Discrete Mathematics

Proofs, Structures and Applications, Third Edition

Taking an approach to the subject that is suitable for a broad readership, Discrete Mathematics: Proofs, Structures, and Applications, Third Edition provides a rigorous yet accessible exposition of discrete mathematics, including the core mathematical foundation of computer science. The approach is comprehensive yet maintains an easy-to-follow progression from the basic mathematical ideas to the more sophisticated concepts examined later in the book. This edition preserves the philosophy of its predecessors while updating and revising some of the content. New to the Third Edition In the expanded first chapter, the text includes a new section on the formal proof of the validity of arguments in propositional logic before moving on to predicate logic. This edition also contains a new chapter on elementary number theory and congruences. This chapter explores groups that arise in modular arithmetic and RSA encryption, a widely used public key encryption scheme that enables practical and secure means of encrypting data. This third edition also offers a detailed solutions manual for qualifying instructors. Exploring the relationship between mathematics and computer science, this text continues to provide a secure grounding in the theory of discrete mathematics and to augment the theoretical foundation with salient applications. It is designed to help readers develop the rigorous logical thinking required to adapt to the demands of the ever-evolving discipline of computer science.

Exploring the relationship between mathematics and computer science, this text continues to provide a secure grounding in the theory of discrete mathematics and to augment the theoretical foundation with salient applications.

Pearls of Discrete Mathematics

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.

Through intriguing examples, problems, theorems, and proofs, the book illustrates the relationship of these structures to algebra, geometry, number theory, and combinatorics.

Discrete Mathematics and Applications, Second Edition

This book is intended for a one-semester course in discrete mathematics. Such a course is typically taken by mathematics, mathematics education, and computer science majors, usually in their sophomore year. Calculus is not a prerequisite to use this book. Part one focuses on how to write proofs, then moves on to topics in number theory, employing set theory in the process. Part two focuses on computations, combinatorics, graph theory, trees, and algorithms.

This book is intended for a one-semester course in discrete mathematics.

Discrete Structures and Their Interactions

Discover the Connections between Different Structures and Fields Discrete Structures and Their Interactions highlights the connections among various discrete structures, including graphs, directed graphs, hypergraphs, partial orders, finite topologies, and simplicial complexes. It also explores their relationships to classical areas of mathematics, such as linear and multilinear algebra, analysis, probability, logic, and topology. The text introduces a number of discrete structures, such as hypergraphs, finite topologies, preorders, simplicial complexes, and order ideals of monomials, that most graduate students in combinatorics, and even some researchers in the field, seldom experience. The author explains how these structures have important applications in many areas inside and outside of combinatorics. He also discusses how to recognize valuable research connections through the structures. Intended for graduate and upper-level undergraduate students in mathematics who have taken an initial course in discrete mathematics or graph theory, this book shows how discrete structures offer new insights into the classical fields of mathematics. It illustrates how to use discrete structures to represent the salient features and discover the underlying combinatorial principles of seemingly unrelated areas of mathematics.

Intended for graduate and upper-level undergraduate students in mathematics who have taken an initial course in discrete mathematics or graph theory, this book shows how discrete structures offer new insights into the classical fields of ...

Discrete Mathematics with Ducks

Containing exercises and materials that engage students at all levels, Discrete Mathematics with Ducks presents a gentle introduction for students who find the proofs and abstractions of mathematics challenging. This classroom-tested text uses discrete mathematics as the context for introducing proofwriting. Facilitating effective and active learning, each chapter contains a mixture of discovery activities, expository text, in-class exercises, and homework problems. Elementary exercises at the end of each expository section prompt students to review the material Try This! sections encourage students to construct fundamental components of the concepts, theorems, and proofs discussed. Sets of discovery problems and illustrative examples reinforce learning. Bonus sections can be used for take-home exams, projects, or further study Instructor Notes sections offer suggestions on how to use the material in each chapter Discrete Mathematics with Ducks offers students a diverse introduction to the field and a solid foundation for further study in discrete mathematics and complies with SIGCSE guidelines. The book shows how combinatorics and graph theory are used in both computer science and mathematics.

This classroom-tested text uses discrete mathematics as the context for introducing proofwriting.

Handbook of Discrete and Combinatorial Mathematics, Second Edition

Handbook of Discrete and Combinatorial Mathematics provides a comprehensive reference volume for mathematicians, computer scientists, engineers, as well as students and reference librarians. The material is presented so that key information can be located and used quickly and easily. Each chapter includes a glossary. Individual topics are covered in sections and subsections within chapters, each of which is organized into clearly identifiable parts: definitions, facts, and examples. Examples are provided to illustrate some of the key definitions, facts, and algorithms. Some curious and entertaining facts and puzzles are also included. Readers will also find an extensive collection of biographies. This second edition is a major revision. It includes extensive additions and updates. Since the first edition appeared in 1999, many new discoveries have been made and new areas have grown in importance, which are covered in this edition.

This second edition is a major revision. It includes extensive additions and updates. Since the first edition appeared in 1999, many new discoveries have been made and new areas have grown in importance, which are covered in this edition.

Quality Management in Construction Projects, Second Edition

The first edition published in 2010. The response was encouraging and many people appreciated a book that was dedicated to quality management in construction projects. Since it published, ISO 9000: 2008 has been revised and ISO 9000: 2015 has published. The new edition will focus on risk-based thinking which must be considered from the beginning and throughout the project life cycle. There are quality-related topics such as Customer Relationship, Supplier Management, Risk Management, Quality Audits, Tools for Construction Projects, and Quality Management that were not covered in the first edition. Furthermore, some figures and tables needed to be updated to make the book more comprehensive.

Abdul Razzak Rumane ... go to my wife, Noor Jehan, for her patience, as she had
to endure a lot because of my busy schedule. Abdul Razzak Rumane Author
Abdul Razzak Rumane, PhD, is a registered senior consultant Acknowledgments
.

Selected Applications of Modern FT-IR Techniques

This volume is intended to show beginners in modern Fourier Transform-Infrared
(IR) analysis which technique of infrared analysis should be selected and how to
use it to obtain certain information from the most common samples brought into
research and analytical laboratories in production industries such as the polymer.
... U.S.A. in 1991. we decided to translate the original version into English.
fortifying Part I with more theoretical and practical descriptions of infrared
techniques.

Experimental Evidence and Theoretical Approaches in Unsaturated Soils

This volume presents the work of postgraduate and postdoctoral researchers on unsaturated soil mechanincs. Topics covered include: innovative experimental techniques; new experimental data on compacted, collapsible and swelling soils; and advances in constitutive modelling.

This volume presents the work of postgraduate and postdoctoral researchers on unsaturated soil mechanincs.

Water Purification Using Heat Pumps

This book is the result of a long-term co-operative research and professional development programme between the Instituto de Investigaciones Electricas (IIE), Mexico, and the University of Salford, UK. It provides the design basis for the fabrication of small and large scale commercial absorption heat pump systems, and includes a comprehensive treatment of the economics of heat pump systems. It charts the development of heat pump technology from theoretical principles to the operation of practical systems for the purification of water, both for human consumption and a wide variety of industrial purposes. In addition to the increasing demand for potable water there is a rapidly increasing demand for clean water in industries ranging from foodstuffs and pharmaceuticals to electronics. This book will be essential reading for industrial engineers and others concerned with the cost-effective, environmentally friendly production of clean water.

Supranto et al. [1987] carried out experiments on a mechanical vapour
compression heat pump operating with R114 as the working fluid at different
values of the condensing temperature TCO. These authors also observed two
similar sets of data. Figure 4.8 is a plot of (COP)A against the production rate of
distilled water with both water and geothermal brine. It is seen that the production
rate of distilled water increases as (COP)A increases. Figure 4.9 is a plot of the
gross temperature ...