Basic Discrete Mathematics

Author: Richard Kohar
Publisher: World Scientific Publishing Company
ISBN: 9814730416
Format: PDF, ePub, Docs
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This lively introductory text exposes the student in the humanities to the world of discrete mathematics. A problem-solving based approach grounded in the ideas of George Pólya are at the heart of this book. Students learn to handle and solve new problems on their own. A straightforward, clear writing style and well-crafted examples with diagrams invite the students to develop into precise and critical thinkers. Particular attention has been given to the material that some students find challenging, such as proofs. This book illustrates how to spot invalid arguments, to enumerate possibilities, and to construct probabilities. It also presents case studies to students about the possible detrimental effects of ignoring these basic principles. The book is invaluable for a discrete and finite mathematics course at the freshman undergraduate level or for self-study since there are full solutions to the exercises in an appendix. "Written with clarity, humor and relevant real-world examples, Basic Discrete Mathematics is a wonderful introduction to discrete mathematical reasoning."- Arthur Benjamin, Professor of Mathematics at Harvey Mudd College, and author of The Magic of Math

A Beginner s Guide to Discrete Mathematics

Author: W.D. Wallis
Publisher: Springer Science & Business Media
ISBN: 1475738269
Format: PDF, Kindle
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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.

Schaum s Outline of Discrete Mathematics 3rd Ed

Author: Seymour Lipschutz
Publisher: McGraw Hill Professional
ISBN: 0071511016
Format: PDF, ePub, Docs
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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

Discrete Mathematics and Combinatorics

Author: Sengadir T.
Publisher: Pearson Education India
ISBN: 9788131714058
Format: PDF, Docs
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Discrete Mathematics and Combinatorics provides a concise and practical introduction to the core components of discrete mathematics, featuring a balanced mix of basic theories and applications. The book covers both fundamental concepts such as sets and logic, as well as advanced topics such as graph theory and Turing machines. The example-driven approach will help readers in understanding and applying the concepts. Other pedagogical tools - illustrations, practice questions, and suggested reading - facilitate learning and mastering the subject." -- Cover.

Discrete Mathematics

Author: Amanda Chetwynd
Publisher: Elsevier
ISBN: 0080928609
Format: PDF, ePub, Docs
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As an introduction to discrete mathematics, this text provides a straightforward overview of the range of mathematical techniques available to students. Assuming very little prior knowledge, and with the minimum of technical complication, it gives an account of the foundations of modern mathematics: logic; sets; relations and functions. It then develops these ideas in the context of three particular topics: combinatorics (the mathematics of counting); probability (the mathematics of chance) and graph theory (the mathematics of connections in networks). Worked examples and graded exercises are used throughout to develop ideas and concepts. The format of this book is such that it can be easily used as the basis for a complete modular course in discrete mathematics.

Discrete Structures and Their Interactions

Author: Jason I. Brown
Publisher: CRC Press
ISBN: 1466579420
Format: PDF
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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.

Discrete Mathematics

Author: Jean Gallier
Publisher: Springer Science & Business Media
ISBN: 9781441980472
Format: PDF, ePub
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This books gives an introduction to discrete mathematics for beginning undergraduates. One of original features of this book is that it begins with a presentation of the rules of logic as used in mathematics. Many examples of formal and informal proofs are given. With this logical framework firmly in place, the book describes the major axioms of set theory and introduces the natural numbers. The rest of the book is more standard. It deals with functions and relations, directed and undirected graphs, and an introduction to combinatorics. There is a section on public key cryptography and RSA, with complete proofs of Fermat's little theorem and the correctness of the RSA scheme, as well as explicit algorithms to perform modular arithmetic. The last chapter provides more graph theory. Eulerian and Hamiltonian cycles are discussed. Then, we study flows and tensions and state and prove the max flow min-cut theorem. We also discuss matchings, covering, bipartite graphs.

FUNDAMENTALS OF DISCRETE MATHEMATICAL STRUCTURES

Author: K. R. CHOWDHARY
Publisher: PHI Learning Pvt. Ltd.
ISBN: 812035074X
Format: PDF, ePub
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This updated text, now in its Third Edition, continues to provide the basic concepts of discrete mathematics and its applications at an appropriate level of rigour. The text teaches mathematical logic, discusses how to work with discrete structures, analyzes combinatorial approach to problem-solving and develops an ability to create and understand mathematical models and algorithms essentials for writing computer programs. Every concept introduced in the text is first explained from the point of view of mathematics, followed by its relation to Computer Science. In addition, it offers excellent coverage of graph theory, mathematical reasoning, foundational material on set theory, relations and their computer representation, supported by a number of worked-out examples and exercises to reinforce the students’ skill. Primarily intended for undergraduate students of Computer Science and Engineering, and Information Technology, this text will also be useful for undergraduate and postgraduate students of Computer Applications. New to this Edition Incorporates many new sections and subsections such as recurrence relations with constant coefficients, linear recurrence relations with and without constant coefficients, rules for counting and shorting, Peano axioms, graph connecting, graph scanning algorithm, lexicographic shorting, chains, antichains and order-isomorphism, complemented lattices, isomorphic order sets, cyclic groups, automorphism groups, Abelian groups, group homomorphism, subgroups, permutation groups, cosets, and quotient subgroups. Includes many new worked-out examples, definitions, theorems, exercises, and GATE level MCQs with answers.

Discrete Mathematics with Combinatorics

Author: James Andrew Anderson
Publisher:
ISBN: 9780130869982
Format: PDF, ePub, Docs
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This carefully organized, very readable book covers every essential topic in discrete mathematics in a logical fashion. Placing each topic in context, it covers concepts associated with discrete mathematical systems that have applications in computer science, engineering, and mathematics. The author introduces more basic concepts at the freshman level than are found in other books, in a simple, accessible form. Introductory material is balanced with extensive coverage of graphs, trees, recursion, algebra, theory of computing, and combinatorics. Extensive examples throughout the text reinforce concepts. More combinatorics/algebraic structures than in most books. Detailed discussion of and strong emphasis on proofs. Extensive, in-depth presentation of topics. Large selection of applied and computational problems, ranging from the elementary to the more advanced. More topics in probability and more statistical interpretations than other texts. Comprehensive discussion of topics such as finite state machines, automata, and languages. Earlier introduction of matrices and relations, Boolean algebras and circuits than most texts. Includes algorithms for many constructive tasks that occur in discrete systems.