A survey of modern algebra. Bibliography: p. Includes index. 1. Algebra, Abstract. I. MacLane, Saunders, (date) joint author. II. Title. QAB57 “This classic text introduces abstract algebra using familiar and concrete examples that illustrate each concept as it is presented. It covers such topics as the role. A survey of modern algebra / by Garrett Birkhoff and Saunders MacLane Birkhoff, articles: Garrett Birkhoff, Greatest common divisor, Saunders Mac Lane.
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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. Offline Computer — Download Bookshelf software to your desktop so you can view your eBooks with or without Internet access. It began to sell well as soon as the war was over, in at about – annually. For over twenty years this text has been the “classic” work in its field.
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 Boolean algebra, lattice theory, and transfinite numbers, all of which are important in mathematical logic and in the modern theory of real functions. 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.
The present edition represents a refinement of an already highly useful text. Those desiring a text replete with possibilities for courses tailored to various kinds of students should welcome this new edition. Learn More about VitalSource Bookshelf. A famous mathematician once remarked to me that everyone he knew who had worked through A Survey of Modern Algebra had come to love the subject.
Modern algebra also enables one to reinterpret the results of classical algebra, giving them far greater unity and generality.
For example, a semester or quarter course covering linear algebra may be based on Chaptersthe real and complex fields being emphasized. Birkhoff and Mac Lane also want to teach their students to prove things, of course.
He spent most of his career as a professor of mathematics at Harvard University. These responsibilities were in effect combined in our activity. Nowhere can teachers better catch today’s spirit of mathematics. The title will be removed from your cart because it is not available in this region. 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.
Thrall : Review: Garrett Birkhoff and Saunders MacLane, A Survey of Modern Algebra
In algebrs the book is enlivened by striking applications of modern algebra to other branches of science and made eminently teachable by the inclusion of mmaclane excellent problems and exercises. This independence is intended to make the book useful not only for a full-year course, assuming only high-school algebra, but also for various shorter courses. The original comprehensive Survey has been reordered somewhat and augmented to the extent of approximately fifty pages.
Only the last five chapters remain unchanged.
It provided a synthesis formerly obtainable only after much more advanced work. Then the abstract definition appears simple, and the theoretical properties which are deduced from the definition exhibit the power of the concept. One of us would draft a chapter and the other would revise it. Yes, we did know then that research mattered for tenure, but our joy in teaching was somehow modren with our respective research.
For Instructors Request Inspection Copy. Add to Wish List. We enjoyed teaching and writing algebra because it was clear, exciting, and fun to present.
A survey of modern algebra / by Garrett Birkhoff and Saunders MacLane – Details – Trove
Thus there is a careful ,odern of real numbers, such as Dedekind cuts, and such set-theoretic concepts as order, countability and cardinal number are discussed. Many algebra textbooks are so concerned about the process of learning to prove things that they communicate a sense of the subject as forbidding and stiff, dedicated to formalism and precision.
I knew how it should be done and so did Garrett. Already read this title? Some of these exercises are computational, some explore further examples of the new concepts, and others give additional theoretical developments. Nad I taught “modern algebra” in “Math 6” the first time, inI began with sets and ended with groups.
A Survey of Modern Algebra
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. The authors are to be congratulated on having improved an already excellent text. Mac Lane was elected to the National Academy of Sciences in These ideas are still most relevant and worthy of enthusiastic presentation.
Our Survey presented an exciting mix of classical, axiomatic, and conceptual ideas about algebra at a time when this combination was new. Our collaboration involved some compromises. The next year Mac Moderj put group theory first, and set theory Boolean algebra last! He returned to Harvard inthe year after I had given a course in modern algebra on the undergraduate level for the first time. Algsbra other arrangements are possible. The ratio of definitions to theorems and exercises is kept low.
There are contacts with many branches of mathematics and so it can serve as an introduction to nearly the whole of modern mathematics.
Their emphasis is on the methods and spirit of modern algebra rather than on the subject matter for itself. This reviewer can testify to its appeal to students. Toggle navigation Additional Book Information. Our third edition, infinally included tensor products of vector spaces, while the fourth edition clarified the treatment of Boolean algebras and lattices. It could be through conference attendance, group discussion or directed reading to name just a few examples.
Nevertheless, it is still a book well worth reading. CPD consists of any educational activity which helps to maintain and develop knowledge, problem-solving, and technical skills with the aim to provide better health care through higher standards. I would certainly place it in the hands of an interested undergraduate wondering what algebra was all about, particularly one who had already taken linear algebra.
A ‘Survey of Modern Algebra’ made it possible to teach an undergraduate course that reflected the richness, vigour, and unity of the subject as it is growing today. Chapter 11 includes a completely revised introduction to Boolean algebra and lattice theory. A semester course on abstract algebra could deal qnd Chapters, 11, mldern, and