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“Algebra” by MacLane and Birkhoff was the first abstract algebra book I bought and I loved it! It wasn’t the first abstract algebra book I read. This book presents modern algebra from first principles and is accessible to undergraduates or graduates. It combines standard materials and necessary. Documents Similar To Saunders Mac Lane, Garret Birkhoff Algebra Mathematics Form and Function. Uploaded by. jacinto [Charles C. Pinter] a Book.

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Note the order of the authors. A very striking feature of the book is its broad point of view. 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. Sign up using Agebra. Dummit and Foote is great for group theory, but it suffers in other parts and may also too big and encyclopedic.

I think these principles in lecture and text, along with hard work by the students, lots of student-student communication including some forced working togethersome student-professor communication including some forced communication, e.

This has maclwne us in our emphasis on the real and complex fields, on groups of transformations as contrasted with abstract groups, on symmetric matrices and reduction to diagonal form, on the classification of quadratic forms under the orthogonal and Euclidean groups, and finally, in the inclusion of Boolean algebra, lattice theory, and transfinite numbers, all of which are important in mathematical logic and in the modern theory of real functions.

I have however tried to read many algebra books. Our book, first published 50 years ago, was intended to present this exciting new view of algebra to American undergraduate and beginning graduate students.

The most important parts of each theory are included and that is all that can be asked of an introductory textbook. While I’m really enjoying the book,I’ve got a real dilemma gnawing at me. Familiar birkhpff are carefully presented to illustrate each new term or idea which is introduced.

Both are excellent books I have called this book Advanced Modern Algebra in homage to thembut times have changed since their first appearance: Chapters give an introduction to the theory of linear and polynomial equations in commutative rings. In this book Professors Birkhoff and Mac Lane have made an important contribution to the pedagogy of algebra. Certainly, algebraists expect everyone has seen some homological algebra and representation theory by the time they get their Ph.


This exposition of the elements of modern algebra has been planned with great skill, and the plan has been carried through very successfully. Artin 2e, not 1e is also good and emphasizes linear algebra and geometric intuition, which is good considering how often students will need things from linear algebra and how often they will find themselves ignorant of those things.

It is unlikely you will cover the entire book, either, even in a one year course. Of course, the book came partly from England through Garrett, who had been influenced by Philip Hall when he worked with him at Cambridge England.

Math Forum Discussions

Rotman may be a good primary text. I recommend “Algebra” for self study at your leisure. Only the last five chapters remain unchanged. Would it be a good introduction to the subject? I do not believe students are significantly less capable today than they were several decades ago, as you seem to suggest.

Only in this way will they be able maclahe appreciate the full richness of the subject. Vinberg seems similar but more intense, so I imagine it would work well, too.

Although not enough to reconcile this problem, their exposition on categorical notions is quite clear, at least, albeit maybe not as good birkhof some treatments that have since come. Maximum generality entailing sophisticated machinery can seem efficient in the abstract, but it rarely works so well in practice. For over twenty years this text has been the “classic” work in its field.

Nevertheless, it is still a book well worth reading. 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.

Maclanr reviewer can testify to its appeal to students. There should also be specific portions of book and lecture that are intentionally plain, definition-theorem-proof type things, but where all the richness is introduced later down the line, as maxlane not snub the students.


Those are perhaps worth substantial time, even if they are somewhat too odd for most courses. Their emphasis is on the methods and spirit of modern algebra rather than on the subject matter for itself.

Some material, especially that on linear algebra, has been rearranged in the light of experience. Birkhoff and Mac Lane’s book first appeared inand van der Waerden’s book first appeared in I once began writing a massive annotated bibliography of basic mathematics through birkhofg graduate workbut after spending ten pages on algebra texts, I gave up on the project. The classical algebra is nicely embedded in this structure, as are also applications to other fields of thought.

Although two or three books 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.

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

Similarly, books like Cohn, Grillet, and Jacobson can be too advanced or too focused on being references. He had been doing the same maclahe. Some people mistakenly believe they cannot. It wasn’t the first abstract algebra book I read, though, but it probably was the first book that I read carefully.

He returned to Harvard inalgsbra year after I had given a course in modern algebra on the undergraduate level for the first time.

Preliminary Thoughts

Our third edition, infinally included tensor products of vector spaces, while the fourth edition clarified the treatment of Boolean algebras and lattices. To develop the student’s maclabe to think for himself in terms of the new concepts, we have included a wide variety of exercises on each topic. Both are excellent in theory and have a good collection of problems.

Certainly, algerba can survive it, but it is probably suboptimal for most.