Applied Combinatorics 2/e (H) (絕)
- 20本以上，享 8.5折
售價
$
洽詢
- 一般書籍
- ISBN：9780130796035
- 作者：Fred Roberts, Barry Tesman
- 版次：2
- 年份：2005
- 出版商：Pearson Education
- 頁數/規格：824頁/精裝單色
書籍介紹
本書特色
Description
Applied Combinatorics provides readers with an extensive look at combinatorics. Covers many new detailed applications, including material on list colorings, expanding discussion of scheduling legislative committees, material on DNA sequence alignment, and material on cryptography. Includes a section dealing with stable marriages and their many modern applications, including the assignment of interns to hospitals, dynamic labor markets, and strategic behavior. Uses real applications from the current literature and the extensive modern literature citations. Covers problem-solving through a variety of exercises that test routine ideas, introduce new concepts and applications, or attempt to challenge the reader to use the combinatorial techniques developed. Ideal as an introduction to Combinatorics.
Applied Combinatorics provides readers with an extensive look at combinatorics. Covers many new detailed applications, including material on list colorings, expanding discussion of scheduling legislative committees, material on DNA sequence alignment, and material on cryptography. Includes a section dealing with stable marriages and their many modern applications, including the assignment of interns to hospitals, dynamic labor markets, and strategic behavior. Uses real applications from the current literature and the extensive modern literature citations. Covers problem-solving through a variety of exercises that test routine ideas, introduce new concepts and applications, or attempt to challenge the reader to use the combinatorial techniques developed. Ideal as an introduction to Combinatorics.
Features
New to This Edition
Some of the major changes in the second edition are the following:
- Its emphasis on applications from a variety of fields, the treatment of applications as major topics of their own rather than as isolated examples, and the use of applications from the current literature.
- Many examples, especially ones that tie in new topics with old ones and are revisited throughout the book.
- An emphasis on problem solving through a variety of exercises that test routine ideas, introduce new concepts and applications, or attempt to challenge the reader to use the combinatorial techniques developed. The book continues to be based on the philosophy that the best way to learn combinatorial mathematics, indeed any kind of mathematics, is through problem solving.
- A mix of difficulty in topics with careful annotation that makes it po...
New to This Edition
Some of the major changes in the second edition are the following:
- Chapter 1 (What is Combinatorics?): We have added major new material on list colorings, expanding discussion of scheduling legislative committees. List colorings are returned to in various places in the book.
- Chapter 2 (Basic Counting Rules): Section 2.16, that previously only discussed algorithmic methods for generating permutations, has been substantially expanded and broken into subsections. Section 2.18, that introduces the notion of "good algorithms" and NP-completeness, has been substantially rewritten and modernized. A new section on the pigeonhole principle has been added. The section consists of the material from Section 8.1 of the first edition and some of the material from Section 8.2, that deals with Ramsey theory. We have also added a substantial new section on inversion distance between permutations and the study of mutations in evolutionary biology.
- Chapter 3 (Introduction to Graph Theory): A major new subsection has been added to Section 3.3, the graph coloring section. This new subsection deals with the generalizations of graph coloring, such as multi-coloring and T-coloring, that have been motivated by practical problems such as mobile radio telephone problems, traffic phasing, and channel assignment. We have also introduced a major new subsection on phylogenetic tree reconstruction. Much of the material on Ramsey theory from Chapter 8 of the first edition, and not covered in Chapter 2, has been updated and presented in a new section.
- Chapter 4 (Relations): This chapter is brand new. Concepts of binary relations are defined and connected to digraphs. Orders are introduced using digraphs and relations, and parts of the new chapter deal with linear and weak orders; partial orders, linear extensions and dimension; chains and comparability graphs; lattices; boolean algebras; and switching functions and gate networks. The chapter is closely tied to applications ranging from information theory to utility theory to searching and sorting, as well as returning to the earlier applications such as switching functions. This chapter includes some applications not widely discussed in the combinatorics literature, such as preference, search engines, sequencing by hybridization, and psychophysical scaling. Examples based on Chapter 4 concepts have also been added to many subsequent chapters. Coverage of Chapter 4 can be delayed until after Chapter 11.
- Chapter 5 (Generating Functions and their Applications): In the first edition, this was Chapter 4. Many new concepts and examples introduced in earlier chapters are revisited here, for example, weak orders from Chapter 4 and list colorings from Chapter 3.
- Chapter 6 (Recurrence Relations): This was Chapter 5 in the first edition. New material on DNA sequence alignment has been added as has material on the "transposition average" of permutations.
- Chapter 7 (The Principle of Inclusion and Exclusion): This was Chapter 6 in the first edition. We have added major new material on cryptography and factoring integers throughout the chapter (and revisited it later in the book).
- Old Chapter 8 - 1st edition (Pigeonhole Principle): This chapter has been dropped, with important parts of the material added to Chapter 2 and other parts included from time to time throughout the book.
- Chapter 8 (The Polya Theory of Counting): This was Chapter 7 in the first edition. Some examples based on newly-added Chapter 4 concepts such as weak order run through the chapter. A subsection on automorphisms of graphs has been added and returned to throughout the chapter.
- Chapter 9 (Combinatorial Designs): Major additions to this chapter include a section on orthogonal arrays and cryptography, including authentication codes and secret sharing. There is also a new section on connections between modular arithmetic and the RSA cryptosystem and one on resolvable designs with applications to secret sharing. A new section on "Group Testing" includes applications to identifying defective products, screening diseases, mapping genomes, and satellite communication.
- Chapter 10 (Coding Theory): There is a new subsection on "consensus decoding" with connections to finding proteins in molecular sequences and there are added connections of error-correcting codes to compact disks. Material on "reading" DNA to produce proteins is also new.
- Chapter 11 (Existence Problems in Graph Theory): We have added new subsections to Section 11.2 that deal with the one-way street problem. These new subsections deal with recent results about orientations of square and annular grids reflecting different kinds of cities. We have-added a new subsection on testing for connectedness of truly massive graphs, arising from modern applications involving telecommunications traffic and web data. There is also a new subsection on sequencing DNA by hybridization.
- Chapter 12 (Matching and Covering): There are many new examples illustrating the concepts of this chapter, including examples involving smallpox vaccinations, sound systems, and oil drilling. We have introduced a new section dealing with stable marriages and their many modern applications, including the assignment of interns to hospitals, dynamic labor markets, and strategic behavior. A section on maximum-weight matching, that was in Chapter 13 of the first edition, has been moved to this chapter.
- Chapter 13 (Optimization Problems for Graphs and Networks): We have introduced a new subsection on Menger's Theorems. There are also many new examples throughout the chapter, addressing such problems as building evacuation, clustering and data mining, and distributed computing.
