinement of an already highly useful text. Adding in some applications may be good, too; I do not remember many being in Mac Lane.


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. Inwhen the first edition of this book appeared, the curriculum in algebra was the result of a hodge-podge accumulation.

Our book, first published 50 zlgebra ago, was intended to present this exciting new view of algebra to American undergraduate and beginning graduate students.

I think the needs of the graduate student are more complex, in a sense, than the undergraduate’s needs, because many are less obvious than in the undergraduate case. The most striking characteristic of modern algebra is the deduction of the theoretical properties of such formal systems as groups, rings, fields, and vector spaces.

Modern algebra also enables one to reinterpret the results of classical algebra, giving birkhodf far greater unity and generality. Still other arrangements are possible. This approach, which crystallized earlier insights of Cayley, Frobenius, Kronecker, and Dedekind, blossomed in Germany in the s. I doubt they’ll be able to fully appreciate the enormous generalization and unification it provides without a giant stock of examples which is why I love Emily Riehl’s Category Theory In Context as the definitive introduction to category theory for mathematics students.

I do not believe students are significantly less capable today than they were several decades ago, as you seem to suggest. This is when students should come face-to-face with having to understand universality, or else.