Discrete Mathematics in the Schools


Author: Joseph G. Rosenstein
Publisher: American Mathematical Soc.
ISBN: 9780821885789
Category: Mathematics
Page: 452
View: 6477
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This book provides teachers of all levels with a great deal of valuable material to help them introduce discrete mathematics into their classrooms.

Fundamentals of Discrete Math for Computer Science

A Problem-Solving Primer
Author: Tom Jenkyns,Ben Stephenson
Publisher: Springer
ISBN: 3319701517
Category: Computers
Page: 512
View: 4490
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This clearly written textbook presents an accessible introduction to discrete mathematics for computer science students, offering the reader an enjoyable and stimulating path to improve their programming competence. The text empowers students to think critically, to be effective problem solvers, to integrate theory and practice, and to recognize the importance of abstraction. Its motivational and interactive style provokes a conversation with the reader through a questioning commentary, and supplies detailed walkthroughs of several algorithms. This updated and enhanced new edition also includes new material on directed graphs, and on drawing and coloring graphs, in addition to more than 100 new exercises (with solutions to selected exercises). Topics and features: assumes no prior mathematical knowledge, and discusses concepts in programming as and when they are needed; designed for both classroom use and self-study, presenting modular and self-contained chapters that follow ACM curriculum recommendations; describes mathematical processes in an algorithmic manner, often supported by a walkthrough demonstrating how the algorithm performs the desired task; includes an extensive set of exercises throughout the text, together with numerous examples, and shaded boxes highlighting key concepts; selects examples that demonstrate a practical use for the concept in question. Students embarking on the start of their studies of computer science will find this book to be an easy-to-understand and fun-to-read primer, ideal for use in a mathematics course taken concurrently with their first programming course.

Discrete Mathematics Using a Computer


Author: Cordelia Hall,John O'Donnell
Publisher: Springer Science & Business Media
ISBN: 1447136578
Category: Mathematics
Page: 339
View: 2769
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Several areas of mathematics find application throughout computer science, and all students of computer science need a practical working understanding of them. These core subjects are centred on logic, sets, recursion, induction, relations and functions. The material is often called discrete mathematics, to distinguish it from the traditional topics of continuous mathematics such as integration and differential equations. The central theme of this book is the connection between computing and discrete mathematics. This connection is useful in both directions: • Mathematics is used in many branches of computer science, in applica tions including program specification, datastructures,design and analysis of algorithms, database systems, hardware design, reasoning about the correctness of implementations, and much more; • Computers can help to make the mathematics easier to learn and use, by making mathematical terms executable, making abstract concepts more concrete, and through the use of software tools such as proof checkers. These connections are emphasised throughout the book. Software tools (see Appendix A) enable the computer to serve as a calculator, but instead of just doing arithmetic and trigonometric functions, it will be used to calculate with sets, relations, functions, predicates and inferences. There are also special software tools, for example a proof checker for logical proofs using natural deduction.

Introductory Discrete Mathematics


Author: V. K . Balakrishnan
Publisher: Courier Corporation
ISBN: 0486140385
Category: Mathematics
Page: 256
View: 4126
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This concise, undergraduate-level text focuses on combinatorics, graph theory with applications to some standard network optimization problems, and algorithms. More than 200 exercises, many with complete solutions. 1991 edition.

A Logical Approach to Discrete Math


Author: David Gries,Fred B. Schneider
Publisher: Springer Science & Business Media
ISBN: 1475738374
Category: Computers
Page: 516
View: 4258
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Here, the authors strive to change the way logic and discrete math are taught in computer science and mathematics: while many books treat logic simply as another topic of study, this one is unique in its willingness to go one step further. The book traets logic as a basic tool which may be applied in essentially every other area.

Discrete Mathematics for Computer Science


Author: Gary Haggard,John Schlipf,Sue Whitesides
Publisher: Brooks/Cole Publishing Company
ISBN: 9780534495015
Category: Mathematics
Page: 600
View: 5869
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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.

Discrete Mathematics


Author: Martin Aigner
Publisher: American Mathematical Soc.
ISBN: 9780821886151
Category: Mathematics
Page: 388
View: 9104
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The advent of fast computers and the search for efficient algorithms revolutionized combinatorics and brought about the field of discrete mathematics. This book is an introduction to the main ideas and results of discrete mathematics, and with its emphasis on algorithms it should be interesting to mathematicians and computer scientists alike. The book is organized into three parts: enumeration, graphs and algorithms, and algebraic systems. There are 600 exercises with hints andsolutions to about half of them. The only prerequisites for understanding everything in the book are linear algebra and calculus at the undergraduate level. Praise for the German edition ... This book is a well-written introduction to discrete mathematics and is highly recommended to every student ofmathematics and computer science as well as to teachers of these topics. --Konrad Engel for MathSciNet Martin Aigner is a professor of mathematics at the Free University of Berlin. He received his PhD at the University of Vienna and has held a number of positions in the USA and Germany before moving to Berlin. He is the author of several books on discrete mathematics, graph theory, and the theory of search. The Monthly article Turan's graph theorem earned him a 1995 Lester R. Ford Prize of theMAA for expository writing, and his book Proofs from the BOOK with Gunter M. Ziegler has been an international success with translations into 12 languages.

Discrete Mathematics with Proof


Author: Eric Gossett
Publisher: John Wiley & Sons
ISBN: 0470457937
Category: Mathematics
Page: 904
View: 9349
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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.

Discrete Mathematics for Computing


Author: Rod Haggarty
Publisher: Editorial Dunken
ISBN: 9780201730470
Category: Computers
Page: 235
View: 7310
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This book is a short, concise introduction to key mathematical ideas for computing students which develops their understanding of discrete mathematics and its application in computing. The topics are presented in a well defined, logical order that build upon each other and are constantly reinforced by worked examples. Reliance on students' previous mathematical experience is kept to a minimum, though some basic algebraic manipulation is required. This book is appropriate for CS and Math students in an undergraduate Discrete Math course. The content constitutes an accepted core of mathematics for computer scientists (for example, the formal methods used in computer science draw heavily on the discrete methematical concepts covered here, particularly logic, sets, relations and functions). Emphasis is placed on clear and careful explanations of basic ideas and on building confidence in developing mathematical competence through carefully selected exercises. All chapters conclude with short applications/case studies relevant to computing, which provide further motivation to engage with the mathematical ideas involved, and also demonstrate how the mathematics can be applied in a computing context.

A Short Course in Discrete Mathematics


Author: Edward A. Bender,S. Gill Williamson
Publisher: Courier Corporation
ISBN: 0486439461
Category: Mathematics
Page: 240
View: 8719
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What sort of mathematics do I need for computer science? In response to this frequently asked question, a pair of professors at the University of California at San Diego created this text. Its sources are two of the university's most basic courses: Discrete Mathematics, and Mathematics for Algorithm and System Analysis. Intended for use by sophomores in the first of a two-quarter sequence, the text assumes some familiarity with calculus. Topics include Boolean functions and computer arithmetic; logic; number theory and cryptography; sets and functions; equivalence and order; and induction, sequences, and series. Multiple choice questions for review appear throughout the text. Original 2005 edition. Notation Index. Subject Index.

UNDERSTANDING DISCRETE MATHEMATICS WITH APPLICATIONS IN COMPUTER SCIENCE


Author: MUZZAFA RASOOL BHAT & ASHIQ HUSSAIN HELLA
Publisher: Onlinegatha
ISBN: 9386352540
Category:
Page: 288
View: 8857
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Relationen und Graphen


Author: Gunther Schmidt,Thomas Ströhlein
Publisher: Springer-Verlag
ISBN: 3642836089
Category: Mathematics
Page: 306
View: 5395
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Dieses Buch gibt eine neuartige systematische Darstellung der Diskreten Mathematik; sie orientiert sich an Methoden der Relationenalgebra. Ähnlich wie man es sonst nur für die weit entwickelte Analysis im kontinuierlichen Fall und die Matrizenrechnung gewohnt ist, stellt dieses Buch auch für die Behandlung diskreter Probleme geeignete Techniken und Hilfsmittel sowie eine einheitliche Theorie bereit. Die einzelnen Kapitel beginnen jeweils mit anschaulichen und motivierenden Beispielen und behandeln anschließend den Stoff in mathematischer Strenge. Es folgen jeweils praktische Anwendungen. Diese entstammen der Semantik der Programmierung, der Programmverifikation, dem Datenbankbereich, der Spieltheorie oder der Theorie der Zuordnungen und Überdeckungen aus der Graphentheorie; sie reichen aber auch bis zu rein mathematischen "Anwendungen" wie der transfiniten Induktion. Im Anhang ist dem Buch eine Einführung in die Boolesche Algebra und in die Axiomatik der Relationenalgebra beigegeben, sowie ein Abriß der Fixpunkt- und Antimorphismen-Theorie.

Lectures on Discrete Mathematics for Computer Science


Author: Bakhadyr Khoussainov,Nodira Khoussainova
Publisher: World Scientific Publishing Company
ISBN: 9813108126
Category: Mathematics
Page: 364
View: 9936
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This textbook presents fundamental topics in discrete mathematics introduced from the perspectives of a pure mathematician and an applied computer scientist. The synergy between the two complementary perspectives is seen throughout the book; key concepts are motivated and explained through real-world examples, and yet are still formalized with mathematical rigor. The book is an excellent introduction to discrete mathematics for computer science, software engineering, and mathematics students. The first author is a leading mathematician in the area of logic, computability, and theoretical computer science, with more than 25 years of teaching and research experience. The second author is a computer science PhD student at the University of Washington specializing in database systems. The father-and-daughter team merges two different views to create a unified book for students interested in learning discrete mathematics, the connections between discrete mathematics and computer science, and the mathematical foundations of computer science. Readers will learn how to formally define abstract concepts, reason about objects (such as programs, graphs and numbers), investigate properties of algorithms, and prove their correctness. The textbook studies several well-known algorithmic problems including the path problem for graphs and finding the greatest common divisor, inductive definitions, proofs of correctness of algorithms via loop invariants and induction, the basics of formal methods such as propositional logic, finite state machines, counting, probability, as well as the foundations of databases such as relational calculus.

Discrete mathematics in the first two years


Author: Anthony Ralston
Publisher: Mathematical Assn of Amer
ISBN: N.A
Category: Mathematics
Page: 101
View: 3754
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Mathematics of Discrete Structures for Computer Science


Author: Gordon J. Pace
Publisher: Springer Science & Business Media
ISBN: 3642298397
Category: Computers
Page: 296
View: 8310
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Mathematics plays a key role in computer science, some researchers would consider computers as nothing but the physical embodiment of mathematical systems. And whether you are designing a digital circuit, a computer program or a new programming language, you need mathematics to be able to reason about the design -- its correctness, robustness and dependability. This book covers the foundational mathematics necessary for courses in computer science. The common approach to presenting mathematical concepts and operators is to define them in terms of properties they satisfy, and then based on these definitions develop ways of computing the result of applying the operators and prove them correct. This book is mainly written for computer science students, so here the author takes a different approach: he starts by defining ways of calculating the results of applying the operators and then proves that they satisfy various properties. After justifying his underlying approach the author offers detailed chapters covering propositional logic, predicate calculus, sets, relations, discrete structures, structured types, numbers, and reasoning about programs. The book contains chapter and section summaries, detailed proofs and many end-of-section exercises -- key to the learning process. The book is suitable for undergraduate and graduate students, and although the treatment focuses on areas with frequent applications in computer science, the book is also suitable for students of mathematics and engineering.

Discrete Mathematics for Computer Scientists


Author: Clifford Stein,Robert L. Drysdale,Kenneth P. Bogart
Publisher: N.A
ISBN: 9780131377103
Category: Computer science
Page: 525
View: 7330
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Stein/Drysdale/Bogart's Discrete Mathematics for Computer Scientists is ideal for computer science students taking the discrete math course. Written specifically for computer science students, this unique textbook directly addresses their needs by providing a foundation in discrete math while using motivating, relevant CS applications. This text takes an active-learning approach where activities are presented as exercises and the material is then fleshed out through explanations and extensions of the exercises.

Discrete Mathematics with Combinatorics


Author: James Andrew Anderson,Jerome L. Lewis
Publisher: Prentice Hall
ISBN: 9780130457912
Category: Computers
Page: 909
View: 7187
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For one-/two- semester, freshman courses in Discrete Mathematics. This carefully organized, very readable text 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 texts, 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.

ADVANCED DISCRETE MATHEMATICS


Author: UDAY SINGH RAJPUT
Publisher: PHI Learning Pvt. Ltd.
ISBN: 8120345894
Category: Mathematics
Page: 400
View: 5805
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Written in an accessible style, this text provides a complete coverage of discrete mathematics and its applications at an appropriate level of rigour. The book discusses algebraic structures, mathematical logic, lattices, Boolean algebra, graph theory, automata theory, grammars and recurrence relations. It covers the important topics such as coding theory, Dijkstra’s shortest path algorithm, reverse polish notation, Warshall’s algorithm, Menger’s theorem, Turing machine, and LR(k) parsers, which form a part of the fundamental applications of discrete mathematics in computer science. In addition, Pigeonhole principle, ring homomorphism, field and integral domain, trees, network flows, languages, and recurrence relations. The text is supported with a large number of examples, worked-out problems and diagrams that help students understand the theoretical explanations. The book is intended as a text for postgraduate students of mathematics, computer science, and computer applications. In addition, it will be extremely useful for the undergraduate students of computer science and engineering.

Relations and graphs

discrete mathematics for computer scientists
Author: Günther Schmidt,Thomas Ströhlein
Publisher: New York
ISBN: 9783540562542
Category: Computers
Page: 301
View: 9737
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Relational methods can be found at various places in computer science, notably in data base theory, relational semantics of concurrency, relationaltype theory, analysis of rewriting systems, and modern programming language design. In addition, they appear in algorithms analysis and in the bulk of discrete mathematics taught to computer scientists. This book is devoted to the background of these methods. It explains how to use relational and graph-theoretic methods systematically in computer science. A powerful formal framework of relational algebra is developed with respect to applications to a diverse range of problem areas. Results are first motivated by practical examples, often visualized by both Boolean 0-1-matrices and graphs, and then derived algebraically.