Discrete Structures and Their Interactions

ISBN-13: 9780367379858 / Angielski / Miękka / 2019 / 218 str.

Jason I. Brown

Opis

With exercises and research problems, this text 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 author explains how discrete structures have important applications in many areas inside and outside of combinatorics. He also discusses how to recognize valuable research connections through the structures.

Recenzje

"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."
—Miklós Bóna, MAA Reviews, December 2013

Spis treści

Introduction. Discrete Structures—A Common Framework. Graphs and Directed Graphs. Preorders and Partial Orders. Hypergraphs. Complexes and Multicomplexes. Research Problems. Bibliography. Selected Solutions. Appendices. Index.

O autorze

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.