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Basic Posets  무료배송

 
지은이 : Joseph Neggers,Hee Sik Kim
출판사 : World Scientific
판수 : 1 edition
페이지수 : 178
ISBN : 9810235895
예상출고일 : 입금확인후 2일 이내
주문수량 :
도서가격 : 30,000원 ( 무료배송 )
적립금 : 900 Point
     

 
An introduction to the theory of partially-ordered sets, or "posets". The text is presented in rather an informal manner, with examples and computations, which rely on the Hasse diagram to build graphical intuition for the structure of infinite posets. The proofs of a small number of theorems is included in the appendix. Important examples, especially the Letter N poset, which plays a role akin to that of the Petersen graph in providing a candidate counterexample to many propositions, are used repeatedly throughout the text.
1 Definitions and Examples
2 How to Represent a Poset
3 Poset Morphisms
4 Construction of New Posets from Old Rosets
5 Connectedness
6 Linear Extensions

Review


"The text is designed to be accessible to upper division undergraduates in mathematics or secondary mathematics education ... this text is appropriately presented, has good and appropriate examples, and makes the theory of posets accessible to better undergraduates." Mathematical Reviews
"This text proposes to present the pure or basic theory of partially ordered sets(posets) excluding related topics like lattice theory, graph theory, and combinatorics that involve the theory of posets but are not central to it. The text is designed to be accessible to upper division undergraduates in mathematics or mathematics education and is presented at an appropriate level. The material seems appropriately presented, and good and appropriate examples are included, making the theory of posets accessible to better undergraduates."


"The contents comprise a fairly comprehensive survey of the theory of posets.

Rigorous concepts and language from set theory and graph theory are used to convey the ideas. Much of the exposition is in the form of definitions and discussion, without devoting space to develop the theory from axioms. Informal arguments supporting theorems are presented, with formal proofs extracted into an appendix.

The text is not very dense, being typeset in what appears to be a 1 1/2 spaced format, ending up looking somewhat like a university thesis. Lots of graphics (often including Hasse diagrams embedded directly in the running text) are used to illustrate ideas. These are helpful for understanding.

The editing could be better--errata for the book would probably contain one error for every other page, but this doesn't overly hinder reading. You can generally spot an error and immediately know what the authors intended.

All of this leads to the feeling of the text being a "light" overview survey. A good set of references are provided if you end up needing to dig deeper into any of the concepts. The value of this book is, in my opinion, that it collects together in one spot, ideas from much of the literature on posets."
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