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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Teachers of mathematics in secondary schools may want this book in their personal libraries. Still other arrangements are possible.
Our collaboration involved some compromises. 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.
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.
Birkhoff and Shrvey Lane also want to teach their students to prove things, of course. In we prepared a carefully polished second edition, in which polynomials over general fields were treated before specializing to the sudvey field.
Toggle navigation Additional Book Information. Because of the authors’ emphasis on “method” rather than “fact” the book will not be of much use as a reference work. We have done this by illustrating each new term by as many familiar examples as possible.
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. A semester course on abstract algebra could deal with Chapters, 11, 13, and wlgebra Learn More about VitalSource Bookshelf.
Chapter 11 includes a completely revised introduction to Boolean algebra and lattice mavlane. The next year Mac Lane put group theory first, and set theory Boolean algebra last!
A Survey of Modern Algebra
Other more minor changes and additions helped to increase its popularity, with annual sales in the range 14, Here care is taken to keep survwy the foreground the macalne 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 These ideas are still most relevant and worthy of enthusiastic presentation. For the social scientist whose mathematical studies have reached through the calculus, this book can confidently be urged as the thing to study next.
The ratio of definitions to theorems and exercises is kept low. When I taught “modern algebra” in “Math 6” the first time, inI began with sets and ended with groups. Garrett and I combined our preliminary notes to publish with MacMillan in our joint book, Survey of Modern Algebra. One of the best things about this book is the balanced approach to rigour and abstractness in relation to intuitive appreciation and shrvey application.
We got together and, inwe published ‘A Survey of Modern Algebra’. 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.
A Survey of Modern Algebra – CRC Press Book
Exclusive web offer for individuals. Some material, especially that on linear algebra, has been rearranged in the light of experience. Moreover, 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. Byrelatively new concepts inspired by it had begun to influence homology theory, operator theory, the theory of topological groups, and many other domains of mathematics.
The Bookshelf application offers access: A very striking feature of the book is its broad point of view. Only the last five chapters remain unchanged. It is a unified and comprehensive introduction to modern algebra. In addition the book is enlivened by striking applications of modern algebra to other suvey of science and made eminently teachable by the inclusion of numerous excellent problems and exercises.
Survey of Modern Algebra
We have also tried not to lose sight of the fact that, for many students, the value of algebra lies in its applications to other fields: That was characteristic of his freshness, his initiative, and his z of respect for conformity; but it came as a slight shock to me at the time. All instructor resources are now available on our Instructor Hub.
The authors express the belief that “for many students, the value of algebra lies in its maclxne to other fields: Summary This classic, written by two young instructors who became giants in their field, has shaped the understanding of modern algebra for generations of mathematicians and remains a valuable reference and text for self study and college courses.