Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

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

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Set theory, logic and category theory lie at the foundations of mathematics, and have a dramatic effect on the mathematics that we do, through the Axiom of Choice, Gödel's Theorem, and the Skolem Paradox. But they are also rich mathematical theories in their own right, contributing techniques and results to working mathematicians such as the Compactness Theorem and module categories. The book is aimed at those who know some mathematics and want to know more about its building blocks. Set theory is first treated naively an axiomatic treatment is given after the basics of first-order logic have been introduced. The discussion is su pported by a wide range of exercises. The final chapter touches on philosophical issues. The book is supported by a World Wibe Web site containing a variety of supplementary material.

Set theory --- Logic, symbolic and mathematical --- Categories (Mathematics) --- Logic, Symbolic and mathematical --- 510.6 --- 510.6 Mathematical logic --- Mathematical logic --- Aggregates --- Classes (Mathematics) --- Ensembles (Mathematics) --- Mathematical sets --- Sets (Mathematics) --- Theory of sets --- Mathematics --- Algebra of logic --- Logic, Universal --- Symbolic and mathematical logic --- Symbolic logic --- Algebra, Abstract --- Metamathematics --- Syllogism --- Category theory (Mathematics) --- Algebra, Homological --- Algebra, Universal --- Group theory --- Topology --- Functor theory --- Logic, Symbolic and mathematical. --- Logic, symbolic and mathematical. --- Categories (Mathematics). --- Set theory. --- Théorie des ensembles --- Logique symbolique et mathématique --- Catégories (Mathématiques) --- Mathematical logic. --- Category theory (Mathematics). --- Homological algebra. --- K-theory. --- Mathematical Logic and Foundations. --- Category Theory, Homological Algebra. --- K-Theory. --- Algebraic topology --- Homology theory --- Homological algebra

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This edition includes new material on updated and comprehensive introductory chapters, new material on axiom of choice, p-groups and local rings, discussion of theory and applications, and over 300 exercises.

Algebra, Abstract. --- Abstract algebra --- Algebra, Universal --- Logic, Symbolic and mathematical --- Set theory --- Algebra, Abstract

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

The study of permutation groups has always been closely associated with that of highly symmetric structures. The objects considered here are countably infinite, but have only finitely many different substructures of any given finite size. They are precisely those structures which are determined by first-order logical axioms together with the assumption of countability. This book concerns such structures, their substructures and their automorphism groups. A wide range of techniques are used: group theory, combinatorics, Baire category and measure among them. The book arose from lectures given at a research symposium and retains their informal style, whilst including as well many recent results from a variety of sources. It concludes with exercises and unsolved research problems.

Permutation groups. --- Substitution groups --- Group theory

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)