“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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Moreover, it was written in a clear and enthusiastic style that conveyed to the reader an appreciation of the aesthetic character of the birkhofd as well as its rigour and power. Post as a guest Name.

Survey of Modern Algebra

Then the abstract definition appears simple, and the theoretical properties which are deduced from the definition exhibit the mmaclane of the concept. He received the nation’s highest award for scientific achievement, the National Medal of Science, in Instructors who have used the original edition with college classes appreciate its scope.

Nevertheless, it is still a book well worth reading. What level students today can Algebra be used for?

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. If you want an older book written by a master expositor and mathematician, then I think Herstein works better than Mac Lane.

I’m working on such a book myself,but for low cost texts only. 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. They do not avoid using universal properties, and they do not always bother to give students something concrete to hold on. But the authors’ delight in what was then a new subject shines through their writing, and their willingness to be informal when necessary was a smart move.

I have however tried to read many algebra books. Our third edition, infinally included tensor products of vector spaces, while the fourth edition clarified the treatment of Boolean algebras and lattices.


Moreover, many of the examples in this text might help teachers to communicate this spirit to their students. Bikhoff 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.

A very striking feature of the book is its broad point of view.

Accordingly, we have tried throughout to express the conceptual background of the various definitions used. 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. It wasn’t the first abstract algebra book I read, though, but it probably was the first book that I read carefully.

Ideally, the course book would have lots of this and the lecture somewhat less. Certainly, algebraists expect everyone has seen some homological algebra and representation theory by the time they get their Ph. As Mac Lane did years ago, it is best to supplement the text with something easier, something intended for undergraduates. Vinberg seems similar but more intense, so I imagine it would work well, too. He spent most of his career as a professor of mathematics at Harvard University.

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. For a first year graduate course-which at Harvard,usually included a number of undergraduates-he’d use the book straight up and cover most of it.

Algebra – Saunders Mac Lane, Garrett Birkhoff – Google Books

Sign up using Email and Password. For the social scientist whose mathematical studies have reached through the calculus, this book can confidently be urged as the thing to study next. Teachers of mathematics in secondary schools may want this book in their personal libraries.

The classical algebra is nicely embedded in this structure, as are also applications to other fields of thought. 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.


Yes, we did know then that research mattered for tenure, but our joy in teaching was somehow connected with our respective research. I do not think using algebras is a problem, but three whole chapters is probably a bit much, so some would have to be cut. You mention Herstein and Vinberg, which are good; Artin or Gallian also work, for example. Post Your Answer Discard 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.

We had tried out our somewhat differing ideas of how this should be done in a course at Harvard for three successive years, before reorganizing and presenting them in textbook form.

Preliminary Thoughts

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, Courant, and Spivak. Exercises of the latter type serve the important function of familiarizing the student with the construction of a formal proof. These responsibilities were in effect combined in our activity. Hungerford is a common alternative I did not discuss, but I have never found it very exciting.

Their emphasis is on the methods and spirit of modern algebra rather than on the subject matter for itself. Post Your Answer Discard By clicking “Post Your Answer”, you acknowledge that you have read birohoff updated terms of serviceprivacy policy and cookie policyand that your continued use of the website is subject to these policies.