“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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For a first year graduate course-which at Harvard,usually included a birkhocf of undergraduates-he’d use the book straight up and cover most of it. They embody the elegance, precision, and generality which are the hallmark of mathematics!

For lagebra, a semester or quarter course covering linear algebra may be based on Chaptersthe real and complex fields being emphasized. On the other hand, there should be parts where the students are discovering things or work from ideas, trying to work alvebra the formality.

I also think there should probably be more commutative algebra. I’m working on such a book myself,but for low cost texts only.

We hope that the present book will prove an adequate reference for those wishing to apply the basic concepts of modern algebra to other branches of mathematics, physics, and statistics.

We aimed to combine the abstract ideas with suitable emphasis on examples and illustrations.

The size and plan of the book preclude a comprehensive treatment of any one topic; in xlgebra, the authors are able to virkhoff something about nearly every important topic, and they usually succeed in saying the really important things.

If you are looking for strengthening your intuition, please look into Gallian’s book “Contemporary Abstract Algebra”. 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. Some of these exercises are computational, some explore further examples of the new concepts, and others give additional theoretical developments.

Moreover, it was written in a clear and enthusiastic style that conveyed to the reader an appreciation of the aesthetic character of the subject as well as its rigour and power. One of the best things about this book is the balanced approach to rigour and abstractness in relation to intuitive appreciation and concrete application. The short version is I think the book can be used for either undergraduates or graduates with some success, but I think it is less than ideal in both cases.


While I’m really enjoying the book,I’ve got a real dilemma gnawing at me. There are still many overqualified students and many underqualified students, and I can provide a constructive proof of that fact.

Rotman may be a good primary text. This book is distinguished also by the great clarity with which all details akgebra been presented. Email Required, but never shown. I think using many texts is often and in this case almost certainly a good idea.

I agree, I do agebra believe Rowen is all that fitting for a standard or nearly standard course. 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.

Those are perhaps worth substantial time, even if they are somewhat too odd for most courses. Throughout the study of matrices and quadratic forms the geometric point of view is emphasized. A wonderful and detailed response.

When I taught “modern algebra” in “Math 6” the first time, inI began with sets and ended with groups. If you want an older book written by a master expositor and mathematician, then I think Herstein works better than Mac Lane.

Survey of Modern Algebra

Sign up or log in Sign up using Google. This reviewer can testify to its appeal to students. It’s a projected book to accompany my new publishing company to instruct penniless students on low-cost mathematics sources for self study.

This is one of the primary reasons an undergraduate course ought to supplement this book. 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 birkhpff from class to class.


The authors are to be congratulated on having improved an already excellent text. But at the same time, since the book contains very little homological algebra and no representation theory beyond the definition,can it really be used as graduate course today? Probably the best way to appreciate the vitality and growth of mathematics today is to study modern algebra. Being able to handle abstraction does not mean students should not learn many concrete, basic examples, however, nor does it mean they should learn things at the most abstract possible level and be expected to figure out the less abstract consequences on their own.

It is a good, once standard book, but there are texts that better suit the needs of modern students. Note the order of the authors. Would like to hear feedback on this question. Saunders Mac Lane was the author or co-author of more than research papers and six books.

Because of it’s unorthodox structure and old fashioned style,though,I’m not sure I’d use the book birkoff a graduate course. The word “survey” in the title is quite accurate; for, although many topics are treated, none of them is really completely developed.

Preliminary Thoughts

Linear algebra is first, because students have the best intuition there; ring theory is next, because the examples and applications are nicer there than in groups and biekhoff quotient construction is easier. The present edition represents a refinement of an already highly useful text. You mention Herstein and Vinberg, which are good; Artin or Gallian also work, for example.