Basic Algebra by Anthony W Knapp

Basic Algebra by Anthony W Knapp

This text presents a unifying approach to algebra for students who are planning a career in which advanced mathematics will be used professionally. Key concepts, tools, and results are systematically developed. Most importantly, the student achieves a global perspective of the subject by seeing its vital role in analysis, topology, geometry, and number theory. Three prominent themes recur: the analogy between integers and polynomials in one variable over a field, the interplay between linear algebra and group theory, and the relationship between number theory and geometry. More than 400 problems at the ends of chapters develop related topics and point to additional applications.

From the reviews:

Finally, the author's notorious masterly style of writing, which stands out by its high degree of clarity, elegance, refinement, and accuracy, also rules over this newest textbook of his, which is very likely to become one of the great standard texts in algebra for generations—Zentralblatt Math

``Anthony W. Knapp Basic Algebra aims to teach the student algebra in a somewhat different way than is the norm. Together with its sequel, Advanced Algebra, the book proposes to take an aspiring mathematician from his first exposure to algebra proper, right after calculus, through his graduate training in algebra -- and a bit further...

``To use Basic Algebra in a standard undergraduate curriculum would entail spreading the material over several semesters, since the book can be used for linear algebra, group theory (Chapter IV is a gem!), rings and fields, Galois theory, a second course in group theory, and even a course on modules.

``Basic Algebra is a very interesting and well-written book, and is indeed well suited for the approach to algebra the author intends, and, for that matter, usable for commonplace approaches as well."    —MAA Reviews

"This is a basic textbook in abstract algebra suitable for a first-year graduate algebra course or perhaps a rather challenging upper level undergraduate course. … The appendices contain some basic set theory. … There are many interesting problems, in which a considerable amount of additional material is developed. In particular the theme of coding theory is pursued through many of the chapter exercises and topics such as MacWilliams identity and BCH codes are broached." (Ronald Solomon, Mathematical Reviews, Issue 2007 e)

“This book is written as a textbook for students who are learning algebra for the first time. Much of the material corresponds to the contents of a usual algebra course. … numerousfurther topics are included which go beyond the level of an undergraduate or even first year graduate student.” (H. Mitsch, Monatshefte für Mathematik, Vol. 156 (4), April, 2009)

Anthony W.Knapp is a mathematics professor in the State University of New York at Stony Brook. He is the author of two Princeton University Press books: Representation Theory of Semisimple Groups: An Overview Based on Examples and Lie Groups, Lie Algebras, and Cohomology.

SKU	Unavailable
ISBN 13	9780817632489
ISBN 10	0817632484
Title	Basic Algebra
Author	Anthony W Knapp
Series	Cornerstones
Condition	Unavailable
Binding Type	Hardback
Publisher	Birkhauser Boston Inc
Year published	2006-09-28
Number of pages	735
Cover note	Book picture is for illustrative purposes only, actual binding, cover or edition may vary.