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. In Garrett Birkhoff and Saunders Mac Lane published A Survey of Modern Algebra. The book became a classic undergraduate text. Below we examine a. Garrett BirkhoffHarvard University Saunders Mac Lane The University of Chicago A SURVEY OF ern fourth.
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A typical first undergraduate course may cover group theory through the isomorphism theorems and the structure theorem for finite abelian groups,possibly including group actions and the Sylow theorems c.
He had been doing the same thing. Thus there is a careful development of real numbers, such as Dedekind cuts, and such set-theoretic concepts as order, countability and cardinal number are discussed.
This book is distinguished by its procedure from the concrete to the abstract. Here care is taken to keep in the foreground the fundamental role played by algebra in Euclidean, affine, and projective geometry. He received the nation’s highest award for scientific achievement, the National Medal of Science, in 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.
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.
Survey of Modern Algebra
The size and plan of the book preclude a comprehensive treatment of any one topic; in compensation, the authors are able to say something about nearly every important topic, and they usually succeed in saying the really important things. I feel there is a need in mathematics for detailed discussion of available resources.
That may overstate things, since my friend probably knows more mathematicians than students who got fed up and left. This approach, which crystallized earlier insights of Cayley, Frobenius, Kronecker, and Dedekind, blossomed in Germany in the s. It has a lot of linear algebra, algeba is good, and it is not too hard, but it requires some work.
This reviewer can testify to its appeal to students. Those desiring a text replete with possibilities for courses tailored to various kinds of students should welcome this new edition. But they want to teach them algebra even more.
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 algebbra how often they will find themselves ignorant of those things.
Getting across the rich motivation, ideas, analogies, history, and so forth should be an explicit goal, but it will not always be possible.
Chapter 6 introduces noncommutative algebra through its simplest and most fundamental concept: The authors express the belief that “for many students, the value of algebra lies in its applications to other fields: I don’t think hitting students with category theory unless they’ve already had considerable exposure to algebra is a good idea.
We had tried out our somewhat algehra ideas of how this should ans done in a course at Harvard for three successive years, before reorganizing and presenting them in textbook form. The present edition represents a refinement of an already highly useful text. The truth, though, is that undergraduates are fairly unlikely to read algevra textbook.
Maclanee, 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 rigour and power. 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.
Dual spaces and tensor products are also discussed, but generalizations to modules over rings are not considered.
Algebra – Saunders Mac Lane, Garrett Birkhoff – Google Books
I mentioned flaws of a few books in my answer. In this book Professors Birkhoff and Mac Lane have made an important contribution to the pedagogy of algebra. In the new third edition, the authors have modernized and improved the material in many details.
Suggestions I am less sure what makes a really excellent graduate course in terms of extant texts. brkhoff
Chapter 11 includes a completely revised birkhofg to Boolean algebra and lattice theory. There are today major directions that either did not exist over 60 years ago, or that were not then recognized to be so important. These ideas are still most relevant and worthy of enthusiastic presentation. Some people mistakenly believe they cannot. In fact, I think this book works better as the supplement.