Algebra, [Saunders Maclane; Garrett Birkhoff] on *FREE* shipping on qualifying offers. From the dust cover: The text begins with the notions. In Garrett Birkhoff and Saunders Mac Lane published A Survey of Modern Algebra. The book became a classic undergraduate text. Below we examine 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.


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In spite of the similarity of the titles and the coincidence of the names although not the sequence of names of the authors, this is not a new edition of the 'Survey of Modern Algebra' Macmillan Co. The motivation for it is summarized in the first paragraph of the Preface: These developments use certain new concepts such as 'module,' 'category,' and 'morphism' which are algebraic in character and which indeed can be introduced naturally on the basis of elementary materials.

The efficiency of these ideas suggests a fresh presentation of algebra. But most of these chapters are used now also for the purpose of mac lane birkhoff algebra and mac lane birkhoff algebra the concepts of "category," "functor," and "universal element" which, in the penultimate chapter on 'Categories and adjoint functors' become the main topic of the book.

Survey of Modern Algebra

Monthly 74 10 It is natural to compare this book with the authors' A Survey of Modern Algebra since it is directed to the same mac lane birkhoff algebra. Most of the topics covered in the earlier book appear in some form in the present book; there is one notable exception: Galois Theory is omitted.

Despite the large intersection of topics mac lane birkhoff algebra in Survey and in Algebra, the new book is not just an updating of the old.

The treatment of many topics and the general tone differ greatly from that of Survey. The notation and terminology are "categorical," as are many proofs.

A Survey of Modern Algebra

Universal mac lane birkhoff algebra and duality are introduced in the first chapter and play an essential role throughout most of the book. Many concepts are defined in terms of, or are related to, universal mac lane birkhoff algebra properties; and these properties are used when the concepts are applied.

Mathematical Reviews MR 35 The concrete examples which underlie undergraduate algebra courses - integers, real and complex numbers, polynomials, vectors, matrices, determinants - are neither modern nor abstract. A textbook in which these objects are presented becomes a book on "modern algebra'' by the kind of scaffolding it erects to exhibit these objects.

Algebra - Saunders Mac Lane, Garrett Birkhoff - Google книги

An earlier generation of mathematicians mac lane birkhoff algebra, for example in the authors' A survey of modern algebra ; ; that these objects are examples of groups, rings, fields, and vector spaces, and saw that the standard constructions in algebra often reduce to finding the right equivalence relation.

It is refreshing to see in this book the standard material of undergraduate algebra presented systematically from a new point of view.

This time the axiomatic systems and equivalence relations mac lane birkhoff algebra there, but are governed in turn by the language of categories, functors, universal objects, and dualities.


From the Preface of the 2nd edition. The treatment of many of the topics in the first edition has been simplified - and clarified - in this second edition.

Birkhoff-MacLane books

The material on universal constructions, formerly introduced at the end of the first mac lane birkhoff algebra, has now been assembled in Chapter IV, at a point where there are at hand many more effective examples of these constructions.

A great many points in the exposition have been clarified, for instance in mac lane birkhoff algebra simpler construction of the integers, a more elementary description of polynomials, and a more direct treatment of dual spaces.

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The chapter on special fields now includes power series fields and a treatment of the p-adic numbers. There is a wholly new chapter on Galois theory; in exchange, the chapter on affine geometry has been dropped.

New exercises have been added and mac lane birkhoff algebra old slips have been excised. Review of 3rd edition by: