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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.
Combinatorial analysis --- Analyse combinatoire --- Combinatorial analysis. --- Combinatorics --- Algebra --- Mathematical analysis
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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.
Algebra, Abstract. --- Algèbre abstraite --- Algebra, Abstract --- 512.5 --- General algebra --- 512.5 General algebra --- Algèbre abstraite --- Abstract algebra --- Algebra, Universal --- Logic, Symbolic and mathematical --- Set theory
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Block designs. --- Coding theory. --- Graph theory. --- Discrete mathematics --- 519.12 --- Block designs --- Coding theory --- Graph theory --- Graphs, Theory of --- Theory of graphs --- Combinatorial analysis --- Topology --- Data compression (Telecommunication) --- Digital electronics --- Information theory --- Machine theory --- Signal theory (Telecommunication) --- Computer programming --- Designs, Block --- Combinatorial designs and configurations --- Experimental design --- 519.12 Permutations in general. Groups where order is taken into account --- Permutations in general. Groups where order is taken into account --- Extremal problems --- Codage --- Théorie des graphes --- CODING THEORY --- Graphes, Théorie des --- Block design
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