Mathematics of Discrete Structures for Computer Science PDF Download

Author: Gordon J. Pace
Publisher: Springer Science & Business Media
ISBN: 3642298400
Category : Computers
Languages : en
Pages : 302

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Book Description
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.

Author: Barbara A. Oakley
Publisher: TarcherPerigee
ISBN: 039916524X
Category : Mathematics
Languages : en
Pages : 338

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Book Description
Engineering professor Barbara Oakley knows firsthand how it feels to struggle with math. In her book, she offers you the tools needed to get a better grasp of that intimidating but inescapable field.

Author: Judith L. Gersting
Publisher: Macmillan Higher Education
ISBN: 1464193827
Category : Mathematics
Languages : en
Pages : 986

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Book Description
Judith Gerstings Mathematical Structures for Computer Science has long been acclaimed for its clear presentation of essential concepts and its exceptional range of applications relevant to computer science majors. Now with this new edition, it is the first discrete mathematics textbook revised to meet the proposed new ACM/IEEE standards for the course.

Author: B. V. Senthil Kumar
Publisher: CRC Press
ISBN: 0429624743
Category : Computers
Languages : en
Pages : 275

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Book Description
This book contains fundamental concepts on discrete mathematical structures in an easy to understand style so that the reader can grasp the contents and explanation easily. The concepts of discrete mathematical structures have application to computer science, engineering and information technology including in coding techniques, switching circuits, pointers and linked allocation, error corrections, as well as in data networking, Chemistry, Biology and many other scientific areas. The book is for undergraduate and graduate levels learners and educators associated with various courses and progammes in Mathematics, Computer Science, Engineering and Information Technology. The book should serve as a text and reference guide to many undergraduate and graduate programmes offered by many institutions including colleges and universities. Readers will find solved examples and end of chapter exercises to enhance reader comprehension. Features Offers comprehensive coverage of basic ideas of Logic, Mathematical Induction, Graph Theory, Algebraic Structures and Lattices and Boolean Algebra Provides end of chapter solved examples and practice problems Delivers materials on valid arguments and rules of inference with illustrations Focuses on algebraic structures to enable the reader to work with discrete structures

Author: Eric Lehman
Publisher:
ISBN: 9789888407064
Category : Business & Economics
Languages : en
Pages : 988

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Book Description
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.

Author: Bernard De Neumann
Publisher:
ISBN:
Category : Computers
Languages : en
Pages : 384

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Book Description
This volume is concerned with the application of formal mathematical methods in software engineering. As the design, writing and testing of software becomes a major sector of economic activity, the need for rigorous techniques has also grown. The papers in this book are devoted to various mathematical structures which find use in aspects of software design, and they cover topics such as the formal specification of systems, the design of communications software, and concurrent processing. All the contributors are experts in their respective fields. As a result, this collection provides a timely survey of this rapidly growing area. Software engineers and computer scientists will find this work to be an invaluable reference source. Mathematicians will appreciate the discussions of the contribution that their discipline can make and the interesting challenges for the future.

Author: Ronald L. Graham
Publisher: Addison-Wesley Professional
ISBN: 0134389980
Category : Computers
Languages : en
Pages : 811

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Book Description
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.

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: James L. Hein
Publisher: Jones & Bartlett Learning
ISBN: 9780763718435
Category : Computers
Languages : en
Pages : 976

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Book Description
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.

Author: Alexander Stepanov
Publisher: Lulu.com
ISBN: 0578222140
Category : Computers
Languages : en
Pages : 282

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Book Description
Elements of Programming provides a different understanding of programming than is presented elsewhere. Its major premise is that practical programming, like other areas of science and engineering, must be based on a solid mathematical foundation. This book shows that algorithms implemented in a real programming language, such as C++, can operate in the most general mathematical setting. For example, the fast exponentiation algorithm is defined to work with any associative operation. Using abstract algorithms leads to efficient, reliable, secure, and economical software.