“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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You should have never given up on the project. 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. Although many of the basic results stem back to Kronecker, Dedekind and Steinitz, the present-day subject is largely the creation of the great woman mathematician, Emmy Noether.
Some combination of the approaches of the above books ought to make an excellent undergraduate course.
We have websites like Math Stack Exchange where we can ask users for opinions, but it would be nice to have many more bibliographies of mathematical subjects than there currently are. In addition the book is enlivened by striking applications of modern algebra to other branches of science and made eminently teachable by the inclusion of numerous excellent problems and exercises. I often found it dry, too.
Post as a guest Name. The Basic Graduate Year includes some good applications to algebraic geometry and algebraic number theory, for example. It wasn’t the first abstract algebra book I read, though, but it probably was the first book that I read carefully. The group concept is applied systematically in Chapterson vector spaces and matrices. 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.
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This book also does not match a clear unorthodox vision of how the subject should be taught, unlike, say, Aluffi or Adkins.
Getting across the rich motivation, ideas, analogies, history, and so forth should be an explicit goal, but it will not always be possible. Adopting this as the main textbook for an undergraduate abstract algebra course would today be an eccentric move. I mentioned flaws of a few books in my answer. Those are perhaps worth substantial time, even if they are somewhat too odd for most courses. In preparing the revised edition we have added several important topics equations of stable type, dual spaces, the projective group, the Jordan and rational canonical forms for matrices, etc.
That was characteristic of his freshness, his initiative, and his lack of respect for conformity; but it came as a slight shock to me at the time.
Aluffi is really something special, but it is probably a bit too category theory-centric for students new to the subject in the sense that they will not have enough familiarity with the lower-level stuff.
One of the best things about this book is the balanced approach to rigour and abstractness in relation to intuitive appreciation and concrete application.
These theorems are then applied to some familiar and to some less familiar examples, thus broadening the student’s viewpoint without getting him lost in abstractions. The book was prepared at a time when both birkhiff us were assistant professors, so without tenure. Also, I apologize for such a long response. The Mathemagician 2 6.
It could probably work for teaching a first course to students who have never seen abstract algrbra, if the instructor is at ease with it. His paper, “On the Structure of Abstract Algebras” founded a new branch of mathematics, universal algebra. Our Survey in presented an exciting mix of classical and conceptual ideas about algebra.
They embody the elegance, precision, and generality which are the hallmark of mathematics!
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. Artin 2e, not 1e is also good and emphasizes linear algebra and geometric intuition, which is good considering how often students will need things from linear algebra and how often they will find themselves ignorant of those things. Post as a guest Name. Birkhoff and Mac Lane also want to teach their students to prove things, of course.
Anyway, let me say a bit about my thinking for how this book would work for either audience. 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.
This exposition of the elements of modern algebra has been planned with great skill, and the plan has been carried through very successfully.