basic discrete mathematics logic set theory and probability

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Basic Discrete Mathematics

Author : Richard Kohar
ISBN : 9789814730419
Genre : Mathematics
File Size : 66. 10 MB
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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
ISBN : 9781475738261
Genre : Mathematics
File Size : 48. 78 MB
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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.

Fundamentals Of Discrete Mathematical Structures

Author : K. R. CHOWDHARY
ISBN : 9788120350748
Genre : Mathematics
File Size : 64. 20 MB
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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

Author : Jean Gallier
ISBN : 1441980474
Genre : Mathematics
File Size : 31. 81 MB
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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.

Schaum S Outline Of Discrete Mathematics 3rd Ed

Author : Seymour Lipschutz
ISBN : 9780071511018
Genre : Mathematics
File Size : 74. 58 MB
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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

Invitation To Discrete Mathematics

Author : Ji%rí Matousek
ISBN : 9780198570431
Genre : Mathematics
File Size : 86. 84 MB
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Invitation to Discrete Mathematics is an introduction and a thoroughly comprehensive text at the same time. A lively and entertaining style with mathematical precision and maturity uniquely combine into an intellectual happening and should delight the interested reader. A master example of teaching contemporary discrete mathematics, and of teaching science in general.

Discrete Mathematics With Proof

Author : Eric Gossett
ISBN : 9780470457931
Genre : Mathematics
File Size : 69. 23 MB
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"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. 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."--Jacket.

Mathematics Of Fuzzy Sets

Author : Ulrich Höhle
ISBN : 0792383885
Genre : Business & Economics
File Size : 62. 95 MB
Format : PDF
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Mathematics of Fuzzy Sets: Logic, Topology and Measure Theory is a major attempt to provide much-needed coherence for the mathematics of fuzzy sets. Much of this book is new material required to standardize this mathematics, making this volume a reference tool with broad appeal as well as a platform for future research. Fourteen chapters are organized into three parts: mathematical logic and foundations (Chapters 1-2), general topology (Chapters 3-10), and measure and probability theory (Chapters 11-14). Chapter 1 deals with non-classical logics and their syntactic and semantic foundations. Chapter 2 details the lattice-theoretic foundations of image and preimage powerset operators. Chapters 3 and 4 lay down the axiomatic and categorical foundations of general topology using lattice-valued mappings as a fundamental tool. Chapter 3 focuses on the fixed-basis case, including a convergence theory demonstrating the utility of the underlying axioms. Chapter 4 focuses on the more general variable-basis case, providing a categorical unification of locales, fixed-basis topological spaces, and variable-basis compactifications. Chapter 5 relates lattice-valued topologies to probabilistic topological spaces and fuzzy neighborhood spaces. Chapter 6 investigates the important role of separation axioms in lattice-valued topology from the perspective of space embedding and mapping extension problems, while Chapter 7 examines separation axioms from the perspective of Stone-Cech-compactification and Stone-representation theorems. Chapters 8 and 9 introduce the most important concepts and properties of uniformities, including the covering and entourage approaches and the basic theory of precompact or complete [0,1]-valued uniform spaces. Chapter 10 sets out the algebraic, topological, and uniform structures of the fundamentally important fuzzy real line and fuzzy unit interval. Chapter 11 lays the foundations of generalized measure theory and representation by Markov kernels. Chapter 12 develops the important theory of conditioning operators with applications to measure-free conditioning. Chapter 13 presents elements of pseudo-analysis with applications to the Hamilton–Jacobi equation and optimization problems. Chapter 14 surveys briefly the fundamentals of fuzzy random variables which are [0,1]-valued interpretations of random sets.

Introduction To Discrete Mathematics

Author : Koo-Guan Choo
ISBN : 0582800552
Genre : Computer science
File Size : 82. 47 MB
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Discrete Mathematics covers such a wide range of topics that it is difficult to give a simple definition of the subject. Whereas calculus deals with continuous or even smooth objects, discrete mathematics deals with things that come in "chunks" that can be counted. We will be a lot more precise about just what sort of "chunks" we are dealing with in the later chapters. If your mathematical background is only high school calculus you could well believe that mathematics is only about numbers functions and formulas for solving problems. If this is the case, the topics in this book may be quite a surprise because for mathemati­cians, computer scientists and engineers, Discrete Mathematics includes logic, set theory, enumeration, networks, automata, for­mal languages and many other discrete structures. That is what this book is about. On the other hand, in 19 lectures we can only present an introduction to the subject and we must leave other important topics such as graph theory, error-correcting codes, discrete probability theory and applications to theoretical computer science to a sec­ond or third course. The topics covered are set theory, logic, Boolean algebra, count­ing, generating functions, recurrence relations, finite automata and formal languages with a lot of emphasis on counting. The set theory and logic is basic material which will be useful many courses besides Discrete Mathematics. Counting problems which look quite hard when stated in ordinary English can often be solved easily when translated into the language of set theory. We give many examples that reduce to counting the number of functions of various types between sets, or counting the number of subsets of a set.

Schaum S Outline Of Discrete Mathematics Revised Third Edition

Author : Seymour Lipschutz
ISBN : 9780071615877
Genre : Mathematics
File Size : 81. 44 MB
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Tough Test Questions? Missed Lectures? Not Enough Time? Fortunately for you, there's Schaum's Outlines. More than 40 million students have trusted Schaum's to help them succeed in the classroom and on exams. Schaum's is the key to faster learning and higher grades in every subject. Each Outline presents all the essential course information in an easy-to-follow, topic-by-topic format. You also get hundreds of examples, solved problems, and practice exercises to test your skills. This Schaum's Outline gives you: Practice problems with full explanations that reinforce knowledge Coverage of the most up-to-date developments in your course field In-depth review of practices and applications Fully compatible with your classroom text, Schaum's highlights all the important facts you need to know. Use Schaum's to shorten your study time-and get your best test scores! Schaum's Outlines-Problem Solved.

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