Books in Discrete mathematics combinatorics

Handbook of Combinatorics

1st Edition
December 11, 1995
R.L. Graham
English
eBook
9 7 8 0 0 8 0 9 3 3 8 4 9

Discrete Mathematics

1st Edition
September 17, 1995
Amanda Chetwynd + 1 more
English
eBook
9 7 8 0 0 8 0 9 2 8 6 0 9

As an introduction to discrete mathematics, this text provides a straightforward overview of the range of mathematical techniques available to students. Assuming very little prior knowledge, and with the minimum of technical complication, it gives an account of the foundations of modern mathematics: logic; sets; relations and functions. It then develops these ideas in the context of three particular topics: combinatorics (the mathematics of counting); probability (the mathematics of chance) and graph theory (the mathematics of connections in networks).Worked examples and graded exercises are used throughout to develop ideas and concepts. The format of this book is such that it can be easily used as the basis for a complete modular course in discrete mathematics.

Threshold Graphs and Related Topics

1st Edition
Volume 56
September 13, 1995
N.V.R. Mahadev + 1 more
English
eBook
9 7 8 0 0 8 0 5 4 3 0 0 0

Threshold graphs have a beautiful structure and possess many important mathematical properties. They have applications in many areas including computer science and psychology. Over the last 20 years the interest in threshold graphs has increased significantly, and the subject continues to attract much attention.The book contains many open problems and research ideas which will appeal to graduate students and researchers interested in graph theory. But above all Threshold Graphs and Related Topics provides a valuable source of information for all those working in this field.

Combinatorial Problems and Exercises

2nd Edition
August 11, 1993
L. Lovász
English
eBook
9 7 8 0 0 8 0 9 3 3 0 9 2

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.

Theory of Convex Structures

1st Edition
Volume 50
August 2, 1993
M.L.J. van de Vel
English
eBook
9 7 8 0 0 8 0 9 3 3 1 0 8

Presented in this monograph is the current state-of-the-art in the theory of convex structures. The notion of convexity covered here is considerably broader than the classic one; specifically, it is not restricted to the context of vector spaces. Classical concepts of order-convex sets (Birkhoff) and of geodesically convex sets (Menger) are directly inspired by intuition; they go back to the first half of this century. An axiomatic approach started to develop in the early Fifties. The author became attracted to it in the mid-Seventies, resulting in the present volume, in which graphs appear side-by-side with Banach spaces, classical geometry with matroids, and ordered sets with metric spaces. A wide variety of results has been included (ranging for instance from the area of partition calculus to that of continuous selection). The tools involved are borrowed from areas ranging from discrete mathematics to infinite-dimensional topology.Although addressed primarily to the researcher, parts of this monograph can be used as a basis for a well-balanced, one-semester graduate course.

Quo Vadis, Graph Theory?

1st Edition
Volume 55
March 17, 1993
J. Gimbel + 2 more
English
eBook
9 7 8 0 0 8 0 8 6 7 9 5 3

Graph Theory (as a recognized discipline) is a relative newcomer to Mathematics. The first formal paper is found in the work of Leonhard Euler in 1736. In recent years the subject has grown so rapidly that in today's literature, graph theory papers abound with new mathematical developments and significant applications.As with any academic field, it is good to step back occasionally and ask Where is all this activity taking us?, What are the outstanding fundamental problems?, What are the next important steps to take?. In short, Quo Vadis, Graph Theory?. The contributors to this volume have together provided a comprehensive reference source for future directions and open questions in the field.

The Steiner Tree Problem

1st Edition
Volume 53
October 20, 1992
F.K. Hwang + 2 more
English
eBook
9 7 8 0 0 8 0 8 6 7 9 3 9

The Steiner problem asks for a shortest network which spans a given set of points. Minimum spanning networks have been well-studied when all connections are required to be between the given points. The novelty of the Steiner tree problem is that new auxiliary points can be introduced between the original points so that a spanning network of all the points will be shorter than otherwise possible. These new points are called Steiner points - locating them has proved problematic and research has diverged along many different avenues.This volume is devoted to the assimilation of the rich field of intriguing analyses and the consolidation of the fragments. A section has been given to each of the three major areas of interest which have emerged. The first concerns the Euclidean Steiner Problem, historically the original Steiner tree problem proposed by Jarník and Kössler in 1934. The second deals with the Steiner Problem in Networks, which was propounded independently by Hakimi and Levin and has enjoyed the most prolific research amongst the three areas. The Rectilinear Steiner Problem, introduced by Hanan in 1965, is discussed in the third part. Additionally, a forth section has been included, with chapters discussing areas where the body of results is still emerging.The collaboration of three authors with different styles and outlooks affords individual insights within a cohesive whole.

Combinatorics '90

1st Edition
Volume 52
August 17, 1992
A. Barlotti + 3 more
English
eBook
9 7 8 0 0 8 0 8 6 7 9 2 2

This volume forms a valuable source of information on recent developments in research in combinatorics, with special regard to the geometric point of view. Topics covered include: finite geometries (arcs, caps, special varieties in a Galois space; generalized quadrangles; Benz planes; foundation of geometry), partial geometries, Buekenhout geometries, transitive permutation sets, flat-transitive geometries, design theory, finite groups, near-rings and semifields, MV-algebras, coding theory, cryptography and graph theory in its geometric and design aspects.

Markov Processes

1st Edition
October 8, 1991
Daniel T. Gillespie
English
Hardback
9 7 8 0 1 2 2 8 3 9 5 5 9
eBook
9 7 8 0 0 8 0 9 1 8 3 7 2

Markov process theory is basically an extension of ordinary calculus to accommodate functions whos time evolutions are not entirely deterministic. It is a subject that is becoming increasingly important for many fields of science. This book develops the single-variable theory of both continuous and jump Markov processes in a way that should appeal especially to physicists and chemists at the senior and graduate level.

Truth, Possibility and Probability

1st Edition
Volume 166
June 20, 1991
R. Chuaqui
English
eBook
9 7 8 0 0 8 0 8 7 2 7 7 3

Anyone involved in the philosophy of science is naturally drawn into the study of the foundations of probability. Different interpretations of probability, based on competing philosophical ideas, lead to different statistical techniques, and frequently to mutually contradictory consequences.This unique book presents a new interpretation of probability, rooted in the traditional interpretation that was current in the 17th and 18th centuries. Mathematical models are constructed based on this interpretation, and statistical inference and decision theory are applied, including some examples in artificial intelligence, solving the main foundational problems. Nonstandard analysis is extensively developed for the construction of the models and in some of the proofs. Many nonstandard theorems are proved, some of them new, in particular, a representation theorem that asserts that any stochastic process can be approximated by a process defined over a space with equiprobable outcomes.

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