Discrete Structures and Their Interactions (Hardcover)

Jason I. Brown

商品描述

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.

商品描述(中文翻譯)

「發現不同結構和領域之間的聯繫」

《離散結構及其相互作用》強調了各種離散結構之間的聯繫,包括圖、有向圖、超圖、偏序、有限拓撲和單體複合體。它還探討了它們與線性和多線性代數、分析、概率、邏輯和拓撲等經典數學領域的關係。

本書介紹了一些離散結構,如超圖、有限拓撲、預序、單體複合體和單項式的順序理想,這些結構在組合學的研究生和一些研究人員中很少接觸到。作者解釋了這些結構在組合學內外的許多領域中具有重要應用。他還討論了如何通過這些結構來識別有價值的研究聯繫。

本書面向已修過離散數學或圖論初級課程的研究生和高年級本科生,展示了離散結構如何為傳統數學領域提供新的見解。它演示了如何使用離散結構來表示重要特徵並發現看似無關的數學領域的基本組合原理。