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Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Many examples and hundreds of problems are included, along with hints or complete solutions for most of the problems. The focus is on algebraic number theory and algebraic geometry, and the distinctions and influences of each topic on the other. Material vital to the knowledge of the professional mathematician is presented. Advanced Algebra presents its subject matter in a forward-looking way that takes into account the historical development of the subject. Together the two books give the reader a global view of algebra and its role in mathematics as a whole. They are suitable as texts in a two-semester advanced undergraduate or first-year graduate sequence in algebra.
Inhaltsverzeichnis
From the reviews:
" This textbook is a sequel to the author' s textbook
Basic Algebra
. . . which is an excellent introduction to groups, linear algebra, commutative rings, and Galois theory. The text under review contains the basic theory of noncommutative rings, and delves quite deeply into algebraic number theory and algebraic geometry. This reviewer finds the author' s writing style extremely engaging, and shares his propensity for aiming whenever possible at an interesting and important theorem which illustrates the theory which the chapter develops. . . This is a beautiful book, which should serve well as a basic graduate textbook in algebra. "
Mathematical Reviews
" All together, this is another outstanding textbook written by the renowned and versatile mathematical researcher, teacher, and author Anthony W. Knapp that reflects his spirit, his devotion to mathematics, and his rich experiences in expository writing at best. . . This textbook is the second volume of Anthony W. Knapp' s comprehensive introduction to the fundamental concepts and tools in modern abstract algebra. Together with its foregoing companion volume
Basic Algebra
, which was published in the autumn of 2006, the current book is to provide a global view of the subject, thereby particularly emphasizing both its various applications and its ubiquitous role in contemporary mathematics. As the author already pointed out in the preface to the first volume, his leading idea was to give a systematic account of what a budding mathematician needs to know about the principles of modern algebra in order to communicate well with colleagues in all branches of mathematics and related sciences. This rewarding program was masterly begun in the companion volume
Basic Algebra
, where the fundamentals of linear algebra, multilinear algebra, group theory, commutative algebra, field theory, Galois theory, and module theory over noncommutative rings were profoundly developed. "
Zentralblatt Math
"
Advanced Algebra
is a wonderfully useful and well-written book, characterized by clear and `user-friendly treatments of many important algebraic topics. Finally,
Advanced Algebra
contains a thorough coverage of Gröbner bases and continues the trend set in
Basic Algebra
of providing good, meaningful (and plentiful) exercises. I highly recommend this wonderful book. "
(Michael Berg, MAA Online, January, 2008)
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