Faticoni

Bridges combinatorics and probability and uniquely includes detailed formulas and proofs to promote mathematical thinkingCombinatorics: An Introduction introduces readers to counting combinatorics, of

Praise for the First Edition". . . an enchanting book for those people in computer science or mathematics who are fascinated by the concept of infinity."—Computing Reviews". . . a very well writt

This is an extensive synthesis of recent work in the study of endomorphism rings and their modules, bringing together direct sum decompositions of modules, the class number of an algebraic number field, point set topological spaces, and classical noncommutative localization. The main idea behind the book is to study modules G over a ring R via their endomorphism ring EndR(G). The author discusses a wealth of results that classify G and EndR(G) via numerous properties, and in particular results from point set topology are used to provide a complete characterization of the direct sum decomposition properties of G. For graduate students this is a useful introduction, while the more experienced mathematician will discover that the book contains results that are not otherwise available. Each chapter contains a list of exercises and problems for future research, which provide a springboard for students entering modern professional mathematics.