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.
FREE Two-Day Shipping for students on millions of items. Learn more |
Book Description
Editorial Reviews
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
Product Details
Would you like to update product info or give feedback on images?
|
Customer Reviews
|
Share your thoughts with other customers:
|
||||||||||||||||||||||
|
Most Helpful Customer Reviews
6 of 6 people found the following review helpful:
5.0 out of 5 stars
A good presentation of the theory of partially ordered sets,
By
This review is from: Basic Posets (Hardcover)
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.
3 of 3 people found the following review helpful:
3.0 out of 5 stars
Good coverage, poor editing,
By
This review is from: Basic Posets (Hardcover)
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.
Share your thoughts with other customers: Create your own review
|
|
Front Cover | Front Flap | Table of Contents | First Pages | Index | Back Flap | Back Cover | Surprise Me!
Inside This Book
(learn more)
First Sentence:
Partially ordered sets (posets) have a long history beginning with the first recognition of ordering in the integers. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
full subposet, connected poset, labeled poset, order preserving mapping, poset morphisms, new posets, natural labeling, finite poset, poset structure, weak inclusion, ordinal sum, two posets, given poset, maximal antichain, preserving mappings, linear extensions, incomparable elements New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Front Flap | Table of Contents | First Pages | Index | Back Flap | Back Cover | Surprise Me!
Partially ordered sets (posets) have a long history beginning with the first recognition of ordering in the integers. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
full subposet, connected poset, labeled poset, order preserving mapping, poset morphisms, new posets, natural labeling, finite poset, poset structure, weak inclusion, ordinal sum, two posets, given poset, maximal antichain, preserving mappings, linear extensions, incomparable elements New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Front Flap | Table of Contents | First Pages | Index | Back Flap | Back Cover | Surprise Me!
Citations (learn more)
This book cites 5
books:
1
book
cites this book:
- Ordered Sets (NATO Science Series C: (closed)) by Ivan Rival in Back Matter (1), and Back Matter (2)
- Introduction to Lattices and Order by B. A. Davey in Back Matter
- Combinatorial Theory (Classics in Mathematics) by Martin Aigner in Back Matter
- Combinatorics and Partially Ordered Sets: Dimension Theory (Johns Hopkins Studies in the Mathematical Sciences) by William T. Trotter in Back Matter
- Enumerative Combinatorics, Volume 2 by Richard P. Stanley in Back Matter
- Ordered Sets by Bernd Schröder in Back Matter
Tag this product(What's this?)Think of a tag as a keyword or label you consider is strongly related to this product.
Tags will help all customers organize and find favorite items. |
Sell a Digital Version of This Book in the Kindle Store
If you are a publisher or author and hold the digital rights to a book, you can sell a digital version of it in our Kindle Store.
Learn more
Customer Discussions
|
This product's forum
Active discussions in related forums
Search Customer Discussions
|
Related forums
|
