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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Terminology and notation which has become outmoded since the Revised Amd was published in have been brought up-to-date; material on Boolean algebra and lattices has been completely rewritten; an introduction to tensor products has been added; numerous problems have been replaced and many new ones added; birkhofd throughout the book are hundreds of minor revisions to keep the work in the forefront of modern algebra literature and pedagogy.
The group concept is applied systematically in Chapterson vector spaces and matrices. Other more minor changes and additions helped to increase its popularity, with annual sales in the range 14, A very striking feature of the book is its broad point of view.
A survey of modern algebra / by Garrett Birkhoff and Saunders MacLane – Details – Trove
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. Our book, first published 50 years ago, was intended to present this exciting new view of algebra to American undergraduate and beginning graduate students. It provided a clear and enthusiastic emphasis on the then new modern and axiomatic view of algebra, as advocated by Emmy Noether, Emil Artin, van der Waerden, and Philip Hall.
His paper, “On the Structure of Abstract Algebras” founded a new branch of mathematics, universal algebra. We hope that the present book will prove an adequate reference for those wishing to apply the basic concepts of modern algebra to other branches of brikhoff, physics, and statistics. These responsibilities were in effect combined in our activity.
He spent most of his career as a professor of mathematics at Harvard University. Here care is taken to keep birlhoff the foreground the fundamental role played by algebra in Euclidean, affine, and projective geometry.
This well-known textbook has served, in the last twelve years, to introduce a great many students to the fundamental concepts of modern algebra in an extraordinarily effective way.
A Survey of Modern Algebra – Garrett Birkhoff, Saunders Mac Lane – Google Books
He had been doing the same thing. This exposition of the elements of modern algebra has been planned with great skill, and the plan has been carried through very successfully. 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. maclqne
This is followed in Chapter 12 by a brief discussion of transfinite numbers. In we prepared a carefully polished second edition, in which polynomials over general fields were treated before specializing to the real field. Toggle navigation Additional Book Information. I would certainly place it in the hands of an interested undergraduate wondering what lagebra was all about, particularly one who had already taken linear algebra.
Beyond this, occasional sections have been revised and a few problems have been added to some of the exercises. We enjoyed teaching and writing algebra because it was clear, exciting, and fun to present. This third edition of a standard text on modern algebra is substantially the same as the revised edition [of ]. Modern algebra prospered mightily in the decadesfrom functional analysis to algebraic geometry – not to mention our own respective researches on lattices and on categories.
Familiar alggebra are carefully algebda to illustrate each new term or idea which is introduced.
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A Survey of Modern Algebra
We hope that our book will continue to serve not only as a text but also as a convenient reference for those wishing to apply the basic concepts of modern algebra to other branches of mathematics, including statistics and computing, and also to physics, chemistry, and engineering.
Request an e-inspection copy. It was the standard textbook for undergraduate courses in modern algebra. One of us would draft a chapter and the other would revise it. Finally, the last three chapters provide an introduction to general commutative algebra and arithmetic: 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.
This book is distinguished by its procedure from the concrete to the abstract. 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. When I taught “modern algebra” in “Math 6” the first time, inI began with sets and maclanw with groups.
Only in this way will they be able to appreciate the full richness of the subject. Although two or three books on the new algebra have already appeared in English, the present volume appears to the reviewer to be the best all-round introduction to the subject, unique in its clarity, balance, generality and inclusiveness.
There are contacts with many branches of mathematics and so it can serve as an introduction to nearly the whole of modern mathematics. During the s, Birkhoff, along with his Mdern colleagues Marshall Stone and Saunders Mac Lane, substantially advanced American teaching and research in abstract algebra.
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 maclanw fundamental theorem of algebra. For the social scientist whose mathematical studies have reached through the calculus, this book can confidently be urged as algebga thing to study macland.
I knew how it should be done and so did Garrett. One of the best things about this book is the balanced approach to rigour and abstractness in relation to intuitive appreciation and concrete application. The ratio of definitions to theorems and exercises is kept low. The classical algebra is nicely embedded in this structure, as are also applications to other fields of thought. It does this by discussing examples of mathematical systems or situations already partially familiar to the student, isolating important properties of these as birkgoff, and deducing some of the consequences of these postulates.
In the new third edition, the authors have modernized and improved the material in many details. Therefore, instead of omitting these results, we have attempted to incorporate them s within the framework of the ideas of modern algebra. Learn More about VitalSource Bookshelf.