“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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But, hey, at least there are lattices!
Although some additions and rearrangements have been algebrx for this edition, the content remains essentially the same [as the edition]. Also, your review page is quite comprehensive! This has influenced us in our emphasis on the real and complex fields, on groups of transformations as contrasted with abstract groups, on symmetric matrices and reduction to diagonal form, on the classification of quadratic forms under the orthogonal and Euclidean groups, and finally, in the inclusion of Algebr algebra, lattice theory, and transfinite numbers, all of which are important in mathematical logic and in the modern theory of real functions.
I have however tried to read many algebra books.
This is one of the primary reasons an undergraduate course ought to supplement this book. It is a unified and comprehensive introduction to modern algebra.
Mac Lane has an enduring reputation as a great expositor. Then and later we took part in the flow hirkhoff new ideas from discovery to use and to present to students. For the social scientist whose mathematical studies have reached through the calculus, this book can confidently algebrq urged as the thing to study next.
But knowing what others have to say sure makes it easier to commit to a book and, by extension, the price tag attached to said book. Adopting this as the main textbook for an undergraduate abstract algebra course would today be an eccentric move.
There is also contact with the field of mathematical logic in the chapter on the algebra of classes and with the ideas of topology in the proof of the fundamental theorem of algebra.
Those desiring a text replete with possibilities for courses tailored to various kinds of students should welcome this new edition. I don’t think hitting students with category theory unless they’ve already had considerable exposure to algebra is a good idea. The familiar domain of integers and the rational field are emphasized, together with the rings of integers modulo n and associated polynomial rings. The authors are quick to indicate applications and careful to motivate birkhff illustrate abstractions.
Modern algebra prospered mightily in the decadesfrom functional analysis to algebraic geometry – not to mention our own respective researches on lattices and on categories.
In this book Professors Birkhoff and Mac Lane have made an important contribution to the pedagogy of algebra. 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. He had been doing the same thing.
Chapter 11 includes a completely revised introduction to Boolean algebra and lattice theory. I mentioned flaws of a few books in my answer.
Other more minor changes and additions helped to increase its popularity, with annual sales in the range 14, The style in which the book is written is like a story. 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.
It has a lot of linear algebra, which is good, and it is not too hard, but it requires some work. It is also worth noting Mac Lane does cover multilinear algebra pretty well, which is frequently forgotten.
The selection of exercises is sufficient to allow an instructor to adapt the text to students of quite varied degrees of maturity, of undergraduate or first year graduate level. 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.
This is followed in Chapter 12 by a brief discussion of transfinite numbers. Only the last five chapters remain unchanged. 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. Our book, first published 50 years ago, was intended to present this exciting new view of algebra to American undergraduate and beginning graduate students.
Obviously, the answers are bound to be highly personal. In fact, they may be better when it comes to algebra. Would it be suitable for self-study? Inwhen the first edition of this book appeared, the curriculum in algebra was the result of a hodge-podge accumulation. After teaching the course again the next year, I suggested that we co-author a book, usable by our colleagues, so that we wouldn’t have to alternate teaching it forever, and he agreed.
Perhaps a lecture reviewing 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, then modules and advanced linear algebra, followed by field and Galois theory, representation theory using algebras and specializing quickly to groupscommutative algebra including some applications to algebraic geometry and the likeand finally homological algebra, with some advanced or extra topics at the end, if possible e.
It is unlikely you will cover the entire book, either, even in a one year course. 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. Dummit and Foote is great for group theory, but it suffers in other parts and may also too big and encyclopedic.
Because of the authors’ emphasis on “method” rather than “fact” the book will not be of much use as a reference work.
Chapters give an introduction to the theory of linear and polynomial equations in commutative rings. I think you could cover the entire book, minus perhaps Chapter XIV on lattices, which are not typically emphasized and birjhoff partly historical, and possibly Chapter VIII, which is a bit odd, in my birknoff.
This book is distinguished by its procedure from the concrete to the abstract. We aimed to combine the abstract ideas with suitable emphasis on examples and illustrations. In writing the present text we have endeavoured to set forth this formal or “abstract” approach, but we have been guided by a much broader interpretation of the significance of modern algebra.
Familiar examples are carefully presented to illustrate each new term or idea which is introduced. I’m working on such a book myself,but for low cost texts only.
A second course may cover a bit more group theory c. I recommend “Algebra” for self study at your leisure.