A textbook suitable for undergraduate courses. The materials are presented very explicitly so that students will find it very easy to read. A wide range of examples, about 500 combinatorial problems taken from various mathematical competitions and exercises are also included.

Author: Peter J. Cameron
Publisher: Cambridge University Press
ISBN: 9781107393370
Release Date: 1994-10-06
Genre: Mathematics

Combinatorics is a subject of increasing importance, owing to its links with computer science, statistics and algebra. This is a textbook aimed at second-year undergraduates to beginning graduates. It stresses common techniques (such as generating functions and recursive construction) which underlie the great variety of subject matter and also stresses the fact that a constructive or algorithmic proof is more valuable than an existence proof. The book is divided into two parts, the second at a higher level and with a wider range than the first. Historical notes are included which give a wider perspective on the subject. More advanced topics are given as projects and there are a number of exercises, some with solutions given.

Author: George E. Martin
Publisher: Springer Science & Business Media
ISBN: 9781475748789
Release Date: 2013-03-09
Genre: Mathematics

This book provides an introduction to discrete mathematics. At the end of the book the reader should be able to answer counting questions such as: How many ways are there to stack n poker chips, each of which can be red, white, blue, or green, such that each red chip is adjacent to at least 1 green chip? The book can be used as a textbook for a semester course at the sophomore level. The first five chapters can also serve as a basis for a graduate course for in-service teachers.

Author: J. H. van Lint
Publisher: Cambridge University Press
ISBN: 0521006015
Release Date: 2001-11-22
Genre: Mathematics

This is the second edition of a popular book on combinatorics, a subject dealing with ways of arranging and distributing objects, and which involves ideas from geometry, algebra and analysis. The breadth of the theory is matched by that of its applications, which include topics as diverse as codes, circuit design and algorithm complexity. It has thus become essential for workers in many scientific fields to have some familiarity with the subject. The authors have tried to be as comprehensive as possible, dealing in a unified manner with, for example, graph theory, extremal problems, designs, colorings and codes. The depth and breadth of the coverage make the book a unique guide to the whole of the subject. The book is ideal for courses on combinatorical mathematics at the advanced undergraduate or beginning graduate level. Working mathematicians and scientists will also find it a valuable introduction and reference.

Berge's Principles of Combinatorics is now an acknowledged classic work of the field. Complementary to his previous books, Berge's introduction deals largely with enumeration. The choice of topics is balanced, the presentation elegant, and the text can be followed by anyone with an interest in the subject with only a little algebra required as a background. Some topics were here described for the first time, including Robinston-Shensted theorum, the Eden-Schutzenberger theorum, and facts connecting Young diagrams, trees, and the symmetric group.

Introductory text surveys the theory of permutations and combinations associated with elementary algebra; the principle of inclusion and exclusion; and the theory of distributions and partitions in cyclic representation. Includes problems. 1958 edition.

Suitable for an introductory combinatorics course lasting one or two semesters, this book includes an extensive list of problems, ranging from routine exercises to research questions. It walks the reader through the classic parts of combinatorial enumeration and graph theory, while also discussing some the progress made in the area.

The aim of this book is to introduce a range of combinatorial methods for those who want to apply these methods in the solution of practical and theoretical problems. Various tricks and techniques are taught by means of exercises. Hints are given in a separate section and a third section contains all solutions in detail. A dictionary section gives definitions of the combinatorial notions occurring in the book. Combinatorial Problems and Exercises was first published in 1979. This revised edition has the same basic structure but has been brought up to date with a series of exercises on random walks on graphs and their relations to eigenvalues, expansion properties and electrical resistance. In various chapters the author found lines of thought that have been extended in a natural and significant way in recent years. About 60 new exercises (more counting sub-problems) have been added and several solutions have been simplified.

Author: Jonathan L. Gross
Publisher: CRC Press
ISBN: 9781584887447
Release Date: 2016-04-19
Genre: Mathematics

Combinatorial Methods with Computer Applications provides in-depth coverage of recurrences, generating functions, partitions, and permutations, along with some of the most interesting graph and network topics, design constructions, and finite geometries. Requiring only a foundation in discrete mathematics, it can serve as the textbook in a combinatorial methods course or in a combined graph theory and combinatorics course. After an introduction to combinatorics, the book explores six systematic approaches within a comprehensive framework: sequences, solving recurrences, evaluating summation expressions, binomial coefficients, partitions and permutations, and integer methods. The author then focuses on graph theory, covering topics such as trees, isomorphism, automorphism, planarity, coloring, and network flows. The final chapters discuss automorphism groups in algebraic counting methods and describe combinatorial designs, including Latin squares, block designs, projective planes, and affine planes. In addition, the appendix supplies background material on relations, functions, algebraic systems, finite fields, and vector spaces. Paving the way for students to understand and perform combinatorial calculations, this accessible text presents the discrete methods necessary for applications to algorithmic analysis, performance evaluation, and statistics as well as for the solution of combinatorial problems in engineering and the social sciences.

Useful guide covers two major subdivisions of combinatorics — enumeration and graph theory — with emphasis on conceptual needs of computer science. Each part is divided into a "basic concepts" chapter emphasizing intuitive needs of the subject, followed by four "topics" chapters that explore these ideas in depth. Invaluable practical resource for graduate students, advanced undergraduates, and professionals with an interest in algorithm design and other aspects of computer science and combinatorics. References for Linear Order & for Graphs, Trees, and Recursions. 219 figures.

Author: Alan Tucker
Publisher: Wiley Global Education
ISBN: 9781118210116
Release Date: 2012-01-09
Genre: Mathematics

The new 6th edition of Applied Combinatorics builds on the previous editions with more in depth analysis of computer systems in order to help develop proficiency in basic discrete math problem solving. As one of the most widely used books in combinatorial problems, this edition explains how to reason and model combinatorically while stressing the systematic analysis of different possibilities, exploration of the logical structure of a problem, and ingenuity. Although important uses of combinatorics in computer science, operations research, and finite probability are mentioned, these applications are often used solely for motivation. Numerical examples involving the same concepts use more interesting settings such as poker probabilities or logical games.

Author: Theodore G. Faticoni
Publisher: John Wiley & Sons
ISBN: 9781118407486
Release Date: 2014-08-21
Genre: Mathematics

Bridges combinatorics and probability and uniquely includes detailed formulas and proofs to promote mathematical thinking Combinatorics: An Introduction introduces readers to counting combinatorics, offers examples that feature unique approaches and ideas, and presents case-by-case methods for solving problems. Detailing how combinatorial problems arise in many areas of pure mathematics, most notably in algebra, probability theory, topology, and geometry, this book provides discussion on logic and paradoxes; sets and set notations; power sets and their cardinality; Venn diagrams; the multiplication principal; and permutations, combinations, and problems combining the multiplication principal. Additional features of this enlightening introduction include: Worked examples, proofs, and exercises in every chapter Detailed explanations of formulas to promote fundamental understanding Promotion of mathematical thinking by examining presented ideas and seeing proofs before reaching conclusions Elementary applications that do not advance beyond the use of Venn diagrams, the inclusion/exclusion formula, the multiplication principal, permutations, and combinations Combinatorics: An Introduction is an excellent book for discrete and finite mathematics courses at the upper-undergraduate level. This book is also ideal for readers who wish to better understand the various applications of elementary combinatorics.