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| 2000 solved problems in discrete mathematics: 2000 Solved Problems in Discrete Mathematics Seymour Lipschutz, 2012-09-17 Master discrete mathematics with Schaum's--the high-performance solved-problem guide. It will help you cut study time, hone problem-solving skills, and achieve your personal best on exams! Students love Schaum's Solved Problem Guides because they produce results. Each year, thousands of students improve their test scores and final grades with these indispensable guides. Get the edge on your classmates. Use Schaum's! If you don't have a lot of time but want to excel in class, use this book to: Brush up before tests Study quickly and more effectively Learn the best strategies for solving tough problems in step-by-step detail Review what you've learned in class by solving thousands of relevant problems that test your skill Compatible with any classroom text, Schaum's Solved Problem Guides let you practice at your own pace and remind you of all the important problem-solving techniques you need to remember--fast! And Schaum's are so complete, they're perfect for preparing for graduate or professional exams. Inside you will find: 2,000 solved problems with complete solutions--the largest selection of solved problems yet published on this subject An index to help you quickly locate the types of problems you want to solve Problems like those you'll find on your exams Techniques for choosing the correct approach to problems Guidance toward the quickest, most efficient solutions If you want top grades and thorough understanding of discrete mathematics, this powerful study tool is the best tutor you can have! |
| 2000 solved problems in discrete mathematics: Two Thousand Solved Problems in Discrete Mathematics Seymour Lipschutz, Marc Lipson, 1992 |
| 2000 solved problems in discrete mathematics: 2000 Solved Problems in Discrete Mathematics Seymour Lipschutz, Marc Lipson, 1992 Master discrete mathematics with Schaum's--the high-performance solved-problem guide. It will help you cut study time, hone problem-solving skills, and achieve your personal best on exams! Students love Schaum's Solved Problem Guides because they produce results. Each year, thousands of students improve their test scores and final grades with these indispensable guides. Get the edge on your classmates. Use Schaum's! If you don't have a lot of time but want to excel in class, use this book to: Brush up before tests Study quickly and more effectively Learn the best strategies for solving tough problems in step-by-step detail Review what you've learned in class by solving thousands of relevant problems that test your skill Compatible with any classroom text, Schaum's Solved Problem Guides let you practice at your own pace and remind you of all the important problem-solving techniques you need to remember--fast! And Schaum's are so complete, they're perfect for preparing for graduate or professional exams. Inside you will find: 2,000 solved problems with complete solutions--the largest selection of solved problems yet published on this subject An index to help you quickly locate the types of problems you want to solve Problems like those you'll find on your exams Techniques for choosing the correct approach to problems Guidance toward the quickest, most efficient solutions If you want top grades and thorough understanding of discrete mathematics, this powerful study tool is the best tutor you can have! |
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| 2000 solved problems in discrete mathematics: Schaum's Outline of Discrete Mathematics, 3rd Ed. Seymour Lipschutz, Marc Lipson, 2007-06-01 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 |
| 2000 solved problems in discrete mathematics: Applied Discrete Structures Ken Levasseur, Al Doerr, 2012-02-25 ''In writing this book, care was taken to use language and examples that gradually wean students from a simpleminded mechanical approach and move them toward mathematical maturity. We also recognize that many students who hesitate to ask for help from an instructor need a readable text, and we have tried to anticipate the questions that go unasked. The wide range of examples in the text are meant to augment the favorite examples that most instructors have for teaching the topcs in discrete mathematics. To provide diagnostic help and encouragement, we have included solutions and/or hints to the odd-numbered exercises. These solutions include detailed answers whenever warranted and complete proofs, not just terse outlines of proofs. Our use of standard terminology and notation makes Applied Discrete Structures a valuable reference book for future courses. Although many advanced books have a short review of elementary topics, they cannot be complete. The text is divided into lecture-length sections, facilitating the organization of an instructor's presentation.Topics are presented in such a way that students' understanding can be monitored through thought-provoking exercises. The exercises require an understanding of the topics and how they are interrelated, not just a familiarity with the key words. An Instructor's Guide is available to any instructor who uses the text. It includes: Chapter-by-chapter comments on subtopics that emphasize the pitfalls to avoid; Suggested coverage times; Detailed solutions to most even-numbered exercises; Sample quizzes, exams, and final exams. This textbook has been used in classes at Casper College (WY), Grinnell College (IA), Luzurne Community College (PA), University of the Puget Sound (WA).''-- |
| 2000 solved problems in discrete mathematics: Discrete Mathematics for Computer Science Gary Haggard, John Schlipf, Sue Whitesides, 2006 Master the fundamentals of discrete mathematics with DISCRETE MATHEMATICS FOR COMPUTER SCIENCE with Student Solutions Manual CD-ROM! An increasing number of computer scientists from diverse areas are using discrete mathematical structures to explain concepts and problems and this mathematics text shows you how to express precise ideas in clear mathematical language. Through a wealth of exercises and examples, you will learn how mastering discrete mathematics will help you develop important reasoning skills that will continue to be useful throughout your career. |
| 2000 solved problems in discrete mathematics: Journey into Discrete Mathematics Owen D. Byer, Deirdre L. Smeltzer, Kenneth L. Wantz, 2018-11-13 Journey into Discrete Mathematics is designed for use in a first course in mathematical abstraction for early-career undergraduate mathematics majors. The important ideas of discrete mathematics are included—logic, sets, proof writing, relations, counting, number theory, and graph theory—in a manner that promotes development of a mathematical mindset and prepares students for further study. While the treatment is designed to prepare the student reader for the mathematics major, the book remains attractive and appealing to students of computer science and other problem-solving disciplines. The exposition is exquisite and engaging and features detailed descriptions of the thought processes that one might follow to attack the problems of mathematics. The problems are appealing and vary widely in depth and difficulty. Careful design of the book helps the student reader learn to think like a mathematician through the exposition and the problems provided. Several of the core topics, including counting, number theory, and graph theory, are visited twice: once in an introductory manner and then again in a later chapter with more advanced concepts and with a deeper perspective. Owen D. Byer and Deirdre L. Smeltzer are both Professors of Mathematics at Eastern Mennonite University. Kenneth L. Wantz is Professor of Mathematics at Regent University. Collectively the authors have specialized expertise and research publications ranging widely over discrete mathematics and have over fifty semesters of combined experience in teaching this subject. |
| 2000 solved problems in discrete mathematics: Problems and Exercises in Discrete Mathematics G.P. Gavrilov, A.A. Sapozhenko, 2013-03-09 Many years of practical experience in teaching discrete mathematics form the basis of this text book. Part I contains problems on such topics as Boolean algebra, k-valued logics, graphs and networks, elements of coding theory, automata theory, algorithms theory, combinatorics, Boolean minimization and logical design. The exercises are preceded by ample theoretical background material. For further study the reader is referred to the extensive bibliography. Part II follows the same structure as Part I, and gives helpful hints and solutions. Audience:This book will be of great value to undergraduate students of discrete mathematics, whereas the more difficult exercises, which comprise about one-third of the material, will also appeal to postgraduates and researchers. |
| 2000 solved problems in discrete mathematics: Discrete Mathematics Seymour Lipschutz, Marc Lipson, 2006 |
| 2000 solved problems in discrete mathematics: Counting and Configurations Jiri Herman, Radan Kucera, Jaromir Simsa, 2013-03-14 This book presents methods of solving problems in three areas of elementary combinatorial mathematics: classical combinatorics, combinatorial arithmetic, and combinatorial geometry. Brief theoretical discussions are immediately followed by carefully worked-out examples of increasing degrees of difficulty and by exercises that range from routine to rather challenging. The book features approximately 310 examples and 650 exercises. |
| 2000 solved problems in discrete mathematics: Discrete Mathematics R. K. Bisht, H. S. Dhami, 2015-10-15 Discrete Mathematics is a textbook designed for the students of computer science engineering, information technology, and computer applications to help them develop the foundation of theoretical computer science. |
| 2000 solved problems in discrete mathematics: Discrete Mathematics László Lovász, József Pelikán, Katalin Vesztergombi, 2006-05-10 Aimed at undergraduate mathematics and computer science students, this book is an excellent introduction to a lot of problems of discrete mathematics. It discusses a number of selected results and methods, mostly from areas of combinatorics and graph theory, and it uses proofs and problem solving to help students understand the solutions to problems. Numerous examples, figures, and exercises are spread throughout the book. |
| 2000 solved problems in discrete mathematics: Discrete Mathematics Oscar Levin, 2016-08-16 This gentle introduction to discrete mathematics is written for first and second year math majors, especially those who intend to teach. The text began as a set of lecture notes for the discrete mathematics course at the University of Northern Colorado. This course serves both as an introduction to topics in discrete math and as the introduction to proof course for math majors. The course is usually taught with a large amount of student inquiry, and this text is written to help facilitate this. Four main topics are covered: counting, sequences, logic, and graph theory. Along the way proofs are introduced, including proofs by contradiction, proofs by induction, and combinatorial proofs. The book contains over 360 exercises, including 230 with solutions and 130 more involved problems suitable for homework. There are also Investigate! activities throughout the text to support active, inquiry based learning. While there are many fine discrete math textbooks available, this text has the following advantages: It is written to be used in an inquiry rich course. It is written to be used in a course for future math teachers. It is open source, with low cost print editions and free electronic editions. |
| 2000 solved problems in discrete mathematics: Schaum's Outline of Discrete Mathematics, Fourth Edition Seymour Lipschutz, Marc Lipson, 2021-11-30 Study smarter and stay on top of your discrete mathematics course with the bestselling Schaum’s Outline—now with the NEW Schaum’s app and website! Schaum’s Outline of Discrete Mathematics, Fourth Edition is the go-to study guide for more than 115,000 math majors and first- and second-year university students taking basic computer science courses. With an outline format that facilitates quick and easy review, Schaum’s Outline of Discrete Mathematics, Fourth Edition helps you understand basic concepts and get the extra practice you need to excel in these courses. Coverage includes set theory; relations; functions and algorithms; logic and propositional calculus; techniques of counting; advanced counting techniques, recursion; probability; graph theory; directed graphs; binary trees; properties of the integers; languages, automata, machines; finite state machines and Turning machines; ordered sets and lattices, and Boolean algebra. Features • NEW to this edition: the new Schaum’s app and website! • NEW to this edition: 20 NEW problem-solving videos online • 467 solved problems, and hundreds of additional practice problems • Outline format to provide a concise guide to the standard college course in discrete mathematics • Clear, concise explanations of discrete mathematics concepts • Expanded coverage of logic, the rules of inference and basic types of proofs in mathematical reasoning • Increased emphasis on discrete probability and aspects of probability theory, and greater accessibility to counting techniques. • Logic chapter emphasizes the IF-THEN and IF-THEN-ELSE sequencing that occurs in computer programming • Computer arithmetic chapter covers binary and hexagon addition and multiplication • Cryptology chapter includes substitution and RSA method • Supports these major texts: Discrete Mathematics and Its Applications (Rosen), and Discrete Mathematics (Epp) • Appropriate for the following courses: Introductory Discrete Mathematics and Discrete Mathematics |
| 2000 solved problems in discrete mathematics: 2000 Solved Problems In Discrete Mathematics: Schaum S Solved Problems Series Lipschutz, |
| 2000 solved problems in discrete mathematics: Discrete Mathematical Structures for Computer Science Bernard Kolman, Robert C. Busby, 1987 This text has been designed as a complete introduction to discrete mathematics, primarily for computer science majors in either a one or two semester course. The topics addressed are of genuine use in computer science, and are presented in a logically coherent fashion. The material has been organized and interrelated to minimize the mass of definitions and the abstraction of some of the theory. For example, relations and directed graphs are treated as two aspects of the same mathematical idea. Whenever possible each new idea uses previously encountered material, and then developed in such a way that it simplifies the more complex ideas that follow. |
| 2000 solved problems in discrete mathematics: Discrete Mathematics Babu Ram, 2012 Discrete Mathematics will be of use to any undergraduate as well as post graduate courses in Computer Science and Mathematics. The syllabi of all these courses have been studied in depth and utmost care has been taken to ensure that all the essential topics in discrete structures are adequately emphasized. The book will enable the students to develop the requisite computational skills needed in software engineering. |
| 2000 solved problems in discrete mathematics: Discrete Mathematics with Proof Eric Gossett, 2009-06-22 A Trusted Guide to Discrete Mathematics with Proof?Now in a Newly Revised Edition 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. The book begins with an introductory chapter that provides an accessible explanation of discrete mathematics. Subsequent chapters explore additional related topics including counting, finite probability theory, recursion, formal models in computer science, graph theory, trees, the concepts of functions, and relations. Additional features of the Second Edition include: An intense focus on the formal settings of proofs and their techniques, such as constructive proofs, proof by contradiction, and combinatorial proofs New sections on applications of elementary number theory, multidimensional induction, counting tulips, and the binomial distribution Important examples from the field of computer science presented as applications including the Halting problem, Shannon's mathematical model of information, regular expressions, XML, and Normal Forms in relational databases Numerous examples that are not often found in books on discrete mathematics including the deferred acceptance algorithm, the Boyer-Moore algorithm for pattern matching, Sierpinski curves, adaptive quadrature, the Josephus problem, and the five-color theorem Extensive appendices that outline supplemental material on analyzing claims and writing mathematics, along with solutions to selected chapter exercises Combinatorics receives a full chapter treatment that extends beyond the combinations and permutations material by delving into non-standard topics such as Latin squares, finite projective planes, balanced incomplete block designs, coding theory, partitions, occupancy problems, Stirling numbers, Ramsey numbers, and systems of distinct representatives. A related Web site features animations and visualizations of combinatorial proofs that assist readers with comprehension. In addition, approximately 500 examples and over 2,800 exercises are presented throughout the book to motivate ideas and illustrate the proofs and conclusions of theorems. 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. |
| 2000 solved problems in discrete mathematics: Discrete Mathematics and Computing Malik Magdon-Ismail, 2019-12-14 This text is a semester course in the basic mathematical and theoretical foundations of computer science. Students who make heavy use of computing should learn these foundations well, setting a base for a follow-on course in algorithms. A solid theoretical and algorithmic foundation in computer science sets the stage for developing good programs, programs that work, always and efficiently.Each chapter is a lecture that has been taught as such. Part I starts with basic logic, proofs and discrete mathematics, including: induction, recursion, summation, asymptotics and number theory. We then continue with graphs, counting and combinatorics, and wrap up the coverage of discrete mathematics with discrete probability. Part II presents the blockbuster application of discrete mathematics: the digital computer and a theory of computing. The goal is to understand what a computer can and cannot do. We start small, with automata, and end big with Turing Machines.Our approach is Socratic. The reader is encouraged to participate actively in the learning process by doing the quizzes and exercises that are liberally sprinkled through the text. The pace and level is appropriate for readers with one year of training in programming and calculus (college sophomores). |
| 2000 solved problems in discrete mathematics: Number Theory and Discrete Mathematics A. K. Agarwal, Bruce C. Berndt, Christian F. Krattenthaler, Gary L. Mullen, K. Ramachandra, Michel Waldschmidt, 2002-01-01 |
| 2000 solved problems in discrete mathematics: Schaum's Outline of Graph Theory: Including Hundreds of Solved Problems V. K. Balakrishnan, 1997-02-22 Confusing Textbooks? 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. |
| 2000 solved problems in discrete mathematics: Problem-Solving Strategies Arthur Engel, 2008-01-19 A unique collection of competition problems from over twenty major national and international mathematical competitions for high school students. Written for trainers and participants of contests of all levels up to the highest level, this will appeal to high school teachers conducting a mathematics club who need a range of simple to complex problems and to those instructors wishing to pose a problem of the week, thus bringing a creative atmosphere into the classrooms. Equally, this is a must-have for individuals interested in solving difficult and challenging problems. Each chapter starts with typical examples illustrating the central concepts and is followed by a number of carefully selected problems and their solutions. Most of the solutions are complete, but some merely point to the road leading to the final solution. In addition to being a valuable resource of mathematical problems and solution strategies, this is the most complete training book on the market. |
| 2000 solved problems in discrete mathematics: Street-Fighting Mathematics Sanjoy Mahajan, 2010-03-05 An antidote to mathematical rigor mortis, teaching how to guess answers without needing a proof or an exact calculation. In problem solving, as in street fighting, rules are for fools: do whatever works—don't just stand there! Yet we often fear an unjustified leap even though it may land us on a correct result. Traditional mathematics teaching is largely about solving exactly stated problems exactly, yet life often hands us partly defined problems needing only moderately accurate solutions. This engaging book is an antidote to the rigor mortis brought on by too much mathematical rigor, teaching us how to guess answers without needing a proof or an exact calculation. In Street-Fighting Mathematics, Sanjoy Mahajan builds, sharpens, and demonstrates tools for educated guessing and down-and-dirty, opportunistic problem solving across diverse fields of knowledge—from mathematics to management. Mahajan describes six tools: dimensional analysis, easy cases, lumping, picture proofs, successive approximation, and reasoning by analogy. Illustrating each tool with numerous examples, he carefully separates the tool—the general principle—from the particular application so that the reader can most easily grasp the tool itself to use on problems of particular interest. Street-Fighting Mathematics grew out of a short course taught by the author at MIT for students ranging from first-year undergraduates to graduate students ready for careers in physics, mathematics, management, electrical engineering, computer science, and biology. They benefited from an approach that avoided rigor and taught them how to use mathematics to solve real problems. Street-Fighting Mathematics will appear in print and online under a Creative Commons Noncommercial Share Alike license. |
| 2000 solved problems in discrete mathematics: Discrete Structures, Logic, and Computability James L. Hein, 2001 Discrete Structure, Logic, and Computability introduces the beginning computer science student to some of the fundamental ideas and techniques used by computer scientists today, focusing on discrete structures, logic, and computability. The emphasis is on the computational aspects, so that the reader can see how the concepts are actually used. Because of logic's fundamental importance to computer science, the topic is examined extensively in three phases that cover informal logic, the technique of inductive proof; and formal logic and its applications to computer science. |
| 2000 solved problems in discrete mathematics: Schaum's Outline of Discrete Mathematics Seymour Lipschutz, 2007 |
| 2000 solved problems in discrete mathematics: The Probabilistic Method Noga Alon, Joel H. Spencer, 2015-11-02 Praise for the Third Edition “Researchers of any kind of extremal combinatorics or theoretical computer science will welcome the new edition of this book.” - MAA Reviews Maintaining a standard of excellence that establishes The Probabilistic Method as the leading reference on probabilistic methods in combinatorics, the Fourth Edition continues to feature a clear writing style, illustrative examples, and illuminating exercises. The new edition includes numerous updates to reflect the most recent developments and advances in discrete mathematics and the connections to other areas in mathematics, theoretical computer science, and statistical physics. Emphasizing the methodology and techniques that enable problem-solving, The Probabilistic Method, Fourth Edition begins with a description of tools applied to probabilistic arguments, including basic techniques that use expectation and variance as well as the more advanced applications of martingales and correlation inequalities. The authors explore where probabilistic techniques have been applied successfully and also examine topical coverage such as discrepancy and random graphs, circuit complexity, computational geometry, and derandomization of randomized algorithms. Written by two well-known authorities in the field, the Fourth Edition features: Additional exercises throughout with hints and solutions to select problems in an appendix to help readers obtain a deeper understanding of the best methods and techniques New coverage on topics such as the Local Lemma, Six Standard Deviations result in Discrepancy Theory, Property B, and graph limits Updated sections to reflect major developments on the newest topics, discussions of the hypergraph container method, and many new references and improved results The Probabilistic Method, Fourth Edition is an ideal textbook for upper-undergraduate and graduate-level students majoring in mathematics, computer science, operations research, and statistics. The Fourth Edition is also an excellent reference for researchers and combinatorists who use probabilistic methods, discrete mathematics, and number theory. Noga Alon, PhD, is Baumritter Professor of Mathematics and Computer Science at Tel Aviv University. He is a member of the Israel National Academy of Sciences and Academia Europaea. A coeditor of the journal Random Structures and Algorithms, Dr. Alon is the recipient of the Polya Prize, The Gödel Prize, The Israel Prize, and the EMET Prize. Joel H. Spencer, PhD, is Professor of Mathematics and Computer Science at the Courant Institute of New York University. He is the cofounder and coeditor of the journal Random Structures and Algorithms and is a Sloane Foundation Fellow. Dr. Spencer has written more than 200 published articles and is the coauthor of Ramsey Theory, Second Edition, also published by Wiley. |
| 2000 solved problems in discrete mathematics: Discrete Mathematics with Applications, Metric Edition Susanna Epp, 2019 DISCRETE MATHEMATICS WITH APPLICATIONS, 5th Edition, Metric Edition explains complex, abstract concepts with clarity and precision and provides a strong foundation for computer science and upper-level mathematics courses of the computer age. Author Susanna Epp presents not only the major themes of discrete mathematics, but also the reasoning that underlies mathematical thought. Students develop the ability to think abstractly as they study the ideas of logic and proof. While learning about such concepts as logic circuits and computer addition, algorithm analysis, recursive thinking, computability, automata, cryptography and combinatorics, students discover that the ideas of discrete mathematics underlie and are essential to today's science and technology. |
| 2000 solved problems in discrete mathematics: Templates for the Solution of Algebraic Eigenvalue Problems Zhaojun Bai, James Demmel, Jack Dongarra, Axel Ruhe, Henk van der Vorst, 2000-01-01 Mathematics of Computing -- Numerical Analysis. |
| 2000 solved problems in discrete mathematics: Schaum's Outline of Discrete Mathematics Seymor Lipschutz, Marc Lipson, 1997-06-22 The first edition of this book sold more than 100,000 copies—and this new edition will show you why! Schaum’s Outline of Discrete Mathematics shows you step by step how to solve the kind of problems you’re going to find on your exams. And this new edition features all the latest applications of discrete mathematics to computer science! This guide can be used as a supplement, to reinforce and strengthen the work you do with your class text. (It works well with virtually any discrete mathematics textbook.) But it is so comprehensive that it can even be used alone as a text in discrete mathematics or as independent study tool! |
| 2000 solved problems in discrete mathematics: Probability and Statistical Inference Nitis Mukhopadhyay, 2020-08-30 Priced very competitively compared with other textbooks at this level! This gracefully organized textbook reveals the rigorous theory of probability and statistical inference in the style of a tutorial, using worked examples, exercises, numerous figures and tables, and computer simulations to develop and illustrate concepts. Beginning wi |
| 2000 solved problems in discrete mathematics: How to Prove It Daniel J. Velleman, 2006-01-16 Many students have trouble the first time they take a mathematics course in which proofs play a significant role. This new edition of Velleman's successful text will prepare students to make the transition from solving problems to proving theorems by teaching them the techniques needed to read and write proofs. The book begins with the basic concepts of logic and set theory, to familiarize students with the language of mathematics and how it is interpreted. These concepts are used as the basis for a step-by-step breakdown of the most important techniques used in constructing proofs. The author shows how complex proofs are built up from these smaller steps, using detailed 'scratch work' sections to expose the machinery of proofs about the natural numbers, relations, functions, and infinite sets. To give students the opportunity to construct their own proofs, this new edition contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software. No background beyond standard high school mathematics is assumed. This book will be useful to anyone interested in logic and proofs: computer scientists, philosophers, linguists, and of course mathematicians. |
| 2000 solved problems in discrete mathematics: Discrete Probability Hugh Gordon, 2012-12-06 Intended as a first course in probability at post-calculus level, this book is of special interest to students majoring in computer science as well as in mathematics. Since calculus is used only occasionally in the text, students who have forgotten their calculus can nevertheless easily understand the book, and its slow, gentle style and clear exposition will also appeal. Basic concepts such as counting, independence, conditional probability, random variables, approximation of probabilities, generating functions, random walks and Markov chains are all clearly explained and backed by many worked exercises. The 1,196 numerical answers to the 405 exercises, many with multiple parts, are included at the end of the book, and throughout, there are various historical comments on the study of probability. These include biographical information on such famous contributors as Fermat, Pascal, the Bernoullis, DeMoivre, Bayes, Laplace, Poisson, and Markov. Of interest to a wide range of readers and useful in many undergraduate programs. |
| 2000 solved problems in discrete mathematics: Fundamental Approach To Discrete Mathematics D.P. Acharjya, 2005 Salient Features * Mathematical Logic, Fundamental Concepts, Proofs And Mathematical Induction (Chapter 1) * Set Theory, Fundamental Concepts, Theorems, Proofs, Venn Diagrams, Product Of Sets, Application Of Set Theory And Fundamental Products (Chapter 2) * An Introduction To Binary Relations And Concepts, Graphs, Arrow Diagrams, Relation Matrix, Composition Of Relations, Types Of Relation, Partial Order Relations, Total Order Relation, Closure Of Relations, Poset, Equivalence Classes And Partitions. (Chapter 3) * An Introduction To Functions And Basic Concepts, Graphs, Composition Of Functions, Floor And Ceiling Function, Characteristic Function, Remainder Function, Signum Function And Introduction To Hash Function. (Chapter 4) * The Algebraic Structure Includes Group Theory And Ring Theory. Group Theory Includes Group, Subgroups, Cyclic Group, Cosets, Homomorphism, Introduction To Codes And Group Codes And Error Correction For Block Code. The Ring Theory Includes General Definition, Fundamental Concepts, Integral Domain, Division Ring, Subring, Homomorphism, An Isomorphism And Pigeonhole Principle (Chapters 5, 6 And 7) * A Treatment Of Boolean Algebras That Emphasizes The Relation Of Boolean Algebras To Combinatorial Circuits. (Chapter 8) * An Introduction To Lattices And Basic Concepts (Chapter 9) * A Brief Introduction To Graph Theory Is Discussed. Elements Of Graph Theory Are Indispensable In Almost All Computer Science Areas. Examples Are Given Of Its Use In Such Areas As Minimum Spanning Tree, Shortest Path Problems (Dijkastra'S Algorithm And Floyd-Warshall Algorithm) And Traveling Salesman Problem. The Computer Representation And Manipulation Of Graphs Are Also Discussed So That Certain Important Algorithms Can Be Included(Chapters 10 And 11) * A Strong Emphasis Is Given On Understanding The Theorems And Its Applications * Numbers Of Illustrations Are Used Throughout The Book For Explaining The Concepts And Its Applications. * Figures And Tables Are Used To Illustrate Concepts, To Elucidate Proofs And To Motivate The Material. The Captions Of These Figures Provide Additional Explanation. Besides This, A Number Of Exercises Are Given For Practice |
| 2000 solved problems in discrete mathematics: The Mathematics of Diffusion John Crank, 1979 Though it incorporates much new material, this new edition preserves the general character of the book in providing a collection of solutions of the equations of diffusion and describing how these solutions may be obtained. |
| 2000 solved problems in discrete mathematics: A Problem Book in Real Analysis Asuman G. Aksoy, Mohamed A. Khamsi, 2010-03-10 Education is an admirable thing, but it is well to remember from time to time that nothing worth knowing can be taught. Oscar Wilde, “The Critic as Artist,” 1890. Analysis is a profound subject; it is neither easy to understand nor summarize. However, Real Analysis can be discovered by solving problems. This book aims to give independent students the opportunity to discover Real Analysis by themselves through problem solving. ThedepthandcomplexityofthetheoryofAnalysiscanbeappreciatedbytakingaglimpseatits developmental history. Although Analysis was conceived in the 17th century during the Scienti?c Revolution, it has taken nearly two hundred years to establish its theoretical basis. Kepler, Galileo, Descartes, Fermat, Newton and Leibniz were among those who contributed to its genesis. Deep conceptual changes in Analysis were brought about in the 19th century by Cauchy and Weierstrass. Furthermore, modern concepts such as open and closed sets were introduced in the 1900s. Today nearly every undergraduate mathematics program requires at least one semester of Real Analysis. Often, students consider this course to be the most challenging or even intimidating of all their mathematics major requirements. The primary goal of this book is to alleviate those concerns by systematically solving the problems related to the core concepts of most analysis courses. In doing so, we hope that learning analysis becomes less taxing and thereby more satisfying. |
| 2000 solved problems in discrete mathematics: Discrete Mathematics DeMYSTiFied Steven G. Krantz, 2008-12-15 MULTIPLY your chances of understanding DISCRETE MATHEMATICS If you're interested in learning the fundamentals of discrete mathematics but can't seem to get your brain to function, then here's your solution. Add this easy-to-follow guide to the equation and calculate how quickly you learn the essential concepts. Written by award-winning math professor Steven Krantz, Discrete Mathematics Demystified explains this challenging topic in an effective and enlightening way. You will learn about logic, proofs, functions, matrices, sequences, series, and much more. Concise explanations, real-world examples, and worked equations make it easy to understand the material, and end-of-chapter exercises and a final exam help reinforce learning. This fast and easy guide offers: Numerous figures to illustrate key concepts Sample problems with worked solutions Coverage of set theory, graph theory, and number theory Chapters on cryptography and Boolean algebra A time-saving approach to performing better on an exam or at work Simple enough for a beginner, but challenging enough for an advanced student, Discrete Mathematics Demystified is your integral tool for mastering this complex subject. |
| 2000 solved problems in discrete mathematics: 1000 Solved Problems in Modern Physics Ahmad A. Kamal, 2010-06-23 This book is targeted mainly to the undergraduate students of USA, UK and other European countries, and the M. Sc of Asian countries, but will be found useful for the graduate students, Graduate Record Examination (GRE), Teachers and Tutors. This is a by-product of lectures given at the Osmania University, University of Ottawa and University of Tebrez over several years, and is intended to assist the students in their assignments and examinations. The book covers a wide spectrum of disciplines in Modern Physics, and is mainly based on the actual examination papers of UK and the Indian Universities. The selected problems display a large variety and conform to syllabi which are currently being used in various countries. The book is divided into ten chapters. Each chapter begins with basic concepts containing a set of formulae and explanatory notes for quick reference, followed by a number of problems and their detailed solutions. The problems are judiciously selected and are arranged section-wise. The so- tions are neither pedantic nor terse. The approach is straight forward and step-- step solutions are elaborately provided. More importantly the relevant formulas used for solving the problems can be located in the beginning of each chapter. There are approximately 150 line diagrams for illustration. Basic quantum mechanics, elementary calculus, vector calculus and Algebra are the pre-requisites. |
| 2000 solved problems in discrete mathematics: Discrete Mathematics with Ducks Sarah-marie Belcastro, 2018-11-15 Discrete Mathematics with Ducks, Second Edition is a gentle introduction for students who find the proofs and abstractions of mathematics challenging. At the same time, it provides stimulating material that instructors can use for more advanced students. The first edition was widely well received, with its whimsical writing style and numerous exercises and materials that engaged students at all levels. The new, expanded edition continues to facilitate effective and active learning. It is designed to help students learn about discrete mathematics through problem-based activities. These are created to inspire students to understand mathematics by actively practicing and doing, which helps students better retain what they’ve learned. As such, each chapter contains a mixture of discovery-based activities, projects, expository text, in-class exercises, and homework problems. The author’s lively and friendly writing style is appealing to both instructors and students alike and encourages readers to learn. The book’s light-hearted approach to the subject is a guiding principle and helps students learn mathematical abstraction. Features: The book’s Try This! sections encourage students to construct components of discussed concepts, theorems, and proofs Provided sets of discovery problems and illustrative examples reinforce learning Bonus sections can be used by instructors as part of their regular curriculum, for projects, or for further study |
| 2000 solved problems in discrete mathematics: Problems and Solutions in Mathematics Ji-Xiu Chen, 2011 This book contains a selection of more than 500 mathematical problems and their solutions from the PhD qualifying examination papers of more than ten famous American universities. The mathematical problems cover six aspects of graduate school mathematics: Algebra, Topology, Differential Geometry, Real Analysis, Complex Analysis and Partial Differential Equations. While the depth of knowledge involved is not beyond the contents of the textbooks for graduate students, discovering the solution of the problems requires a deep understanding of the mathematical principles plus skilled techniques. For students, this book is a valuable complement to textbooks. Whereas for lecturers teaching graduate school mathematics, it is a helpful reference. |
2000 Solved Problems In Discrete Mathematics
23 Feb 2024 · 2000 Solved Problems in Discrete Mathematics Seymour Lipschutz,2012-09-17 Master discrete mathematics with Schaum's--the high-performance solved-problem guide. It will help you cut study time, hone problem-solving skills, and
Solved exercises in Discrete mathematics Sample problems
This le contains an English version of exercises in the course of Discrete mathematics. Most of the problems were prepared by Michael Kubesa, Tereza Kova rov a, and Petr Kov a r.
2000 Solved Problems In Discrete Mathematics ? / …
mathematics • Clear, concise explanations of discrete mathematics concepts • Expanded coverage of logic, the rules of inference and basic types of proofs in mathematical reasoning • Increased emphasis on discrete probability and aspects of …
Practice Questions with Solutions - University of Victoria
Department of Mathematics MATH 222 - Discrete and Combinatorial Mathematics Practice Questions with Solutions Contributors: Elise Marchessault Ashna Wright This work is licensed under the Creative Commons Attribution 4.0 International License. To …
2000 Solved Problems In Discrete Mathematics (2024)
Structure and Content: "2000 Solved Problems" typically organizes its content around core topics of discrete mathematics, including: Logic and Set Theory: Boolean algebra, propositional and predicate logic, set operations, relations, functions, and cardinality.
Sample Problems in Discrete Mathematics - Rensselaer …
This handout lists some sample problems that you should be able to solve as a pre-requisite to Design and Analysis of Algorithms. Try to solve all of them. You should also read Chapters 2 and 3 of the textbook, and look at the Exercises at the end of these chapters.
Solved Problems In Discrete Mathematics
2000 Solved Problems in Discrete Mathematics Seymour Lipschutz,2012-09-17 Master discrete mathematics with Schaum's--the high-performance solved-problem guide. It will help you cut study time, hone problem-solving skills, and achieve your personal best on exams! Students love Schaum's Solved Problem Guides because they produce results. Each
2000 Solved Problems In Discrete Mathematics - K. D. Joshi
of problems of discrete mathematics. It discusses a number of selected results and methods, mostly from areas of combinatorics and graph theory, and it uses proofs and problem solving to help students understand the solutions to
2000 Solved Problems In Discrete Mathematics (Download Only)
Structure and Content: "2000 Solved Problems" typically organizes its content around core topics of discrete mathematics, including: Logic and Set Theory: Boolean algebra, propositional and predicate logic, set operations, relations, functions, and cardinality.
2000 Solved Problems In Discrete Mathematics - MotoGP
This powerful problem-solver gives you 2,000 problems in discrete mathematics, fully solved step- by-step! From SchaumÕs, the originator of the solved-problem guide, and...
Discrete Maths: Exercises and Solutions
Discrete Maths: Exercises and Solutions. Basic Structures: Sets, Functions, Sequences, Sums and Matrices. Sequences, Sums and Matrices . Much of discrete mathematics is devoted to the study of discrete structures, used to represent discrete objects. Many important discrete structures are built using sets, which are collections of objects.
Problems on Discrete Mathematics1 LTEX at January 11, 2007
These problems are collections of home works, quizzes, and exams over the past few years. Most of the problems are from Discrete Mathematics with ap-plications by H. F. Mattson, Jr. (Wiley). We hope that these notes will prepare a student to better understand basic mathematics necessary of computer scientists.
2000 Solved Problems In Discrete Mathematics(2) - American …
What is a 2000 Solved Problems In Discrete Mathematics(2) PDF? A PDF (Portable Document Format) is a file format developed by Adobe that preserves the layout and formatting of a document, regardless of the software, hardware, or
2000 Solved Problems In Discrete Mathematics Seymour …
in their fields Perfect for last minute test preparation So small and light that they fit in a backpack Shaum's 2000 Solved Problems in Discrete Mathematics Seymour Lipschutz,Marc Lars,1992 Schaum's Outline of Discrete Mathematics Seymor Lipschutz,Marc Lipson,1997-06-22 The first edition of this book sold more than 100 000 copies and ...
2000 solved problems in discrete mathematics - zenyatta
2000 solved problems in discrete mathematics User-Friendly Interface 2000 solved problems in discrete mathematics 4. At zenyatta.ca, our goal is simple: to democratize knowledge and cultivate a enthusiasm for reading 2000 solved problems in discrete mathematics. We are convinced that each
2000 Solved Problems In Discrete Mathematics
2000 Solved Problems in Discrete Mathematics (Schaum's Solved Problems Series) - Kindle edition by Seymour Lipschutz. Download it once and read it on your Kindle...
2000 Solved Problems In Discrete Mathematics
2000 Solved Problems In Discrete Mathematics Seymour Lipschutz WEBWith roughly 200 different problems, the reader is challenged to approach problems from different angles. Mathematics as Problem Solving is aimed at students from high
2000 Solved Problems In Discrete Mathematics
2000 Solved Problems in Discrete Mathematics - Seymour Lipschutz 2012-09-17 Master discrete mathematics with Schaum's--the high-performance solved-problem guide. It will help you cut study time, hone problem-solving skills, and achieve your personal best on exams! Students love Schaum's Solved Problem Guides because they produce results. Each year,
2000 Solved Problems In Discrete Mathematics
23 Feb 2024 · 2000 Solved Problems in Discrete Mathematics Seymour Lipschutz,2012-09-17 Master discrete mathematics with Schaum's--the high-performance solved-problem guide. It will help you cut study time, hone problem-solving skills, and
Solved exercises in Discrete mathematics Sample problems
This le contains an English version of exercises in the course of Discrete mathematics. Most of the problems were prepared by Michael Kubesa, Tereza Kova rov a, and Petr Kov a r.
2000 Solved Problems In Discrete Mathematics ? / …
mathematics • Clear, concise explanations of discrete mathematics concepts • Expanded coverage of logic, the rules of inference and basic types of proofs in mathematical reasoning • Increased emphasis on discrete probability and aspects of …
Practice Questions with Solutions - University of Victoria
Department of Mathematics MATH 222 - Discrete and Combinatorial Mathematics Practice Questions with Solutions Contributors: Elise Marchessault Ashna Wright This work is licensed under the Creative Commons Attribution 4.0 International License. To …
2000 Solved Problems In Discrete Mathematics (2024)
Structure and Content: "2000 Solved Problems" typically organizes its content around core topics of discrete mathematics, including: Logic and Set Theory: Boolean algebra, propositional and predicate logic, set operations, relations, functions, and cardinality.
Sample Problems in Discrete Mathematics - Rensselaer …
This handout lists some sample problems that you should be able to solve as a pre-requisite to Design and Analysis of Algorithms. Try to solve all of them. You should also read Chapters 2 and 3 of the textbook, and look at the Exercises at the end of these chapters.
Solved Problems In Discrete Mathematics
2000 Solved Problems in Discrete Mathematics Seymour Lipschutz,2012-09-17 Master discrete mathematics with Schaum's--the high-performance solved-problem guide. It will help you cut study time, hone problem-solving skills, and achieve your personal best on exams! Students love Schaum's Solved Problem Guides because they produce results. Each
2000 Solved Problems In Discrete Mathematics - K. D. Joshi
of problems of discrete mathematics. It discusses a number of selected results and methods, mostly from areas of combinatorics and graph theory, and it uses proofs and problem solving to help students understand the solutions to
2000 Solved Problems In Discrete Mathematics (Download Only)
Structure and Content: "2000 Solved Problems" typically organizes its content around core topics of discrete mathematics, including: Logic and Set Theory: Boolean algebra, propositional and predicate logic, set operations, relations, functions, and cardinality.
2000 Solved Problems In Discrete Mathematics - MotoGP
This powerful problem-solver gives you 2,000 problems in discrete mathematics, fully solved step- by-step! From SchaumÕs, the originator of the solved-problem guide, and...
Discrete Maths: Exercises and Solutions
Discrete Maths: Exercises and Solutions. Basic Structures: Sets, Functions, Sequences, Sums and Matrices. Sequences, Sums and Matrices . Much of discrete mathematics is devoted to the study of discrete structures, used to represent discrete objects. Many important discrete structures are built using sets, which are collections of objects.
Problems on Discrete Mathematics1 LTEX at January 11, 2007
These problems are collections of home works, quizzes, and exams over the past few years. Most of the problems are from Discrete Mathematics with ap-plications by H. F. Mattson, Jr. (Wiley). We hope that these notes will prepare a student to better understand basic mathematics necessary of computer scientists.
2000 Solved Problems In Discrete Mathematics(2) - American …
What is a 2000 Solved Problems In Discrete Mathematics(2) PDF? A PDF (Portable Document Format) is a file format developed by Adobe that preserves the layout and formatting of a document, regardless of the software, hardware, or
2000 Solved Problems In Discrete Mathematics Seymour …
in their fields Perfect for last minute test preparation So small and light that they fit in a backpack Shaum's 2000 Solved Problems in Discrete Mathematics Seymour Lipschutz,Marc Lars,1992 Schaum's Outline of Discrete Mathematics Seymor Lipschutz,Marc Lipson,1997-06-22 The first edition of this book sold more than 100 000 copies and ...
2000 solved problems in discrete mathematics - zenyatta
2000 solved problems in discrete mathematics User-Friendly Interface 2000 solved problems in discrete mathematics 4. At zenyatta.ca, our goal is simple: to democratize knowledge and cultivate a enthusiasm for reading 2000 solved problems in discrete mathematics. We are convinced that each
2000 Solved Problems In Discrete Mathematics
2000 Solved Problems in Discrete Mathematics (Schaum's Solved Problems Series) - Kindle edition by Seymour Lipschutz. Download it once and read it on your Kindle...
2000 Solved Problems In Discrete Mathematics
2000 Solved Problems In Discrete Mathematics Seymour Lipschutz WEBWith roughly 200 different problems, the reader is challenged to approach problems from different angles. Mathematics as Problem Solving is aimed at students from high
2000 Solved Problems In Discrete Mathematics
2000 Solved Problems in Discrete Mathematics - Seymour Lipschutz 2012-09-17 Master discrete mathematics with Schaum's--the high-performance solved-problem guide. It will help you cut study time, hone problem-solving skills, and achieve your personal best on exams! Students love Schaum's Solved Problem Guides because they produce results. Each year,
