Combinatorial Optimization: Networks and Matroids

Combinatorial Optimization: Networks and Matroids
~
Lawler E.L.

Perceptively written text examines optimization problems that can be formulated in terms of networks and algebraic structures called matroids. Chapters cover shortest paths, network flows, bipartite matching, nonbipartite matching, matroids and the greedy algorithm, matroid intersections, and the matroid parity problems. A suitable text or reference for courses in combinatorial computing and concrete computational complexity in departments of computer science and mathematics.

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Arrangements of curves in the plane- topology, combinatorics, and algorithms (1988)

Arrangements of curves in the plane- topology, combinatorics, and algorithms (1988)
~
Edelsbrunner, Herbert; Pach, Janos; Pollack, Richard; Sharir, Micha

Publisher: New York: Courant Institute of Mathematical Sciences, New York University
Possible copyright status: NOT_IN_COPYRIGHT
Language: English
Call number: 13602251
Digitizing sponsor: Sloan Foundation
Book contributor: New York University, Institute of Fine Arts Library

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The Canterbury puzzles, and other curious problems (1908)

The Canterbury puzzles, and other curious problems (1908)
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Dudeney, Henry Ernest, (1857-1930.)

Publisher: New York : E. P. Dutton and co.
Language: English
Call number: GV1493.D8
Digitizing sponsor: Internet Archive
Book contributor: University of California Berkeley

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An Introduction to Computational Combinatorics (Cambridge Computer Science Texts - 9)

An Introduction to Computational Combinatorics (Cambridge Computer Science Texts - 9)
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Page E.S., Wilson L.B.

Product Description
By the time students have done some programming in one or two languages and have learnt the common ways of representing information in a computer, they will want to embark upon further study of theoretical or applied topics in computer science. Most will encounter problems that require for their solution one or more of the techniques described in this book: for example problems depending upon the formation and solution of different equations; the task of making lists of possible alternatives and of answering questions about them; or the search for discrete optima. Written by the same authors as the highly successful Information Representation and Manipulation in a Computer, this book describes algorithms of mathematical methods and illustrates their application with examples. The mathematical background needed is elementary algebra and calculus. Numerous exercises are provided, with hints to their solutions.


Book Description
Written by the same authors as the highly successful Information Representation and Manipulation in a Computer, this book describes algorithms of mathematical methods and illustrates their application with examples. The mathematical background needed is elementary algebra and calculus. Numerous exercises are provided, with hints to their solutions.
Product Details

* Paperback: 228 pages
* Publisher: Cambridge University Press (May 31, 1979)
* Language: English
* ISBN-10: 0521294924
* ISBN-13: 978-0521294928

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Enumerative Combinatorics: Volume 1, 2nd Edition

Enumerative Combinatorics: Volume 1, 2nd Edition
by: Richard P. Stanley

Details

* Publisher: Cambridge University Press
* Number Of Pages: 326
* Publication Date: 2000-05
* Sales Rank: 254841
* ISBN / ASIN: 0521663512
* EAN: 9780521663519
* Binding: Paperback
* Manufacturer: Cambridge University Press
* Studio: Cambridge University Press
* Average Rating: 5
* Total Reviews: 3

Description

This book, the first of a two-volume basic introduction to enumerative combinatorics, concentrates on the theory and application of generating functions, a fundamental tool in enumerative combinatorics. Richard Stanley covers those parts of enumerative combinatorics with the greatest applications to other areas of mathematics. The four chapters are devoted to an accessible introduction to enumeration, sieve methods--including the Principle of Inclusion-Exclusion, partially ordered sets, and rational generating functions. A large number of exercises, almost all with solutions, augment the text and provide entry into many areas not covered directly. Graduate students and research mathematicians who wish to apply combinatorics to their work will find this an authoritative reference.

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Introduction to Combinatorics

Introduction to Combinatorics
by: Gerald Berman

Details

# Publisher: Academic Pr
# Number Of Pages: 300
# Publication Date: 1972-05
# Sales Rank: 1933899
# ISBN / ASIN: 0120927500
# EAN: 9780120927500
# Binding: Hardcover
# Manufacturer: Academic Pr
# Studio: Academic Pr
# Average Rating:
# Total Reviews:

Description

Combinatorics, or discrete mathematics, and its applications are becoming increasingly important. Polya has said that Combinatorics is an experimental science today just as analysis was decades ago. It is well that students encounencounter this branch of mathematics at an early level so that they may appreciate that Combinatorics has become a partner with traditional mathematics and with computer science. This book is written to provide an introductory course at the sophomore or junior level.

Because there is so much elementary Combinatorics it is not necessary to wait until the senior years to study the subject. Extensive prerequisites are not necessary. Some knowledge of permutations and combinations, mathematical induction, the binomial theorem, and set theory will allow the student to investigate a host of combinatorial problems and applications. Matrices and determinants are useful but are not prerequisites at the level of this book.


It is possible to- select topics which present to the student some quite challenging mathematics. Indeed, in offering him a kaleidoscope of interesting and easily understood topics, chosen to appeal to his imagination, it is often possible to point to some current related research. In addition, a beginning course in these areas can have considerable charm. Its charm does not come from a lack of discipline in the course but from the mathematics involved.

Much Combinatorics has arisen from games and puzzles. Giants such as Gauss, Euler, and Hamilton were interested in puzzles and J. L. Synge has said " The mind is at its best when at play." It is not inappropriate to exploit this point of view in an introductory combinatorics course, again, one hopes stimulating an increase in interest in Mathematics on the part of the student.

A formal definition of Combinatorics is difficult to formulate. Combinatorial problems occur in every branch of mathematics. Roughly speaking, Combinatorics is a study of the arrangements of elements into sets and deals with two general types of problems, enumeration and existence. Recent activity in Combinatorics has been stimulated by applications to other subjects. Thus it seemed logical to us to organize this book into three sections, Enumeration, Existence, and Applications. These three sections follow a chapter of introductory examples. Each of these sections has its own introduction which the reader may consult for further information.

The authors have provided more material than normally can be covered in a term course so that the instructor using the book will have considerable latitude in selecting his course content.

The book is primarily problem-oriented. Exercises appear at the end of each section. We believe that mathematics can be learned only by doing mathematics and this involves the solution of a wide range of problems. In offering a course using this text we have found that formal lectures are not
always necessary. We have experimented successfully with the group method. The class has been divided into groups of five students, each group with a leader from among the five students. The groups have spent classroom hours primarily discussing theory and working problems, with supplementary lectures from time to time, where deemed necessary. Graduate students have been available both in the classroom and outside at specified tutorial hours to help group leaders prepare for their next class discussion or to clear up unsolved problems. It is our hope that the students gain more understanding from this active involvement in the class structure.
In order that this book be readable and, we hope, of interest to and useable by a wide range of students, we have written with an approach somewhere between the intuitive and the rigorous, but much closer to the former.

We have discussed theorems, for example, in a number of different ways. Some we have proved formally; more have been presented informally. Occasionally proofs are demonstrated by examples which give all the steps and reasoning necessary for a formal proof and the reader is asked to com-
complete many of these in the Exercises. Some difficult theorems are stated without proof but with references given.
Combinatorics has become an important tool of the computer scientist. For this reason we have attempted to provide problems that could be of interest to the student of computer science. These problems can be omitted by students who do not have access to a computer without loss of comprehen-
comprehension in the rest of the course. A course based on this book can be useful not only to the student of computer science and to the mathematics major but also to the student in liberal arts or social science, especially in economics and psychology where Combinatorics is beginning to play an important role.
Finally, we hope that this book will be to many students what the title
states, an introduction to Combinatorics, which will lead him to a desire to learn more about this fascinating subject.

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A Walk Through Combinatorics: An Introduction to Enumeration and Graph Theory (Second Edition)

A Walk Through Combinatorics: An Introduction to Enumeration and Graph Theory (Second Edition)
by: Miklos Bona

Details

* Publisher: World Scientific Publishing Company
* Number Of Pages: 492
* Publication Date: 2006-10-09
* ISBN-10 / ASIN: 9812568859
* ISBN-13 / EAN: 9789812568854
* Binding: Hardcover

Description

This is a textbook for an introductory combinatorics course that can take up one or two semesters. An extensive list of exercises, ranging in difficulty from "routine" to "worthy of independent publication", is included. In each section, there are also exercises that contain material not explicitly discussed in the text before, so as to provide instructors with extra choices if they want to shift the emphasis of their course.

It goes without saying that the text covers the classic areas, i.e. combinatorial choice problems and graph theory. What is unusual, for an undergraduate textbook, is that the author has included a number of more elaborate concepts, such as Ramsey theory, the probabilistic method and - probably the first of its kind - pattern avoidance. While the reader can only skim the surface of these areas, the author believes that they are interesting enough to catch the attention of some students. As the goal of the book is to encourage students to learn more combinatorics, every effort has been made to provide them with a not only useful, but also enjoyable and engaging reading.

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