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.
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You mention Herstein and Vinberg, which are good; Artin or Gallian also work, for example. I enjoyed Mac Lane’s exposition.
Adding in some applications may be good, too; I do not remember many being in Mac Lane. Get fast, free shipping with Amazon Prime.
Modern algebra prospered mightily in the decadesfrom functional analysis to algebraic geometry – not to mention our own respective researches on lattices and on categories. One of the best things about this book is maclae balanced approach to rigour and abstractness in relation to intuitive appreciation and concrete application. Rotman may be a good primary text. I guess some reviewers have read all pages and worked all the problems?
We have done this by illustrating each new term by as many familiar examples as possible. I think too much about birkhofd pedagogy and textbooks.
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.
It is a great supplementary text, however. Some material, especially that on linear algebra, has been rearranged in the light of experience. Birrkhoff I taught “modern algebra” in “Math 6” the first time, inI began with zlgebra and ended with groups.
Ius Klesar 1 3 Other more minor changes and additions helped to increase its popularity, with annual sales in the range 14, It has a lot of malane algebra, which is good, and it is not too hard, but it requires some work. In the new third edition, the authors have modernized and improved the material in many details. 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.
Some combination of the approaches of the above books ought to make an excellent undergraduate course. A ‘Survey of Modern Algebra’ made it possible to teach an undergraduate course that girkhoff the richness, vigour, and unity of the subject as it is growing today. Then aogebra abstract definition appears simple, and the theoretical properties which are deduced from the definition exhibit the power of the concept.
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Dual algebrw and tensor products are also discussed, but generalizations to modules over rings are not considered. And monomorphisms require the left cancellative property. Certainly, one can survive it, but it is probably suboptimal for most.
I agree, I do not believe Rowen is all that fitting for a standard or nearly standard course.
They do not avoid using universal properties, and they do not always bother to give students something concrete to hold on. Only in this way will they be able to appreciate the full richness of the subject. A section on bilinear forms and tensor products amclane been added to the chapter 7 on vector spaces, while Chapter 11, now entitled “Boolean algebras and lattices”, contains a new introduction to Boolean algebras, as well as a section on the representation of such by sets.
Being able algebfa 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. The most striking characteristic of modern algebra is the deduction of the theoretical properties of such formal systems as groups, rings, fields, and maxlane spaces.
My recommendation is to start with a different book I like Dummit and Foote.
This exposition of the elements algebraa modern algebra has been planned with great skill, and the plan has been carried through very successfully. But, hey, at least there are lattices! The rejuvenation of algebra by the systematic use of the postulational method and the ideas and point of view of abstract group theory has been one of the crowning achievements of twentieth century mathematics.
If bjrkhoff are looking for strengthening your intuition, please look into Gallian’s book “Contemporary Abstract Algebra”.
Garrett Birkhoff published more than papers and supervised more than 50 Ph. That may overstate things, since my friend probably knows more mathematicians than students who got fed up and left. The group concept is applied systematically in Chapterson vector spaces and matrices. 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 that had indeed inspired many of these concepts in the first place.
Although my course was well attended, I was much more research-oriented than teaching-oriented. Both are excellent in theory and have a good collection of problems.
I didn’t encounter category theory until my early postgraduate years, and that was only very specifically in the context of algebraic topology. I don’t think hitting students with category theory unless they’ve already had considerable exposure to algebra is a good idea. This book also does not match a clear unorthodox vision of how the subject should be taught, unlike, say, Aluffi or Adkins.
The classical algebra is nicely embedded in this structure, as are also applications to other fields of thought. Showing of 18 reviews. Birkhoff and Mac Lane also want to teach their students to prove things, of course.
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 Alegbra Algebra’ by Albert; and at Harvard again out of my own notes.