Combinatorics Topics Techniques Algorithms Peter Cameron
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Combinatorics
Author: Peter Jephson Cameron
language: en
Publisher: Cambridge University Press
Release Date: 1994-10-06
Combinatorics is a subject of increasing importance because of its links with computer science, statistics, and algebra. This textbook stresses common techniques (such as generating functions and recursive construction) that underlie the great variety of subject matter, and the fact that a constructive or algorithmic proof is more valuable than an existence proof. The author emphasizes techniques as well as topics and includes many algorithms described in simple terms. The text should provide essential background for students in all parts of discrete mathematics.
Combinatorics
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
Author: Peter Jephson Cameron
language: en
Publisher: Oxford University Press, USA
Release Date: 1998
This book is an undergraduate textbook on abstract algebra, beginning with the theories of rings and groups. As this is the first really abstract material students need, the pace here is gentle, and the basic concepts of subring, homomorphism, ideal, etc are developed in detail. Later, asstudents gain confidence with abstractions, they are led to further developments in group and ring theory (simple groups and extensions, Noetherian rings, and outline of universal algebra, lattices and categories) and to applications such as Galois theory and coding theory. There is also a chapteroutlining the construction of the number systems from scratch and proving in three different ways that trascendental numbers exist.