Walter D. Wallis

What Is Combinatorics Anyway?Broadly speaking, combinatorics is the branch of mathematics dealingwith different ways of selecting objects from a set or arranging objects. Ittries to answer two major kinds of questions, namely, counting questions: how many ways can a selection or arrangement be chosen with a particular set of properties; and structural questions: does there exist a selection or arrangement of objects with a particular set of properties?The authors have presented a text for students at all levels of preparation.For some, this will be the first course where the students see several real proofs. Others will have a good background in linear algebra, will have completed the calculus stream, and will have started abstract algebra. The text starts by briefly discussing several examples of typical combinatorial problemsto give the reader a better idea of what the subject covers. The nextchapters explore enumerative ideas and also probability. It then moves on toenumerative functions and the relations between them, and generating functions and recurrences.,Important families of functions, or numbers and then theorems are presented. Brief introductions to computer algebra and group theory come next. Structures of particular interest in combinatorics: posets, graphs, codes, Latin squares, and experimental designs follow. Theauthors conclude with further discussion of the interaction between linear algebraand combinatorics.Features Two new chapters on probability and posets. Numerous new illustrations, exercises, and problems. More examples on current technology use A thorough focus on accuracy Three appendices: sets, induction and proof techniques, vectors and matrices, and biographies with historical notes, Flexible use of MapleTM and MathematicaTM

What Is Combinatorics Anyway?Broadly speaking, combinatorics is the branch of mathematics dealingwith different ways of selecting objects from a set or arranging objects. Ittries to answer two major kinds of questions, namely, counting questions: how many ways can a selection or arrangement be chosen with a particular set of properties; and structural questions: does there exist a selection or arrangement of objects with a particular set of properties?The authors have presented a text for students at all levels of preparation.For some, this will be the first course where the students see several real proofs. Others will have a good background in linear algebra, will have completed the calculus stream, and will have started abstract algebra. The text starts by briefly discussing several examples of typical combinatorial problemsto give the reader a better idea of what the subject covers. The nextchapters explore enumerative ideas and also probability. It then moves on toenumerative functions and the relations between them, and generating functions and recurrences.,Important families of functions, or numbers and then theorems are presented. Brief introductions to computer algebra and group theory come next. Structures of particular interest in combinatorics: posets, graphs, codes, Latin squares, and experimental designs follow. Theauthors conclude with further discussion of the interaction between linear algebraand combinatorics.Features Two new chapters on probability and posets. Numerous new illustrations, exercises, and problems. More examples on current technology use A thorough focus on accuracy Three appendices: sets, induction and proof techniques, vectors and matrices, and biographies with historical notes, Flexible use of MapleTM and MathematicaTM

Networks have become nearly ubiquitous and increasingly complex, and their support of modern enterprise environments has become fundamental. Accordingly, robust network management techniques are essential to ensure optimal performance of these networks. This monograph treats the application of numerous graph-theoretic algorithms to a comprehensive analysis of dynamic enterprise networks. Network dynamics analysis yields valuable information about network performance, efficiency, fault prediction, cost optimization, indicators and warnings. Based on many years of applied research of generic network dynamics, this work covers a number of elegant applications (including many new and experimental results) of traditional graph theory algorithms and techniques to computationally tractable network dynamics analysis to motivate network analysts, practitioners and researchers alike. The material is also suitable for graduate courses addressing state-of-the-art applications of graph theory in analysis of dynamic communication networks, dynamic databasing, and knowledge management.