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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Moreover, many of the examples in this text might help teachers to communicate this spirit to their students.

This exposition of the elements of modern algebra has been planned with great skill, and the plan has been carried through very successfully. I had taught algebra courses at Harvard when I was an instructor, and at Cornell I taught algebra out of the book by Bocher; at Chicago, out of a book, ‘Modern Higher Algebra’ by Albert; and at Harvard again out of my own notes. The familiar domain of integers and the rational field are emphasized, together with the rings of integers modulo n and associated polynomial rings.

For Instructors Request Inspection Copy. Finally, the last three chapters provide an introduction to general commutative algebra and arithmetic: To develop the student’s power to think for himself in terms of the new concepts, we have included a wide variety of exercises on each topic.

Still other arrangements are possible. Chapter 6 introduces noncommutative algebra through its simplest and most fundamental concept: The authors are to be congratulated on having improved an already excellent text.

This is a text on modern algebra that is particularly suited for a first year graduate course or for an advanced undergraduate course. Although many of the basic results stem back to Kronecker, Dedekind and Lf, the present-day subject is largely the creation of the great woman mathematician, Emmy Noether.

Our book, first published 50 years off, was intended to present this exciting new view of algebra to American undergraduate and maflane graduate students. He had been doing the same thing. The book was prepared at a time when both of us were assistant professors, so without tenure.


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 mathematics, physics, and statistics.

The revised edition differs only in minor rearrangements and additions. The present edition represents a refinement of an already highly useful text. But they want to teach usrvey algebra even more. Here care is taken to keep in the foreground the fundamental role played by algebra in Euclidean, affine, and projective geometry.

A Survey of Modern Algebra

Birkhoff and Mac Lane also want to teach their students to prove things, of course. We had the algbera fortune to write a book on the subject at the right time. This reviewer can testify to its appeal to students. We enjoyed teaching and writing algebra because it was clear, exciting, and fun to present. Adopting this as the main textbook for an undergraduate abstract algebra course would today be an eccentric move.

Then the abstract definition appears simple, and the theoretical properties which are deduced from the definition exhibit the power of the concept. Teachers of mathematics in secondary schools may want this book in their personal libraries.

A Survey of Modern Algebra – Garrett Birkhoff, Saunders Mac Lane – Google Books

These theorems are then applied to some familiar and to some less familiar examples, thus broadening the student’s viewpoint without getting him lost in abstractions. Instructors who have used the original edition with college classes appreciate its scope.

We also hope it will give a solid introduction to this fascinating and rapidly growing subject, to those students interested in modern algebra for its own sake. Modern algebra also enables one to reinterpret the results of classical algebra, giving them far greater unity and generality.

After explaining the conceptual content of the classical theory of equations, our book tried to bring out the connections of newer algebraic concepts with geometry and analysis, connections that had indeed inspired many of these concepts in the first place.

We algebar 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. Please accept our apologies for any inconvenience this may cause.


The longer chapters are his; the shorter ones mine. Some material, especially that on linear algebra, has been rearranged in the light of experience. The title will be removed from your cart because it is not available in this region. The authors are quick to indicate applications and careful to motivate and illustrate abstractions. In writing the present text we have endeavoured to set forth moden formal or “abstract” birkhofv, but we have been guided birihoff a much broader interpretation of the significance of modern algebra.

A Survey of Modern Algebra – CRC Press Book

The student resources previously accessed via GarlandScience. The word “survey” in the title is quite accurate; for, although many topics are treated, none of them is really completely developed. Other more minor changes and additions helped to increase its popularity, with annual sales in the range 14, Our third edition, infinally included tensor products of vector spaces, while the fourth edition clarified the treatment of Boolean algebras and lattices.

Exercises of the latter type serve the important function of familiarizing the student with the construction of a formal proof. 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. In addition the book is enlivened by striking applications of modern algebra to other branches of science and made eminently teachable by the inclusion of numerous excellent problems and exercises.

Their emphasis is on the methods and spirit of modern algebra rather than on the subject matter for itself. Throughout the study of matrices and quadratic forms the geometric point of view is emphasized.

Birkhoff and Mac Lane’s book first appeared inand van der Waerden’s book first appeared in