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Schaum's Outline of Discrete Mathematics, 3rd Ed.

This is a topic that becomes increasingly important every year as the digital age extends and grows more encompassing in every facet of life Discrete mathematics, the study of finite systems has become more important as the computer age has advanced, as computer arithmetic, logic, and combinatorics have become standard topics in the discipline. For mathematics majors it is one of the core required courses. This new edition will bring the outline into synch with Rosen, McGraw-Hill’s bestselling textbook in the field as well as up to speed in the current curriculum. New material will include expanded coverage of logic, the rules of inference and basic types of proofs in mathematical reasoning. This will give students a better understanding of proofs of facts about sets and functions. There will be increased emphasis on discrete probability and aspects of probability theory, and greater accessibility to counting techniques. This new edition features: Counting chapter will have new material on generalized combinations New chapter on computer arithmetic, with binary and hexagon addition and multiplication New Cryptology chapter including substitution and RSA method This outline is the perfect supplement to any course in discrete math and can also serve as a stand-alone textbook

This is a topic that becomes increasingly important every year as the digital age extends and grows more encompassing in every facet of life Discrete mathematics, the study of finite systems has become more important as the computer age has ...

A Beginner’s Guide to Discrete Mathematics

This introduction to discrete mathematics is aimed at freshmen and sophomores in mathematics and computer science. It begins with a survey of number systems and elementary set theory before moving on to treat data structures, counting, probability, relations and functions, graph theory, matrices, number theory and cryptography. The end of each section contains problem sets with selected solutions, and good examples occur throughout the text.

Graph study is discussed, including Euler and Hamilton cycles and trees. This is a vehicle for some easy proofs, as well as serving as another example of a data structure. Matrices and vectors are then defined.

DISCRETE MATHEMATICS

Written with a strong pedagogical focus, this second edition of the book continues to provide an exhaustive presentation of the fundamental concepts of discrete mathematical structures and their applications in computer science and mathematics. It aims to develop the ability of the students to apply mathematical thought in order to solve computation-related problems. The book is intended not only for the undergraduate and postgraduate students of mathematics but also, most importantly, for the students of Computer Science & Engineering and Computer Applications. The introductory chapter presents an overview of the foundations of the subject, consisting of topics such as logic, set theory, relations, functions, algebraic structures, and graphs. The subsequent chapters provide detailed coverage of each of these topics as well as major areas of discrete mathematics such as combinatorics, lattices and Boolean algebras. Major applications such as computer models and computation, coding theory, cryptography and databases are dealt with in the final chapters of the book. In addition to this, a new chapter on matrices is included in this edition of the book, which forms a part of MCA course curriculum. The book is replete with features which enable the building of a firm foundation of the underlying principles of the subject and also provide adequate scope for testing the comprehension acquired by the students. Each chapter contains numerous worked-out examples within the main discussion as well as several chapter-end Supplementary Examples for revision. The Self-Test and Exercises at the end of each chapter provide large numbers of objective type questions and problems respectively. Answers to objective type questions and hints to exercises are also provided. All these pedagogic features, together with thorough coverage of the subject matter, make this book a readable text for beginners as well as advanced learners of the subject.

Written with a strong pedagogical focus, this second edition of the book continues to provide an exhaustive presentation of the fundamental concepts of discrete mathematical structures and their applications in computer science and ...

Topics in Discrete Mathematics

Dedicated to Jarik Nešetril on the Occasion of his 60th birthday

This book comprises a collection of high quality papers in selected topics of Discrete Mathematics, to celebrate the 60th birthday of Professor Jarik Nešetril. Leading experts have contributed survey and research papers in the areas of Algebraic Combinatorics, Combinatorial Number Theory, Game theory, Ramsey Theory, Graphs and Hypergraphs, Homomorphisms, Graph Colorings and Graph Embeddings.

This book comprises a collection of high quality papers in selected topics of Discrete Mathematics, to celebrate the 60th birthday of Professor Jarik Nešetril.

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.

Computational Support for Discrete Mathematics

DIMACS Workshop, March 12-14, 1992

With recent technological advances in workstations, graphics, graphical user interfaces, and object oriented programming languages, a significant number of researchers are developing general-purpose software and integrated software systems for domains in discrete mathematics, including graph theory, combinatorics, combinatorial optimization, and sets. This software aims to provide effective computational tools for research, applications prototyping, and teaching. In March 1992, DIMACS sponsored a workshop on Computational Support for Discrete Mathematics in order to facilitate interactions between the researchers, developers, and educators who work in these areas. Containing refereed papers based on talks presented at the workshop, this volume documents current and past research in these areas and should provide impetus for new interactions.

Containing refereed papers based on talks presented at the workshop, this volume documents current and past research in these areas and should provide impetus for new interactions.

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.

Teaching and Learning Discrete Mathematics Worldwide: Curriculum and Research

This book discusses examples of discrete mathematics in school curricula, including in the areas of graph theory, recursion and discrete dynamical systems, combinatorics, logic, game theory, and the mathematics of fairness. In addition, it describes current discrete mathematics curriculum initiatives in several countries, and presents ongoing research, especially in the areas of combinatorial reasoning and the affective dimension of learning discrete mathematics. Discrete mathematics is the math of our time.' So declared the immediate past president of the National Council of Teachers of Mathematics, John Dossey, in 1991. Nearly 30 years later that statement is still true, although the news has not yet fully reached school mathematics curricula. Nevertheless, much valuable work has been done, and continues to be done. This volume reports on some of that work. It provides a glimpse of the state of the art in learning and teaching discrete mathematics around the world, and it makes the case once again that discrete mathematics is indeed mathematics for our time, even more so today in our digital age, and it should be included in the core curricula of all countries for all students.

This book discusses examples of discrete mathematics in school curricula, including in the areas of graph theory, recursion and discrete dynamical systems, combinatorics, logic, game theory, and the mathematics of fairness.

Discrete Mathematics

The long-awaited second edition of Norman Bigg's best-selling Discrete Mathematics includes new chapters on statements and proof, logical framework, natural numbers and the integers, in addition to updated chapters from the previous edition. Carefully structured, coherent and comprehensive, each chapter contains tailored exercises and solutions to selected questions and miscellaneous exercises are presented throughout. This is an invaluable text for students seeking a clear introduction to discrete mathematics, graph theory, combinatorics, number theory and abstract algebra.Key Features:* Contains nine new introductory chapters, in addition to updated chapters from the previous edition* Contains over 1000 individual exercises and selected solutions* Companion website www.oup.com/mathematics/discretemath contains hints and solutions to all exercisesContents:The Language of Mathematics1. Statements and proofs2. Set notation3. The logical framework4. Natural numbers5. Functions6. How to count 7. Integers8. Divisibility and prime numbers9. Fractions and real numbersTechniques10. Principles of counting11. Subsets and designs12. Partition, classification and distribution13. Modular arithmeticAlgorithms and Graphs14. Algorithms and their efficiency15. Graphs16. Trees, sorting and searching17. Bipartite graphs and matching problems18. Digraphs, networks and flows19. Recursive techniquesAlgebraic Methods20. Groups21. Groups of permutations22. Rings, fields and polynomials23. Finite fields and some applications24. Error-correcting codes25. Generating functions26. Partitions of a positive integer27. Symmetry and counting

The text is designed explicitly for mathematicians and computer scientists seeking a first approach to this important topic.

Foundations of Discrete Mathematics

This Book Is Meant To Be More Than Just A Text In Discrete Mathematics. It Is A Forerunner Of Another Book Applied Discrete Structures By The Same Author. The Ultimate Goal Of The Two Books Are To Make A Strong Case For The Inclusion Of Discrete Mathematics In The Undergraduate Curricula Of Mathematics By Creating A Sequence Of Courses In Discrete Mathematics Parallel To The Traditional Sequence Of Calculus-Based Courses.The Present Book Covers The Foundations Of Discrete Mathematics In Seven Chapters. It Lays A Heavy Emphasis On Motivation And Attempts Clarity Without Sacrificing Rigour. A List Of Typical Problems Is Given In The First Chapter. These Problems Are Used Throughout The Book To Motivate Various Concepts. A Review Of Logic Is Included To Gear The Reader Into A Proper Frame Of Mind. The Basic Counting Techniques Are Covered In Chapters 2 And 7. Those In Chapter 2 Are Elementary. But They Are Intentionally Covered In A Formal Manner So As To Acquaint The Reader With The Traditional Definition-Theorem-Proof Pattern Of Mathematics. Chapters 3 Introduces Abstraction And Shows How The Focal Point Of Todays Mathematics Is Not Numbers But Sets Carrying Suitable Structures. Chapter 4 Deals With Boolean Algebras And Their Applications. Chapters 5 And 6 Deal With More Traditional Topics In Algebra, Viz., Groups, Rings, Fields, Vector Spaces And Matrices.The Presentation Is Elementary And Presupposes No Mathematical Maturity On The Part Of The Reader. Instead, Comments Are Inserted Liberally To Increase His Maturity. Each Chapter Has Four Sections. Each Section Is Followed By Exercises (Of Various Degrees Of Difficulty) And By Notes And Guide To Literature. Answers To The Exercises Are Provided At The End Of The Book.

This Book Is Meant To Be More Than Just A Text In Discrete Mathematics.