Books in Discrete mathematics combinatorics

Latin Squares and their Applications

2nd Edition
July 24, 2015
A. Donald Keedwell + 1 more
English
Hardback
9 7 8 0 4 4 4 6 3 5 5 5 6

Latin Squares and Their Applications, Second edition offers a long-awaited update and reissue of this seminal account of the subject. The revision retains foundational, original material from the frequently-cited 1974 volume but is completely updated throughout. As with the earlier version, the author hopes to take the reader ‘from the beginnings of the subject to the frontiers of research’. By omitting a few topics which are no longer of current interest, the book expands upon active and emerging areas. Also, the present state of knowledge regarding the 73 then-unsolved problems given at the end of the first edition is discussed and commented upon. In addition, a number of new unsolved problems are proposed. Using an engaging narrative style, this book provides thorough coverage of most parts of the subject, one of the oldest of all discrete mathematical structures and still one of the most relevant. However, in consequence of the huge expansion of the subject in the past 40 years, some topics have had to be omitted in order to keep the book of a reasonable length. Latin squares, or sets of mutually orthogonal latin squares (MOLS), encode the incidence structure of finite geometries; they prescribe the order in which to apply the different treatments in designing an experiment in order to permit effective statistical analysis of the results; they produce optimal density error-correcting codes; they encapsulate the structure of finite groups and of more general algebraic objects known as quasigroups. As regards more recreational aspects of the subject, latin squares provide the most effective and efficient designs for many kinds of games tournaments and they are the templates for Sudoku puzzles. Also, they provide a number of ways of constructing magic squares, both simple magic squares and also ones with additional properties.

Algebraic and Discrete Mathematical Methods for Modern Biology

1st Edition
March 25, 2015
Raina Robeva
English
Hardback
9 7 8 0 1 2 8 0 1 2 1 3 0
eBook
9 7 8 0 1 2 8 0 1 2 7 1 0

Written by experts in both mathematics and biology, Algebraic and Discrete Mathematical Methods for Modern Biology offers a bridge between math and biology, providing a framework for simulating, analyzing, predicting, and modulating the behavior of complex biological systems. Each chapter begins with a question from modern biology, followed by the description of certain mathematical methods and theory appropriate in the search of answers. Every topic provides a fast-track pathway through the problem by presenting the biological foundation, covering the relevant mathematical theory, and highlighting connections between them. Many of the projects and exercises embedded in each chapter utilize specialized software, providing students with much-needed familiarity and experience with computing applications, critical components of the "modern biology" skill set. This book is appropriate for mathematics courses such as finite mathematics, discrete structures, linear algebra, abstract/modern algebra, graph theory, probability, bioinformatics, statistics, biostatistics, and modeling, as well as for biology courses such as genetics, cell and molecular biology, biochemistry, ecology, and evolution.

Applied Finite Mathematics

1st Edition
May 10, 2014
Howard Anton + 1 more
English
eBook
9 7 8 1 4 8 3 2 7 1 3 7 8

Applied Finite Mathematics presents the fundamentals of finite mathematics in a style tailored for beginners, but at the same time covers the subject matter in sufficient depth so that the student can see a rich variety of realistic and relevant applications. Applications in fields such as business, biology, behavioral sciences, and social sciences are included. Comprised of nine chapters, this book begins with an introduction to set theory, explaining concepts such as sets and union and intersection of sets as well as counting elements in sets. The next chapter deals with coordinate systems and graphs, along with applications of linear equations and graphs of linear inequalities. The discussion then turns to linear programming; matrices and linear systems; probability; and statistics. Examples of applications are given, including those of game theory, Markov chains, and probability. The final chapter is devoted to computers and programming languages such as FORTRAN. This monograph is intended for students and instructors of applied mathematics.

Progress in Combinatorial Optimization

1st Edition
May 10, 2014
William R. Pulleyblank
English
eBook
9 7 8 1 4 8 3 2 6 4 5 3 0

Progress in Combinatorial Optimization provides information pertinent to the fundamental aspects of combinatorial optimization. This book discusses how to determine whether or not a particular structure exists. Organized into 21 chapters, this book begins with an overview of a polar characterization of facets of polyhedra obtained by lifting facets of lower dimensional polyhedra. This text then discusses how to obtain bounds on the value of the objective in a graph partitioning problem in terms of spectral information about the graph. Other chapters consider the notion of a triangulation of an oriented matroid and show that oriented matroid triangulation yield triangulations of the underlying polytopes. This book discusses as well the selected results and problems on perfect ad imperfect graphs. The final chapter deals with the weighted parity problem for gammoids, which can be reduced to the weighted graphic matching problem. This book is a valuable resource for mathematicians and research workers.

Random Graphs '83

1st Edition
Volume 28
October 10, 2011
A. Rucinski + 1 more
English
eBook
9 7 8 0 0 8 0 8 7 2 2 9 2

The range of random graph topics covered in this volume includes structure, colouring, algorithms, mappings, trees, network flows, and percolation. The papers also illustrate the application of probability methods to Ramsey's problems, the application of graph theory methods to probability, and relations between games on graphs and random graphs.

Studies in Integer Programming

1st Edition
Volume 1
October 10, 2011
Peter L. Hammer
English
eBook
9 7 8 0 0 8 0 8 6 7 6 4 9

Advances in Graph Theory

1st Edition
Volume 3
October 10, 2011
B. Bollobás
English
eBook
9 7 8 0 0 8 0 8 6 7 6 6 3

Algorithmic Aspects of Combinatorics

1st Edition
Volume 2
October 10, 2011
B. Alspach + 2 more
English
eBook
9 7 8 0 0 8 0 8 6 7 6 5 6

Surveys in Combinatorial Optimization

1st Edition
Volume 31
September 22, 2011
S. Martello + 3 more
English
eBook
9 7 8 0 0 8 0 8 7 2 4 3 8

A collection of papers surveying recent progress in the field of Combinatorial Optimization.Topics examined include theoretical and computational aspects (Boolean Programming, Probabilistic Analysis of Algorithms, Parallel Computer Models and Combinatorial Algorithms), well-known combinatorial problems (such as the Linear Assignment Problem, the Quadratic Assignment Problem, the Knapsack Problem and Steiner Problems in Graphs) and more applied problems (such as Network Synthesis and Dynamic Network Optimization, Single Facility Location Problems on Networks, the Vehicle Routing Problem and Scheduling Problems).

Random Graphs '85

1st Edition
Volume 33
September 22, 2011
M. Karonski + 1 more
English
eBook
9 7 8 0 0 8 0 8 7 2 5 5 1

Covering a wide range of Random Graphs subjects, this volume examines series-parallel networks, properties of random subgraphs of the n-cube, random binary and recursive trees, random digraphs, induced subgraphs and spanning trees in random graphs as well as matchings, hamiltonian cycles and closure in such structures. Papers in this collection also illustrate various aspects of percolation theory and its applications, properties of random lattices and random walks on such graphs, random allocation schemes, pseudo-random graphs and reliability of planar networks. Several open problems that were presented during a special session at the Seminar are also included at the end of the volume.

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