Discrete Mathematics for Computing presents the essential mathematics needed for the study of computing and information systems. The subject is covered in a gentle and informal style, but without compromising the need for correct methodology. It is perfect for students with a limited background in mathematics. This new edition includes: - An expanded section on encryption - Additional examples of the ways in which theory can be applied to problems in computing - Many more exercises covering a range of levels, from the basic to the more advanced This book is ideal for students taking a one-semester introductory course in discrete mathematics - particularly for first year undergraduates studying Computing and Information Systems. PETER GROSSMAN has worked in both academic and industrial roles as a mathematician and computing professional. As a lecturer in mathematics, he was responsible for coordinating and developing mathematics courses for Computing students. He has also applied his skills in areas as diverse as calculator design, irrigation systems and underground mine layouts. He lives and works in Melbourne, Australia.

This volume offers a new, hands-on approach to teaching Discrete Mathematics. A simple functional language is used to allow students to experiment with mathematical notations which are traditionally difficult to pick up. This practical approach provides students with instant feedback and also allows lecturers to monitor progress easily. All the material needed to use the book will be available via ftp (the software is freely available and runs on Mac, PC and Unix platforms), including a special module which implements the concepts to be learned.No prior knowledge of Functional Programming is required: apart from List Comprehension (which is comprehensively covered in the text) everything the students need is either provided for them or can be picked up easily as they go along. An Instructors Guide will also be available on the WWW to help lecturers adapt existing courses.

DSP System Design presents the investigation of special type of IIR polyphase filter structures combined with frequency transformation techniques used for fast, multi-rate filtering, and their application for custom fixed-point implementation. Detailed theoretical analysis of the polyphase IIR structure has been presented for two and three coefficients in the two-path arrangement. This was then generalized for arbitrary filter order and any number of paths. The use of polyphase IIR structures in decimation and interpolation is being presented and performance assessed in terms of the number of calculations required for the given filter specification and the simplicity of implementation. Specimen decimation filter designs to be used in Sigma-Delta lowpass and bandpass A/D converters are presented which prove to outperform other traditional approaches. New frequency transformation types have been suggested for both real and complex situations. A new exact multi-point frequency transformation approach for arbitrary frequency choice has been suggested and evaluated. Applying such transformations to the existing filter allows to change their frequency response in an intuitive manner without the need of re-designing them, thus simplifying the designer's job when the specification changes during the prototyping and testing. A new bit-flipping' algorithm has been developed to aid in filter design where the coefficient word length is constraint. Also, the standard Downhill Simplex Method (floating-point) was modified to operate with the constrained coefficient word length. Performance of both these advances is being evaluated on a number of filter cases. Novel decimation and interpolation structures have been proposed, which can be implemented very efficiently. These allow an arbitrary order IIR anti-aliasing filter to operate at the lower rate of the decimator/interpolator. Similar structures for polyphase IIR decimator/interpolator structures are being discussed too. A new approach to digital filter design and implementation has been suggested which speeds-up silicon implementation of designs developed in Matlab. The Simulink block description is converted automatically into a bit-to-bit equivalent VHDL description. This in turn can be compiled, simulated, synthesized and fabricated without the need to go through the design process twice, first algorithmic/structural design and then the implementation. The book is full of design and analysis techniques. It contains sufficient introductory material enabling non-expert readers to understand the material given in it. DSP System Design may be of interest to graduate students, researchers, and professionals circuit designers, who would require fast and low-complexity digital filters for both single and multi-rate applications, especially those with low-power specification.

This text is suitable for an introductory course in the mathematics related to computing, generally referred to as discrete mathematics. Topics covered include set theory, logic, and methods of proof, graphs, digraphs and trees, number systems and matrix algebra, and an introduction to binary codes. Throughout the book, the interrelations between the mathematical structures and their representations is stressed, and use is made of 'action diagrams' as a language-independent means of presenting algorithmic processes. Readers who work through this text will acquire the mathematical knowledge and approach to problem solving required by introductory computing courses, and a sound bases from which to pursue the subject further.

An approachable textbook connecting the mathematical foundations of computer science to broad-ranging and compelling applications throughout the field.

This is a new edition of a successful introduction to discrete mathematics for computer scientists, updated and reorganised to be more appropriate for the modern day undergraduate audience. Discrete mathematics forms the theoretical basis for computer science and this text combines a rigorous approach to mathematical concepts with strong motivation of these techniques via practical examples. Key Features Thorough coverage of all area of discrete mathematics, including logic, natural numbers, coding theory, combinatorics, sets, algebraic functions, partially ordered structures, graphs, formal machines & complexity theory Special emphasis on the central role of propositional & predicate logic Full chapters on algorithm analysis & complexity theory Introductory coverage of formal machines & coding theory Over 700 exercises Flexible structure so that the material can be easily adapted for different teaching styles. New to this Edition Improved treatment of induction Coverage of more 'basic' algebra List of symbols including page references for definition/explantion Modern text design and new exercises to aid student comprehension 0201360616B04062001

Mathematical Foundations of Computer Science/Discrete Mathematics caters to all students of JNTU Kakinada and JNTU Anantapur who study the subject. Major topics including, but not limited to Set Theory, Relations, Functions, Algebraic Structures, Combinatorics and Number Theory have been explained in detail along with the examples which are based on the latest examinations of various institutions.

The refereed proceedings of the 4th International Conference on Discrete Mathematics and Theoretical Computer Science, DMTCS 2003, held in Dijon, France, in July 2003. The 18 revised full papers presented together with 5 invited papers were carefully reviewed and selected from 35 submissions. A broad variety of topics in discrete mathematics and the theory of computing is addressed including information theory, coding, algorithms, complexity, automata, computational mathematics, combinatorial computations, graph computations, algorithmic geometry, relational methods, game-theoretic methods, combinatorial optimization, and finite state systems.

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.

Winner at the 46th Annual New England Book Show (2003) in the "College Covers & Jackets" category This introduction to discrete mathematics prepares future computer scientists, engineers, and mathematicians for success by providing extensive and concentrated coverage of logic, functions, algorithmic analysis, and algebraic structures. Discrete Mathematics, Second Edition illustrates the relationships between key concepts through its thematic organization and provides a seamless transition between subjects. Distinct for the depth with which it covers logic, this text emphasizes problem solving and the application of theory as it carefully guides the reader from basic to more complex topics. Discrete Mathematics is an ideal resource for discovering the fundamentals of discrete math. Discrete Mathematics, Second Edition is designed for an introductory course in discrete mathematics for the prospective computer scientist, applied mathematician, or engineer who wants to learn how the ideas apply to computer sciences.The choice of topics-and the breadth of coverage-reflects the desire to provide students with the foundations needed to successfully complete courses at the upper division level in undergraduate computer science courses. This book differs in several ways from current books about discrete mathematics.It presents an elementary and unified introduction to a collection of topics that has not been available in a single source.A major feature of the book is the unification of the material so that it does not fragment into a collection of seemingly unrelated ideas.