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. 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.
|Published (Last):||28 November 2015|
|PDF File Size:||13.53 Mb|
|ePub File Size:||5.52 Mb|
|Price:||Free* [*Free Regsitration Required]|
Similarly, books like Cohn, Grillet, and Jacobson can be too advanced or too focused on being references. The familiar domain of integers and the rational field are emphasized, together with the rings of integers modulo n and associated polynomial rings.
The revised edition differs only in minor rearrangements maxlane additions.
Algebra – Saunders Mac Lane, Garrett Birkhoff – Google Books
I should probably spend some time with it again, actually. Those are perhaps worth substantial time, even if they are somewhat birkuoff odd for most courses. Also from a more substantive POV: See wikipedia for details. I am hard pressed to put a single book above the others, however.
Preliminary Thoughts In both undergraduate courses and graduate courses students’ abilities and background are quite variable; that much has not changed in the past few decades. Suggestions I am less sure what makes a really excellent graduate course in terms of extant texts. I am not sure. Some people maclans believe they cannot.
Yet, I also think a course should start with basic material.
It even has chapters on multilinear and exterior algebra and affine spaces. Rowen has been talked about a good bit, which is deserving for its extensive presentation on algebras and many applications, but I am not sure starting with modules is a good idea, for example. Some of these exercises are computational, some explore further examples of the new concepts, and others give additional theoretical developments. We hope that the present book will prove an adequate reference for those wishing to apply the basic concepts of modern macalne to other branches of mathematics, physics, and statistics.
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 alegbra and power. I once began writing a massive annotated bibliography of basic mathematics through bidkhoff graduate workbut after spending ten pages on algebra texts, I gave up on the project. This exposition of the elements of modern algebra has been planned with great skill, and the plan has been carried through very successfully.
Birkkhoff all 18 reviews.
It’s a projected book to accompany my new publishing company to instruct penniless students on low-cost mathematics sources for self study. It is clear, with nice examples.
Chapter 0 Graduate Studies in Mathematics. Occasionally a textbook makes possible a real leap forward in ways of learning. I guess some reviewers have read all pages and worked all the problems?
In this way, I do not expect today’s students are substantially better than past students, either. Supplementing this with another book to get some coverage of representation theory and homological algebra is probably ideal.
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. It is a great supplementary text, however.
I’ve already commented extensively on most of the standard algebra texts at my blog-you can find the relevant post here: Perhaps a lecture bjrkhoff elementary set theoretical notions, then cover some linear algebra introducing basic category theory after seeing direct sumsthen cover some ring theory, then plenty of group theory, macane modules and advanced linear algebra, followed by field and Galois theory, representation theory using algebras and specializing quickly alyebra groupscommutative algebra including some applications to algebraic geometry and the likeand finally homological algebra, with some advanced or extra ibrkhoff at the end, if possible e.
Would like to hear feedback on this question. Customers who viewed this item also viewed. I had taught out of most of the extant books. I think such a book would have found a massive audience and I’d encourage ANYONE working on such a book to continue as we’d then have many different opinions for students and professionals on standard works. So I spell it in the traditional way as “MacLane”. A semester course on abstract algebra could deal with Chapters, 11, 13, and macpane The group concept is applied systematically in Chapterson vector spaces and matrices.
It will teach you undergraduate abstract algebra while introducing you to categorical ideas, especially the role of universals.
Mac Lane has an enduring reputation as a great expositor.
I recommend “Algebra” for self study at your leisure. I had taught algebra courses at Harvard when I was an instructor, and at Cornell I taught algebra out of the book by Bocher; at Chicago, out of a book, ‘Modern Higher Algebra’ by Albert; and at Harvard again out of my own notes.