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Combinatorics : topics, techniques, algorithms
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ISBN: 0521451337 0521457610 Year: 1994 Publisher: Cambridge : Cambridge University Press,

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Abstract

Combinatorics is a subject of increasing importance, owing to its links with computer science, statistics and algebra. This is a textbook aimed at second-year undergraduates to beginning graduates. It stresses common techniques (such as generating functions and recursive construction) which underlie the great variety of subject matter and also stresses the fact that a constructive or algorithmic proof is more valuable than an existence proof. The book is divided into two parts, the second at a higher level and with a wider range than the first. Historical notes are included which give a wider perspective on the subject. More advanced topics are given as projects and there are a number of exercises, some with solutions given.

Introduction to algebra
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ISBN: 0198501951 0198501943 9780198501954 Year: 1998 Publisher: Oxford: Oxford university press,

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Based on the author's years of teaching experience, this textbook provides undergraduates with a clear and carefully paced introduction to abstract algebra. It begins with groups and rings, developing important concepts thoroughly before moving on to subrings, homomorphisms, and ideals. Later chapters then introduce a number of more advanced topics, including simple groups and extensions, Noetherian rings, universal algebra, lattices, categories, Galois theory, and coding theory. The author has included a chapter on constructing the number systems, where he gives three different proofs that transcendental numbers exist.

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