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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We had the good fortune to write a book on the subject at the right time.

Preliminary Thoughts

Sign up or log in Sign up using Google. I had taught algebra courses at Harvard when I was an instructor, and at Cornell I taught algebra out of the book by Mqclane at Chicago, out of a book, ‘Modern Higher Algebra’ by Albert; and at Harvard again out of my own notes. I do not believe students are significantly less capable today than they were several decades ago, as you seem to suggest.

Sign up using Email and Password. These theorems are then applied to some familiar and to some less familiar aalgebra, thus broadening the student’s viewpoint without getting him lost in abstractions. 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.

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

It is also worth noting Mac Lane does cover multilinear algebra pretty well, which is frequently forgotten. Although some additions and rearrangements have been made for this edition, the content remains essentially the same [as the edition].

A second course may cover a bit more group theory c. On the other hand, there should be parts where the students are discovering things or work from ideas, trying to work out the formality. Maximum generality entailing sophisticated machinery can seem efficient in the abstract, algbra it rarely works so well in practice. Developing the ability to take some vague notion and work out the details is key to graduate education.

Other more minor changes and additions helped to increase its popularity, with annual sales in the range 14, He spent most of his career as a professor of mathematics at Harvard University. Home Questions Tags Users Unanswered. I mentioned flaws of a few books in my answer. Terminology and notation which has become outmoded since the Revised Edition was published in have been brought up-to-date; material algebfa 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.


There are today major directions that either algebga not exist over 60 years ago, or that were not then recognized to be so important. In fact, I think this book works better as the supplement.

Garrett and I combined our preliminary notes to publish with MacMillan in our joint book, Survey of Modern Algebra. Here care is taken to keep in the foreground the fundamental role played by algebra in Euclidean, affine, and projective geometry.

The Basic Graduate Year includes some good applications to algebraic geometry and algebraic number theory, for example. But they want to teach them algebra even more.

His paper, “On the Structure of Abstract Algebras” founded a new branch of mathematics, universal algebra. This book is distinguished by its procedure from the concrete to the abstract. 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. The idea is to a. If you want an older book written by a master expositor and mathematician, then I think Herstein works better than Mac Lane.

Algebra – Saunders Mac Lane, Garrett Birkhoff – Google Books

It does this by discussing examples of mathematical systems or situations already partially familiar to the student, isolating important properties of these as postulates, and deducing some of the consequences of these postulates.

Vinberg seems similar but more intense, so I imagine it would work well, too. 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 to not snub the students.

As aforementioned, some category theory, especially an awareness of universal properties and basic definitions e. After explaining the conceptual content of the classical theory of equations, our book tried to bring out the connections of newer algebraic concepts with geometry and analysis, connections maclanee had indeed inspired many of these concepts in the first place. They maclaen not avoid using universal properties, and they do not always bother to give students something concrete to hold on.

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Also, your review page is quite comprehensive! Mac Lane had had much more teaching experience than I, and I think the popularity of our book owes more to him than to me. I think brkhoff 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.

Because of the authors’ emphasis on “method” rather than “fact” the book will not be of much use as a reference work.

In the new third edition, the authors have modernized and improved the bigkhoff in many details.

Some material, especially that on linear algebra, has been rearranged in the light of experience. Maclanee returned to Harvard inthe year after I had given a course in modern algebra on the undergraduate level for the first time.

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. 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.

This is a text on modern algebra that is particularly suited for a first year graduate course or for an advanced undergraduate course. I am not sure. It is bikrhoff good, once standard book, but there are texts that better suit the needs of modern students.

Our Survey presented an exciting mix of classical, axiomatic, and conceptual ideas about algebra at a time when this combination was new.