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ISBN:
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Languages : en
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Author: A. Donald Keedwell
Publisher: Elsevier
ISBN: 0444635580
Category : Mathematics
Languages : en
Pages : 443

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Book Description
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. Retains the organization and updated foundational material from the original edition Explores current and emerging research topics Includes the original 73 ‘Unsolved Problems’ with the current state of knowledge regarding them, as well as new Unsolved Problems for further study

Author: József Dénes
Publisher:
ISBN: 9789630502559
Category : Magic squares
Languages : en
Pages : 547

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Author: József Dénes
Publisher: Elsevier
ISBN: 9780080867861
Category : Mathematics
Languages : en
Pages : 452

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Book Description
In 1974 the editors of the present volume published a well-received book entitled ``Latin Squares and their Applications''. It included a list of 73 unsolved problems of which about 20 have been completely solved in the intervening period and about 10 more have been partially solved. The present work comprises six contributed chapters and also six further chapters written by the editors themselves. As well as discussing the advances which have been made in the subject matter of most of the chapters of the earlier book, this new book contains one chapter which deals with a subject (r-orthogonal latin squares) which did not exist when the earlier book was written. The success of the former book is shown by the two or three hundred published papers which deal with questions raised by it.

Author: Clive Reis
Publisher: World Scientific Publishing Company
ISBN: 9814730564
Category : Mathematics
Languages : en
Pages : 576

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Book Description
This second edition covers essentially the same topics as the first. However, the presentation of the material has been extensively revised and improved. In addition, there are two new chapters, one dealing with the fundamental theorem of finitely generated abelian groups and the other a brief introduction to semigroup theory and automata. This book is appropriate for second to fourth year undergraduates. In addition to the material traditionally taught at this level, the book contains several applications: Polya–Burnside Enumeration, Mutually Orthogonal Latin Squares, Error-Correcting Codes, and a classification of the finite groups of isometries of the plane and the finite rotation groups in Euclidean 3-space, semigroups and automata. It is hoped that these applications will help the reader achieve a better grasp of the rather abstract ideas presented and convince him/her that pure mathematics, in addition to having an austere beauty of its own, can be applied to solving practical problems. Considerable emphasis is placed on the algebraic system consisting of the congruence classes mod n under the usual operations of addition and multiplication. The reader is thus introduced — via congruence classes — to the idea of cosets and factor groups. This enables the transition to cosets and factor objects to be relatively painless. In this book, cosets, factor objects and homomorphisms are introduced early on so that the reader has at his/her disposal the tools required to give elegant proofs of the fundamental theorems. Moreover, homomorphisms play such a prominent role in algebra that they are used in this text wherever possible.

Author: Jonathan L. Gross
Publisher: CRC Press
ISBN: 158488505X
Category : Mathematics
Languages : en
Pages : 799

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Book Description
Already an international bestseller, with the release of this greatly enhanced second edition, Graph Theory and Its Applications is now an even better choice as a textbook for a variety of courses -- a textbook that will continue to serve your students as a reference for years to come. The superior explanations, broad coverage, and abundance of illustrations and exercises that positioned this as the premier graph theory text remain, but are now augmented by a broad range of improvements. Nearly 200 pages have been added for this edition, including nine new sections and hundreds of new exercises, mostly non-routine. What else is new? New chapters on measurement and analytic graph theory Supplementary exercises in each chapter - ideal for reinforcing, reviewing, and testing. Solutions and hints, often illustrated with figures, to selected exercises - nearly 50 pages worth Reorganization and extensive revisions in more than half of the existing chapters for smoother flow of the exposition Foreshadowing - the first three chapters now preview a number of concepts, mostly via the exercises, to pique the interest of reader Gross and Yellen take a comprehensive approach to graph theory that integrates careful exposition of classical developments with emerging methods, models, and practical needs. Their unparalleled treatment provides a text ideal for a two-semester course and a variety of one-semester classes, from an introductory one-semester course to courses slanted toward classical graph theory, operations research, data structures and algorithms, or algebra and topology.

Author: William J. Gilbert
Publisher: John Wiley & Sons
ISBN: 0471469890
Category : Mathematics
Languages : en
Pages : 352

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Book Description
Praise for the first edition "This book is clearly written and presents a large number ofexamples illustrating the theory . . . there is no other book ofcomparable content available. Because of its detailed coverage ofapplications generally neglected in the literature, it is adesirable if not essential addition to undergraduate mathematicsand computer science libraries." –CHOICE As a cornerstone of mathematical science, the importance ofmodern algebra and discrete structures to many areas of science andtechnology is apparent and growing–with extensive use incomputing science, physics, chemistry, and data communications aswell as in areas of mathematics such as combinatorics. Blending the theoretical with the practical in the instructionof modern algebra, Modern Algebra with Applications, Second Editionprovides interesting and important applications of thissubject–effectively holding your interest and creating a moreseamless method of instruction. Incorporating the applications of modern algebra throughout itsauthoritative treatment of the subject, this book covers the fullcomplement of group, ring, and field theory typically contained ina standard modern algebra course. Numerous examples are included ineach chapter, and answers to odd-numbered exercises are appended inthe back of the text. Chapter topics include: Boolean Algebras Polynomial and Euclidean Rings Groups Quotient Rings Quotient Groups Field Extensions Symmetry Groups in Three Dimensions Latin Squares Pólya—Burnside Method of Enumeration Geometrical Constructions Monoids and Machines Error-Correcting Codes Rings and Fields In addition to improvements in exposition, this fully updatedSecond Edition also contains new material on order of an elementand cyclic groups, more details about the lattice of divisors of aninteger, and new historical notes. Filled with in-depth insights and over 600 exercises of varyingdifficulty, Modern Algebra with Applications, Second Edition canhelp anyone appreciate and understand this subject.

Author: Jonathan L. Gross
Publisher: CRC Press
ISBN: 1439880182
Category : Mathematics
Languages : en
Pages : 1634

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Book Description
In the ten years since the publication of the best-selling first edition, more than 1,000 graph theory papers have been published each year. Reflecting these advances, Handbook of Graph Theory, Second Edition provides comprehensive coverage of the main topics in pure and applied graph theory. This second edition—over 400 pages longer than its predecessor—incorporates 14 new sections. Each chapter includes lists of essential definitions and facts, accompanied by examples, tables, remarks, and, in some cases, conjectures and open problems. A bibliography at the end of each chapter provides an extensive guide to the research literature and pointers to monographs. In addition, a glossary is included in each chapter as well as at the end of each section. This edition also contains notes regarding terminology and notation. With 34 new contributors, this handbook is the most comprehensive single-source guide to graph theory. It emphasizes quick accessibility to topics for non-experts and enables easy cross-referencing among chapters.

Author: James E. De Muth
Publisher: CRC Press
ISBN: 9780849337994
Category : Mathematics
Languages : en
Pages : 754

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Book Description
The first edition of Basic Statistics and Pharmaceutical Statistical Applications successfully provided a practical, easy-to-read, basic statistics book. This second edition not only updates the previous edition, but expands coverage in the area of biostatistics and how it relates to real-world professional practice. Taking you on a roller coaster ride through the world of statistics, Dr. De Muth clearly details the methodology necessary to summarize data and make informed decisions about observed outcomes. What's new or different in the Second Edition? New chapters cover: Measures of association primarily with nominal and ordinal data and and more than 15 tests Survival statistics including actuarial analysis and an introduction to multiple regression with survival data using proportional hazards regression An introduction to the topic of evidence-based practice with discussions of sensitivity and specificity, predictive values, and likelihood ratios Odds ratios and relative risk ratios that provide valuable information for dealing with probability, odds, and risk New sections address Power and sample size determination for two-sample Z-tests of proportions Clinical equivalence and noninferiority studies, process capability, and tolerance limits Methods for assessing repeatability and reproducibility Expanded information includes: Chi square, repeated measures designs, Latin Square designs, nine multiple comparison tests, and outlier testing Inverse prediction with linear regression, handling of multiple data points at different levels of independent variable, and assessment of parallelism of slopes for two samples Additional types of bivariate correlations and various assessments for independence and randomness More nonparametric tests including new information on post hoc comparisons for a significant Kruskal-Wallis test, the Kolmogorov-Smirnov goodness-of-fit test, and the Anderson-Darling test, as well as runs and range tests Eight new tables useful for the interpretation of some of the new inferential statistics De Muth provides concrete examples that enable you to effectively manage information in your day-to-day problem solving and reporting of findings. By avoiding heavy-duty mathematics and theory, even the mathematically challenged can benefit and increase their confidence in using statistics procedures.

Author: Askar Zhussupbekov
Publisher: CRC Press
ISBN: 1000992543
Category : Technology & Engineering
Languages : en
Pages : 4162

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Book Description
Smart Geotechnics for Smart Societies contains the contributions presented at the 17th Asian Regional Conference on Soil Mechanics and Geotechnical Engineering (17th ARC, Astana, Kazakhstan, 14-18 August, 2023). The topics covered include: - Geomaterials for soil improvement - Tunneling and rock engineering - Slope, embankments and dams - Shallow and deep foundations - Soil dynamics and geotechnical earthquake engineering - Geoenvironmental engineering and frost geotechnics - Investigation of foundations of historical structures and monitoring - Offshore, harbor geotechnics and GeoEnergy - Megaprojects and transportation geotechnics Smart Geotechnics for Smart Societies will be of interest to academics and engineers interested or involved in geotechnical engineering.