Discover the Connections between Different Structures and Fields Discrete Structures and Their Interactions highlights the connections among various discrete structures, including graphs, directed graphs, hypergraphs, partial orders, finite topologies, and simplicial complexes. It also explores their relationships to classical areas of mathematics, such as linear and multilinear algebra, analysis, probability, logic, and topology.
The text introduces a number of discrete structures, such as hypergraphs, finite topologies, preorders, simplicial complexes, and order ideals of monomials, that most graduate students in combinatorics, and even some researchers in the field, seldom experience. The author explains how these structures have important applications in many areas inside and outside of combinatorics. He also discusses how to recognize valuable research connections through the structures.
Intended for graduate and upper-level undergraduate students in mathematics who have taken an initial course in discrete mathematics or graph theory, this book shows how discrete structures offer new insights into the classical fields of mathematics. It illustrates how to use discrete structures to represent the salient features and discover the underlying combinatorial principles of seemingly unrelated areas of mathematics.
Jason I. Brown
CRC Press Inc
Country of Publication:
Series: Discrete Mathematics and Its Applications
24 June 2013
Introduction Sets Sequences Asymptotics Computational Complexity Discrete Structures-A Common Framework Isomorphism Substructures Properties, Parameters and Operations Representations and Models Graphs and Directed Graphs Graphs and Directed Graphs as Models Graphs and Other Branches of Mathematics Preorders and Partial Orders Finite Topologies and Preorders Representing Preorders and Partial Orders Hypergraphs Applying Hypergraphs Modeling Hypergraphs Complexes and Multicomplexes Representations of Complexes and Multicomplexes Applications of Complexes and Multicomplexes Research Problems Bibliography Selected Solutions Appendix A Set Theory Appendix B Matrix Theory and Linear Algebra Appendix C Abstract Algebra Appendix D Probability Appendix E Topology Appendix F Logic Index
Jason I. Brown is a professor of mathematics at Dalhousie University. He received a Ph.D. from the University of Toronto and has written over 70 refereed articles. His research interests include graphs, hypergraphs, partial order, finite topologies, and simplicial complexes, with a focus on the applications of other fields of mathematics to discrete problems. His mathematical research that uncovered how the Beatles played the opening chord of A Hard Day's Night was featured in various media, including NPR and BBC radio, Guitar Player Magazine, and the Wall Street Journal website.
Reviews for Discrete Structures and Their Interactions
The book is a collection of examples, each of which shows either how discrete structures interact with each other or how discrete structures interact with other parts of mathematics. ... I am certain I will use some examples I found in this book when I teach combinatorics in the upcoming semester. -Miklos Bona, MAA Reviews, December 2013