Topics in Finite and Discrete Mathematics PDF Download
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Author: Sheldon M. Ross
Publisher: Cambridge University Press
ISBN: 0521772591
Category : Mathematics
Languages : en
Pages : 279
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Book Description
A text for engineering students with many examples not normally found in finite mathematics courses.
Author: Sheldon M. Ross
Publisher: Cambridge University Press
ISBN: 0521772591
Category : Mathematics
Languages : en
Pages : 279
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Book Description
A text for engineering students with many examples not normally found in finite mathematics courses.
Author: Eric Gossett
Publisher: John Wiley & Sons
ISBN: 0470457937
Category : Mathematics
Languages : en
Pages : 932
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Book Description
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.
Author: Research & Education Association Editors
Publisher: Research & Education Assoc.
ISBN: 9780738668338
Category : Mathematics
Languages : en
Pages : 1038
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Book Description
h Problem Solver is an insightful and essential study and solution guide chock-full of clear, concise problem-solving gems. All your questions can be found in one convenient source from one of the most trusted names in reference solution guides. More useful, more practical, and more informative, these study aids are the best review books and textbook companions available. Nothing remotely as comprehensive or as helpful exists in their subject anywhere. Perfect for undergraduate and graduate studies. Here in this highly useful reference is the finest overview of finite and discrete math currently available, with hundreds of finite and discrete math problems that cover everything from graph theory and statistics to probability and Boolean algebra. Each problem is clearly solved with step-by-step detailed solutions. DETAILS - The PROBLEM SOLVERS are unique - the ultimate in study guides. - They are ideal for helping students cope with the toughest subjects. - They greatly simplify study and learning tasks. - They enable students to come to grips with difficult problems by showing them the way, step-by-step, toward solving problems. As a result, they save hours of frustration and time spent on groping for answers and understanding. - They cover material ranging from the elementary to the advanced in each subject. - They work exceptionally well with any text in its field. - PROBLEM SOLVERS are available in 41 subjects. - Each PROBLEM SOLVER is prepared by supremely knowledgeable experts. - Most are over 1000 pages. - PROBLEM SOLVERS are not meant to be read cover to cover. They offer whatever may be needed at a given time. An excellent index helps to locate specific problems rapidly. TABLE OF CONTENTS Introduction Chapter 1: Logic Statements, Negations, Conjunctions, and Disjunctions Truth Table and Proposition Calculus Conditional and Biconditional Statements Mathematical Induction Chapter 2: Set Theory Sets and Subsets Set Operations Venn Diagram Cartesian Product Applications Chapter 3: Relations Relations and Graphs Inverse Relations and Composition of Relations Properties of Relations Equivalence Relations Chapter 4: Functions Functions and Graphs Surjective, Injective, and Bijective Functions Chapter 5: Vectors and Matrices Vectors Matrix Arithmetic The Inverse and Rank of a Matrix Determinants Matrices and Systems of Equations, Cramer's Rule Special Kinds of Matrices Chapter 6: Graph Theory Graphs and Directed Graphs Matrices and Graphs Isomorphic and Homeomorphic Graphs Planar Graphs and Colorations Trees Shortest Path(s) Maximum Flow Chapter 7: Counting and Binomial Theorem Factorial Notation Counting Principles Permutations Combinations The Binomial Theorem Chapter 8: Probability Probability Conditional Probability and Bayes' Theorem Chapter 9: Statistics Descriptive Statistics Probability Distributions The Binomial and Joint Distributions Functions of Random Variables Expected Value Moment Generating Function Special Discrete Distributions Normal Distributions Special Continuous Distributions Sampling Theory Confidence Intervals Point Estimation Hypothesis Testing Regression and Correlation Analysis Non-Parametric Methods Chi-Square and Contingency Tables Miscellaneous Applications Chapter 10: Boolean Algebra Boolean Algebra and Boolean Functions Minimization Switching Circuits Chapter 11: Linear Programming and the Theory of Games Systems of Linear Inequalities Geometric Solutions and Dual of Linear Programming Problems The Simplex Method Linear Programming - Advanced Methods Integer Programming The Theory of Games Index WHAT THIS BOOK IS FOR Students have generally found finite and discrete math difficult subjects to understand and learn. Despite the publication of hundreds of textbooks in this field, each one intended to provide an improvement over previous textbooks, students of finite and discrete math continue to remain perplexed as a result of numerous subject areas that must be remembered and correlated when solving problems. Various interpretations of finite and discrete math terms also contribute to the difficulties of mastering the subject. In a study of finite and discrete math, REA found the following basic reasons underlying the inherent difficulties of finite and discrete math: No systematic rules of analysis were ever developed to follow in a step-by-step manner to solve typically encountered problems. This results from numerous different conditions and principles involved in a problem that leads to many possible different solution methods. To prescribe a set of rules for each of the possible variations would involve an enormous number of additional steps, making this task more burdensome than solving the problem directly due to the expectation of much trial and error. Current textbooks normally explain a given principle in a few pages written by a finite and discrete math professional who has insight into the subject matter not shared by others. These explanations are often written in an abstract manner that causes confusion as to the principle's use and application. Explanations then are often not sufficiently detailed or extensive enough to make the reader aware of the wide range of applications and different aspects of the principle being studied. The numerous possible variations of principles and their applications are usually not discussed, and it is left to the reader to discover this while doing exercises. Accordingly, the average student is expected to rediscover that which has long been established and practiced, but not always published or adequately explained. The examples typically following the explanation of a topic are too few in number and too simple to enable the student to obtain a thorough grasp of the involved principles. The explanations do not provide sufficient basis to solve problems that may be assigned for homework or given on examinations. Poorly solved examples such as these can be presented in abbreviated form which leaves out much explanatory material between steps, and as a result requires the reader to figure out the missing information. This leaves the reader with an impression that the problems and even the subject are hard to learn - completely the opposite of what an example is supposed to do. Poor examples are often worded in a confusing or obscure way. They might not state the nature of the problem or they present a solution, which appears to have no direct relation to the problem. These problems usually offer an overly general discussion - never revealing how or what is to be solved. Many examples do not include accompanying diagrams or graphs, denying the reader the exposure necessary for drawing good diagrams and graphs. Such practice only strengthens understanding by simplifying and organizing finite and discrete math processes. Students can learn the subject only by doing the exercises themselves and reviewing them in class, obtaining experience in applying the principles with their different ramifications. In doing the exercises by themselves, students find that they are required to devote considerable more time to finite and discrete math than to other subjects, because they are uncertain with regard to the selection and application of the theorems and principles involved. It is also often necessary for students to discover those "tricks" not revealed in their texts (or review books) that make it possible to solve problems easily. Students must usually resort to methods of trial and error to discover these "tricks," therefore finding out that they may sometimes spend several hours to solve a single problem. When reviewing the exercises in classrooms, instructors usually request students to take turns in writing solutions on the boards and explaining them to the class. Students often find it difficult to explain in a manner that holds the interest of the class, and enables the remaining students to follow the material written on the boards. The remaining students in the class are thus too occupied with copying the material off the boards to follow the professor's explanations. This book is intended to aid students in finite and discrete math overcome the difficulties described by supplying detailed illustrations of the solution methods that are usually not apparent to students. Solution methods are illustrated by problems that have been selected from those most often assigned for class work and given on examinations. The problems are arranged in order of complexity to enable students to learn and understand a particular topic by reviewing the problems in sequence. The problems are illustrated with detailed, step-by-step explanations, to save the students large amounts of time that is often needed to fill in the gaps that are usually found between steps of illustrations in textbooks or review/outline books. The staff of REA considers finite and discrete math a subject that is best learned by allowing students to view the methods of analysis and solution techniques. This learning approach is similar to that practiced in various scientific laboratories, particularly in the medical fields. In using this book, students may review and study the illustrated problems at their own pace; students are not limited to the time such problems receive in the classroom. When students want to look up a particular type of problem and solution, they can readily locate it in the book by referring to the index that has been extensively prepared. It is also possible to locate a particular type of problem by glancing at just the material within the boxed portions. Each problem is numbered and surrounded by a heavy black border for speedy identification.
Author: W.D. Wallis
Publisher: Springer Science & Business Media
ISBN: 9780817642709
Category : Computers
Languages : en
Pages : 376
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Book Description
This concisely written text in finite mathematics gives a sequential, distinctly applied presentation of topics, employing a pedagogical approach that is ideal for freshmen and sophomores in business, the social sciences, and the liberal arts. The work opens with a brief review of sets and numbers, followed by an introduction to data sets, counting arguments, and the Binomial Theorem, which sets the foundation for elementary probability theory and some basic statistics. Further chapters treat graph theory as it relates to modelling, matrices and vectors, and linear programming. Requiring only two years of high school algebra, this book's many examples and illuminating problem sets - with selected solutions - will appeal to a wide audience of students and teachers.
Author: W.D. Wallis
Publisher: Springer Science & Business Media
ISBN: 0817683194
Category : Mathematics
Languages : en
Pages : 488
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Book Description
This second edition of A Beginner’s Guide to Finite Mathematics takes a distinctly applied approach to finite mathematics at the freshman and sophomore level. Topics are presented sequentially: the book opens with a brief review of sets and numbers, followed by an introduction to data sets, histograms, means and medians. Counting techniques and the Binomial Theorem are covered, which provides the foundation for elementary probability theory; this, in turn, leads to basic statistics. This new edition includes chapters on game theory and financial mathematics. Requiring little mathematical background beyond high school algebra, the text will be especially useful for business and liberal arts majors.
Author: Bernard Kolman
Publisher: Prentice Hall
ISBN:
Category : Computer science
Languages : en
Pages : 488
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Book Description
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.
Author: Norbert W Sauer
Publisher: Springer Science & Business Media
ISBN: 9401120803
Category : Mathematics
Languages : en
Pages : 452
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Book Description
This volume contains the accounts of papers delivered at the Nato Advanced Study Institute on Finite and Infinite Combinatorics in Sets and Logic held at the Banff Centre, Alberta, Canada from April 21 to May 4, 1991. As the title suggests the meeting brought together workers interested in the interplay between finite and infinite combinatorics, set theory, graph theory and logic. It used to be that infinite set theory, finite combinatorics and logic could be viewed as quite separate and independent subjects. But more and more those disciplines grow together and become interdependent of each other with ever more problems and results appearing which concern all of those disciplines. I appreciate the financial support which was provided by the N. A. T. O. Advanced Study Institute programme, the Natural Sciences and Engineering Research Council of Canada and the Department of Mathematics and Statistics of the University of Calgary. 11l'te meeting on Finite and Infinite Combinatorics in Sets and Logic followed two other meetings on discrete mathematics held in Banff, the Symposium on Ordered Sets in 1981 and the Symposium on Graphs and Order in 1984. The growing inter-relation between the different areas in discrete mathematics is maybe best illustrated by the fact that many of the participants who were present at the previous meetings also attended this meeting on Finite and Infinite Combinatorics in Sets and Logic.
Author: Gary Haggard
Publisher: Cengage Learning
ISBN: 9780534495015
Category : Computers
Languages : en
Pages : 0
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Book Description
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.
Author: Babu Ram
Publisher: Pearson Education India
ISBN: 9788131733103
Category : Computer science
Languages : en
Pages : 588
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Book Description
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.
Author: Koo-Guan Choo
Publisher: Longman Publishing Group
ISBN: 9780582800557
Category : Computer science
Languages : en
Pages : 148
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Book Description
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.
