design theory second edition discrete mathematics and its applications

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Introduction To Combinatorial Designs Second Edition

Author : W.D. Wallis
ISBN : 9781584888390
Genre : Mathematics
File Size : 74. 7 MB
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Combinatorial theory is one of the fastest growing areas of modern mathematics. Focusing on a major part of this subject, Introduction to Combinatorial Designs, Second Edition provides a solid foundation in the classical areas of design theory as well as in more contemporary designs based on applications in a variety of fields. After an overview of basic concepts, the text introduces balanced designs and finite geometries. The author then delves into balanced incomplete block designs, covering difference methods, residual and derived designs, and resolvability. Following a chapter on the existence theorem of Bruck, Ryser, and Chowla, the book discusses Latin squares, one-factorizations, triple systems, Hadamard matrices, and Room squares. It concludes with a number of statistical applications of designs. Reflecting recent results in design theory and outlining several applications, this new edition of a standard text presents a comprehensive look at the combinatorial theory of experimental design. Suitable for a one-semester course or for self-study, it will prepare readers for further exploration in the field. To access supplemental materials for this volume, visit the author’s website at http://www.math.siu.edu/Wallis/designs

Design Theory

Author : Charles C. Lindner
ISBN : 1420082973
Genre : Mathematics
File Size : 51. 1 MB
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Design Theory, Second Edition presents some of the most important techniques used for constructing combinatorial designs. It augments the descriptions of the constructions with many figures to help students understand and enjoy this branch of mathematics. This edition now offers a thorough development of the embedding of Latin squares and combinatorial designs. It also presents some pure mathematical ideas, including connections between universal algebra and graph designs. The authors focus on several basic designs, including Steiner triple systems, Latin squares, and finite projective and affine planes. They produce these designs using flexible constructions and then add interesting properties that may be required, such as resolvability, embeddings, and orthogonality. The authors also construct more complicated structures, such as Steiner quadruple systems. By providing both classical and state-of-the-art construction techniques, this book enables students to produce many other types of designs.

An Introduction To Incidence Geometry

Author : Bart De Bruyn
ISBN : 9783319438115
Genre : Mathematics
File Size : 75. 1 MB
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This book gives an introduction to the field of Incidence Geometry by discussing the basic families of point-line geometries and introducing some of the mathematical techniques that are essential for their study. The families of geometries covered in this book include among others the generalized polygons, near polygons, polar spaces, dual polar spaces and designs. Also the various relationships between these geometries are investigated. Ovals and ovoids of projective spaces are studied and some applications to particular geometries will be given. A separate chapter introduces the necessary mathematical tools and techniques from graph theory. This chapter itself can be regarded as a self-contained introduction to strongly regular and distance-regular graphs. This book is essentially self-contained, only assuming the knowledge of basic notions from (linear) algebra and projective and affine geometry. Almost all theorems are accompanied with proofs and a list of exercises with full solutions is given at the end of the book. This book is aimed at graduate students and researchers in the fields of combinatorics and incidence geometry.

A Student S Guide To The Study Practice And Tools Of Modern Mathematics

Author : Donald Bindner
ISBN : 9781439846070
Genre : Mathematics
File Size : 28. 61 MB
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A Student’s Guide to the Study, Practice, and Tools of Modern Mathematics provides an accessible introduction to the world of mathematics. It offers tips on how to study and write mathematics as well as how to use various mathematical tools, from LaTeX and Beamer to Mathematica® and MapleTM to MATLAB® and R. Along with a color insert, the text includes exercises and challenges to stimulate creativity and improve problem solving abilities. The first section of the book covers issues pertaining to studying mathematics. The authors explain how to write mathematical proofs and papers, how to perform mathematical research, and how to give mathematical presentations. The second section focuses on the use of mathematical tools for mathematical typesetting, generating data, finding patterns, and much more. The text describes how to compose a LaTeX file, give a presentation using Beamer, create mathematical diagrams, use computer algebra systems, and display ideas on a web page. The authors cover both popular commercial software programs and free and open source software, such as Linux and R. Showing how to use technology to understand mathematics, this guide supports students on their way to becoming professional mathematicians. For beginning mathematics students, it helps them study for tests and write papers. As time progresses, the book aids them in performing advanced activities, such as computer programming, typesetting, and research.

Design Theory

Author : Thomas Beth
ISBN : 0521444322
Genre : Mathematics
File Size : 21. 16 MB
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This is the first volume of a two-volume text on design theory. Since the first edition, there has been extensive development of the theory. In particular, the growing importance of discrete mathematics to many parts of engineering and science has made designs a useful tool for applications. The authors acknowledge this trend with an additional chapter on applications. It is suitable for advanced courses and as a reference work, not only for researchers in discrete mathematics or finite algebra, but also for those working in computer and communications engineering. The book features exercises throughout and concludes with an extensive and updated bibliography of over 1800 entries.

Graph Theory And Its Applications Second Edition

Author : Jonathan L. Gross
ISBN : 0849339820
Genre : Mathematics
File Size : 90. 16 MB
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Interest in graphs and their applications has grown tremendously in recent years-largely due to the usefulness of graphs as models for computation and optimization. This comprehensive, applications-driven text provides a fresh and accessible approach suitable for several different courses in graph theory. Written for graduate and advanced undergraduate students, for self-study, and as a reference for working professionals, it covers a wide range of topics in algorithmic, combinatorial, and topological graph theory. The authors present numerous applications and examples designed to stimulate interest in and demonstrate the relevance of new concepts. With its generous use of drawings, streamlined proofs, and concise algorithms, Graph Theory and Its Applications offers a less intimidating treatment of the subject. It also includes more than 1,600 exercises-from routine to challenging-providing a rich source of problems that test your understanding. In this text, the authors succeed in presenting the subject in a cohesive framework that transforms important techniques and analytic tools into a unified mathematical methodology.

Pearls Of Discrete Mathematics

Author : Martin Erickson
ISBN : 9781439816172
Genre : Computers
File Size : 85. 68 MB
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Methods Used to Solve Discrete Math Problems Interesting examples highlight the interdisciplinary nature of this area Pearls of Discrete Mathematics presents methods for solving counting problems and other types of problems that involve discrete structures. Through intriguing examples, problems, theorems, and proofs, the book illustrates the relationship of these structures to algebra, geometry, number theory, and combinatorics. Each chapter begins with a mathematical teaser to engage readers and includes a particularly surprising, stunning, elegant, or unusual result. The author covers the upward extension of Pascal’s triangle, a recurrence relation for powers of Fibonacci numbers, ways to make change for a million dollars, integer triangles, the period of Alcuin’s sequence, and Rook and Queen paths and the equivalent Nim and Wythoff’s Nim games. He also examines the probability of a perfect bridge hand, random tournaments, a Fibonacci-like sequence of composite numbers, Shannon’s theorems of information theory, higher-dimensional tic-tac-toe, animal achievement and avoidance games, and an algorithm for solving Sudoku puzzles and polycube packing problems. Exercises ranging from easy to challenging are found in each chapter while hints and solutions are provided in an appendix. With over twenty-five years of teaching experience, the author takes an organic approach that explores concrete problems, introduces theory, and adds generalizations as needed. He delivers an absorbing treatment of the basic principles of discrete mathematics.

Handbook Of Combinatorial Designs Second Edition

Author : Charles J. Colbourn
ISBN : 143983234X
Genre : Mathematics
File Size : 80. 8 MB
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Continuing in the bestselling, informative tradition of the first edition, the Handbook of Combinatorial Designs, Second Edition remains the only resource to contain all of the most important results and tables in the field of combinatorial design. This handbook covers the constructions, properties, and applications of designs as well as existence results. Over 30% longer than the first edition, the book builds upon the groundwork of its predecessor while retaining the original contributors' expertise. The first part contains a brief introduction and history of the subject. The following parts focus on four main classes of combinatorial designs: balanced incomplete block designs, orthogonal arrays and Latin squares, pairwise balanced designs, and Hadamard and orthogonal designs. Closely connected to the preceding sections, the next part surveys 65 additional classes of designs, such as balanced ternary, factorial, graphical, Howell, quasi-symmetric, and spherical. The final part presents mathematical and computational background related to design theory. New to the Second Edition An introductory part that provides a general overview and a historical perspective of the area New chapters on the history of design theory, various codes, bent functions, and numerous types of designs Fully updated tables, including BIBDs, MOLS, PBDs, and Hadamard matrices Nearly 2,200 references in a single bibliographic section Meeting the need for up-to-date and accessible tabular and reference information, this handbook provides the tools to understand combinatorial design theory and applications that span the entire discipline. The author maintains a website with more information.

Discrete Mathematics With Proof 2nd Ed

Author : Eric Gossett
ISBN : 8126527587
Genre :
File Size : 22. 33 MB
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Market_Desc: As a textbook for discrete mathematics courses at the sophomore and/or junior level for both mathematics and computer science majors; and academic libraries. A prerequisite for this book includes completion of the introductory calculus sequence. Special Features: · Emphasizes proof (combinatorial and non-combinatorial) throughout in the text and exercises, and homework problems have been designed to reinforce the book's main concepts· Contains many examples that are not present in most discrete mathematics books, including the deferred acceptance algorithm, the Boyer-Moore algorithm for pattern matching, Sierpinski curves, Persian rugs, adaptive quadrature, the Josephus problem, the five color theorem, and relational databases· Features of the new edition include an increased use of combinatorial proofs, many new exercises, an extended discussion on elementary number theory, a complete reorganization of the definitions and theorems, among others· Supplemented with an Instructor's Manual containing detailed solutions to every exercise (available upon request to the Publisher). Detailed solutions are also available in the back of the book for selected exercises.· Includes Quick Check problems at critical points in the reading, and it is intended for these problems to be solved before moving on to the next section in the chapter. Also, many worked examples can be found throughout, which are used to motivate the presented theorems and illustrate the conclusion of a theorem.· Features many important examples from the field of computer science, including the Halting problem, Shannon's mathematical model of information, XML, and Normal Forms in relational databases About The Book: Discrete mathematics has become increasingly popular in recent years due to its growing applications in the field of computer science. Discrete Mathematics with Proof, Second Edition continues to facilitate an up-to-date understanding of this important topic, exposing readers to a wide range of modern and technological applications. The book begins with an introductory chapter that provides an accessible explanation of discrete mathematics. Subsequent chapters explore additional related topics including counting, finite probability theory, recursion, formal models in computer science, graph theory, trees, the concepts of functions, and relations.In addition, approximately 500 examples and over 2,800 exercises are presented throughout the book to motivate ideas and illustrate the proofs and conclusions of theorems. Assuming only a basic background in calculus, Discrete Mathematics with Proof, Second Edition is an excellent book for mathematics and computer science courses at the undergraduate level. It is also a valuable resource for professionals in various technical fields who would like an introduction to discrete mathematics.

Bulletin Of The Belgian Mathematical Society Simon Stevin

Author :
ISBN : UCSD:31822022722730
Genre : Mathematics
File Size : 48. 25 MB
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