Lectures On Discrete Mathematics For Computer Science

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Lectures On Discrete Mathematics For Computer Science

Khoussainov Bakhadyr M,Khoussainova Nodira
Lectures On Discrete Mathematics For Computer Science Book PDF

Author : Khoussainov Bakhadyr M,Khoussainova Nodira
Publisher : World Scientific Publishing Company
Page : 364 pages
File Size : 51,5 Mb
Release : 2012-03-21
Category : Mathematics
ISBN : 9789813108127

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Lectures On Discrete Mathematics For Computer Science by Khoussainov Bakhadyr M,Khoussainova Nodira Pdf

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 and Computing

Malik Magdon-Ismail
Discrete Mathematics and Computing Book PDF

Author : Malik Magdon-Ismail
Publisher : Unknown
Page : 128 pages
File Size : 47,9 Mb
Release : 2019-12-14
Category : Electronic
ISBN : 0578567873

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Discrete Mathematics and Computing by Malik Magdon-Ismail Pdf

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).

Discrete Mathematics

Oscar Levin
Discrete Mathematics Book PDF

Author : Oscar Levin
Publisher : Createspace Independent Publishing Platform
Page : 238 pages
File Size : 51,6 Mb
Release : 2018-07-30
Category : Electronic
ISBN : 1724572636

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Discrete Mathematics by Oscar Levin Pdf

Note: This is a custom edition of Levin's full Discrete Mathematics text, arranged specifically for use in a discrete math course for future elementary and middle school teachers. (It is NOT a new and updated edition of the main text.)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.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.

Mathematics for Computer Science

Eric Lehman,F. Thomson Leighton,Albert R. Meyer
Mathematics for Computer Science Book PDF

Author : Eric Lehman,F. Thomson Leighton,Albert R. Meyer
Publisher : Unknown
Page : 988 pages
File Size : 49,5 Mb
Release : 2017-03-08
Category : Business & Economics
ISBN : 9888407066

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Mathematics for Computer Science by Eric Lehman,F. Thomson Leighton,Albert R. Meyer Pdf

This book covers elementary discrete mathematics for computer science and engineering. It emphasizes mathematical definitions and proofs as well as applicable methods. Topics include formal logic notation, proof methods; induction, well-ordering; sets, relations; elementary graph theory; integer congruences; asymptotic notation and growth of functions; permutations and combinations, counting principles; discrete probability. Further selected topics may also be covered, such as recursive definition and structural induction; state machines and invariants; recurrences; generating functions.

Discrete Mathematics for Computer Science

Gary Haggard,John Schlipf,Sue Whitesides
Discrete Mathematics for Computer Science Book PDF

Author : Gary Haggard,John Schlipf,Sue Whitesides
Publisher : Cengage Learning
Page : 0 pages
File Size : 46,7 Mb
Release : 2006
Category : Computers
ISBN : 053449501X

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Discrete Mathematics for Computer Science by Gary Haggard,John Schlipf,Sue Whitesides Pdf

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 Mathematical Structures for Computer Science

Bernard Kolman,Robert C. Busby
Discrete Mathematical Structures for Computer Science Book PDF

Author : Bernard Kolman,Robert C. Busby
Publisher : Prentice Hall
Page : 488 pages
File Size : 52,6 Mb
Release : 1987
Category : Computer science
ISBN : UCSC:32106007549386

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Discrete Mathematical Structures for Computer Science by Bernard Kolman,Robert C. Busby Pdf

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.

Computational Discrete Mathematics

Helmut Alt
Computational Discrete Mathematics Book PDF

Author : Helmut Alt
Publisher : Springer
Page : 173 pages
File Size : 41,5 Mb
Release : 2003-06-30
Category : Computers
ISBN : 9783540455066

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Computational Discrete Mathematics by Helmut Alt Pdf

This book is based on a graduate education program on computational discrete mathematics run for several years in Berlin, Germany, as a joint effort of theoretical computer scientists and mathematicians in order to support doctoral students and advanced ongoing education in the field of discrete mathematics and algorithmics. The 12 selected lectures by leading researchers presented in this book provide recent research results and advanced topics in a coherent and consolidated way. Among the areas covered are combinatorics, graph theory, coding theory, discrete and computational geometry, optimization, and algorithmic aspects of algebra.

Mathematics of Discrete Structures for Computer Science

Gordon J. Pace
Mathematics of Discrete Structures for Computer Science Book PDF

Author : Gordon J. Pace
Publisher : Springer Science & Business Media
Page : 302 pages
File Size : 45,5 Mb
Release : 2012-07-09
Category : Computers
ISBN : 9783642298394

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Mathematics of Discrete Structures for Computer Science by Gordon J. Pace Pdf

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 in Statistical Physics

Martin Loebl
Discrete Mathematics in Statistical Physics Book PDF

Author : Martin Loebl
Publisher : Springer Science & Business Media
Page : 187 pages
File Size : 40,9 Mb
Release : 2010-02-16
Category : Science
ISBN : 9783834893291

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Discrete Mathematics in Statistical Physics by Martin Loebl Pdf

The book first describes connections between some basic problems and technics of combinatorics and statistical physics. The discrete mathematics and physics terminology are related to each other. Using the established connections, some exciting activities in one field are shown from a perspective of the other field. The purpose of the book is to emphasize these interactions as a strong and successful tool. In fact, this attitude has been a strong trend in both research communities recently. It also naturally leads to many open problems, some of which seem to be basic. Hopefully, this book will help making these exciting problems attractive to advanced students and researchers.

Discrete Mathematics Using a Computer

Cordelia Hall,John O'Donnell
Discrete Mathematics Using a Computer Book PDF

Author : Cordelia Hall,John O'Donnell
Publisher : Springer Science & Business Media
Page : 345 pages
File Size : 49,7 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781447136576

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Discrete Mathematics Using a Computer by Cordelia Hall,John O'Donnell Pdf

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.

Essential Discrete Mathematics for Computer Science

Harry Lewis,Rachel Zax
Essential Discrete Mathematics for Computer Science Book PDF

Author : Harry Lewis,Rachel Zax
Publisher : Princeton University Press
Page : 408 pages
File Size : 53,7 Mb
Release : 2019-03-19
Category : Computers
ISBN : 9780691179292

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Essential Discrete Mathematics for Computer Science by Harry Lewis,Rachel Zax Pdf

Discrete mathematics is the basis of much of computer science, from algorithms and automata theory to combinatorics and graph theory. Essential Discrete Mathematics for Computer Science aims to teach mathematical reasoning as well as concepts and skills by stressing the art of proof. It is fully illustrated in color, and each chapter includes a concise summary as well as a set of exercises.

Theoretical Aspects of Computer Science

Gholamreza B. Khosrovshahi,Ali Shokoufandeh,Amin Shokrollahi
Theoretical Aspects of Computer Science Book PDF

Author : Gholamreza B. Khosrovshahi,Ali Shokoufandeh,Amin Shokrollahi
Publisher : Springer
Page : 228 pages
File Size : 43,9 Mb
Release : 2003-07-31
Category : Computers
ISBN : 9783540458784

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Theoretical Aspects of Computer Science by Gholamreza B. Khosrovshahi,Ali Shokoufandeh,Amin Shokrollahi Pdf

This book presents the revised final versions of eight lectures given by leading researchers at the First Summer School on Theoretical Aspects of Computer Science in Tehran, Iran, in July 2000. The lectures presented are devoted to quantum computation, approximation algorithms, self-testing/correction, algebraic modeling of data, the regularity lemma, multiple access communication and combinatorial designs, graph-theoretical methods in computer vision, and low-density parity-check codes.

Concrete Mathematics

Ronald L. Graham,Donald E. Knuth,Oren Patashnik
Concrete Mathematics Book PDF

Author : Ronald L. Graham,Donald E. Knuth,Oren Patashnik
Publisher : Addison-Wesley Professional
Page : 811 pages
File Size : 55,5 Mb
Release : 1994-02-28
Category : Computers
ISBN : 9780134389981

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Concrete Mathematics by Ronald L. Graham,Donald E. Knuth,Oren Patashnik Pdf

This book introduces the mathematics that supports advanced computer programming and the analysis of algorithms. The primary aim of its well-known authors is to provide a solid and relevant base of mathematical skills - the skills needed to solve complex problems, to evaluate horrendous sums, and to discover subtle patterns in data. It is an indispensable text and reference not only for computer scientists - the authors themselves rely heavily on it! - but for serious users of mathematics in virtually every discipline. Concrete Mathematics is a blending of CONtinuous and disCRETE mathematics. "More concretely," the authors explain, "it is the controlled manipulation of mathematical formulas, using a collection of techniques for solving problems." The subject matter is primarily an expansion of the Mathematical Preliminaries section in Knuth's classic Art of Computer Programming, but the style of presentation is more leisurely, and individual topics are covered more deeply. Several new topics have been added, and the most significant ideas have been traced to their historical roots. The book includes more than 500 exercises, divided into six categories. Complete answers are provided for all exercises, except research problems, making the book particularly valuable for self-study. Major topics include: Sums Recurrences Integer functions Elementary number theory Binomial coefficients Generating functions Discrete probability Asymptotic methods This second edition includes important new material about mechanical summation. In response to the widespread use of the first edition as a reference book, the bibliography and index have also been expanded, and additional nontrivial improvements can be found on almost every page. Readers will appreciate the informal style of Concrete Mathematics. Particularly enjoyable are the marginal graffiti contributed by students who have taken courses based on this material. The authors want to convey not only the importance of the techniques presented, but some of the fun in learning and using them.

Lectures on Discrete Geometry

Jiri Matousek
Lectures on Discrete Geometry Book PDF

Author : Jiri Matousek
Publisher : Springer Science & Business Media
Page : 491 pages
File Size : 44,9 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461300397

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Lectures on Discrete Geometry by Jiri Matousek Pdf

The main topics in this introductory text to discrete geometry include basics on convex sets, convex polytopes and hyperplane arrangements, combinatorial complexity of geometric configurations, intersection patterns and transversals of convex sets, geometric Ramsey-type results, and embeddings of finite metric spaces into normed spaces. In each area, the text explains several key results and methods.

Fundamentals of Discrete Math for Computer Science

Tom Jenkyns,Ben Stephenson
Fundamentals of Discrete Math for Computer Science Book PDF

Author : Tom Jenkyns,Ben Stephenson
Publisher : Springer Science & Business Media
Page : 424 pages
File Size : 44,9 Mb
Release : 2012-10-16
Category : Computers
ISBN : 9781447140696

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Fundamentals of Discrete Math for Computer Science by Tom Jenkyns,Ben Stephenson Pdf

This textbook provides an engaging and motivational introduction to traditional topics in discrete mathematics, in a manner specifically designed to appeal to computer science students. The text empowers students to think critically, to be effective problem solvers, to integrate theory and practice, and to recognize the importance of abstraction. Clearly structured and interactive in nature, the book presents detailed walkthroughs of several algorithms, stimulating a conversation with the reader through informal commentary and provocative questions. Features: no university-level background in mathematics required; ideally structured for classroom-use and self-study, with modular chapters following ACM curriculum recommendations; describes mathematical processes in an algorithmic manner; contains examples and exercises throughout the text, and highlights the most important concepts in each section; selects examples that demonstrate a practical use for the concept in question.