Mathematics of Discrete Structures for Computer Science

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 circ

Written exclusively with computer science students in mind,?Discrete Mathematics for Computer Science provides a comprehensive treatment of standard course topics for the introductory discrete mathema

Discrete Mathematics is a textbook designed for the students of computer science engineering, information technology, and computer applications to help them develop the foundation of theoretical compu

Discrete Mathematics is designed to serve as a textbook for undergraduate engineering students of computer science and postgraduate students of Computer Applications. The book would also prove useful

Aimed at undergraduates in mathematics, computer science, operational research, and related subjects, this text covers the basics of discrete mathematics. A sampling of topics includes natural numbers

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 programm

This book is a clear and self-contained introduction to discrete mathematics. Aimed mainly at undergraduate and early graduate students of mathematics and computer science. It is written with the goal

Formal specification is the name given to the use of discrete mathematics in computer science for describing the function of both hardware and software systems. Poor specification often gives rise to

Discrete mathematics and theoretical computer science are closely linked research areas with strong impacts on applications and various other scientific disciplines. Both fields deeply cross fertilize

Computing is an exact science and the systematic study of any aspect necessarily involves the use of mathematical models. Moreover, the rate at which the subject is evolving demands a facility for developing new mathematical systems to keep pace with new computing systems and this requires an appreciation of how mathematics works. An understanding of the underlying mathematical structure facilitates the construction of suitable computer programs to perform computations. Assuming no specific knowledge of mathematics, the authors describe all the basic concepts required and progress from sets (rather than numbers) through a variety of algebraic structures that permit the precise description, specification and subsequent analysis of many problems in computing. The material included provides the essential mathematical foundations for core topics of computer science and extends into the areas of language theory, abstract machine theory and computer geometry. Computer Mathematics will be of

Computing developed as a branch of mathematics, only to drift away from this home as computer science diverged towards more general topics such as the theory of how a computer works. Recently the emphasis has become more mathematical and the new disciplines of software engineering and information technology have emerged. This book is designed to form the basis of a one year course in discrete mathematics for first year computer scientists or software engineers. The material presented covers much of undergraduate algebra with a particular bias towards the computing applications. Topics covered include mathematical logic, set theory, finite and infinite relations and mappings, graphs, graphical algorithms and axiom systems. It concludes with implementations of many of the algorithms in Modula-2 to illustrate how the mathematics may be turned into concrete calculations. Numerous examples and exercises are included with selected solutions to the problems appearing in the appendix. Discrete

Data structures are the fundamental building blocks of any computer program, used for storing, representing and manipulating data in a computer. This text presents the basic concepts of data structures as part of the art of writing computer programs. The author concentrates on the fundamentals of what should be done to solve a problem efficiently rather than technical implementation details. The text includes pseudocode and covers all the most common data structures, such as queues, stacks, trees, heaps, and hash tables, along with the basics of searching, sorting, and coding. This book can supplement any undergraduate algorithms or discrete math course and will also be accessible to students and researchers in other quantitative disciplines. No prerequisites beyond introductory programming and basic mathematics are required, and the accessible, conceptual presentation will appeal to undergraduates in many quantitative fields. Carefully designed problem sets with selected solutions wil

Mathematical Logic for Computer Science is a mathematics textbook with theorems and proofs, but the choice of topics has been guided by the needs of students of computer science. The method of semanti

Discrete Mathematics for Computing is suitable for students taking a one-semester introductory course in discrete mathematics, particularly those studying Computing and Informations Systems.It present

Discrete mathematics is fundamental to computer science, and this text covers its ideas and mathematical language. Features counting and listing, functions, decision trees and recursion, and basic con

Proceedings of a high-level conference on discrete mathematics, focusing on group actions in the areas of pure mathematics, applied mathematics, computer science, physics, and chemistry. A useful tool

Computer algebra systems have revolutionized the use of computers within mathematics research, and are currently extending that revolution to the undergraduate mathematics curriculum. But the power of such systems goes beyond simple algebraic or numerical manipulation. This book shows how computer-aided mathematics has reached a level where it can support effectively many of the computations in science and engineering. In addition to treating traditional computer science topics, an introductory course should show scientists and engineers how these computer-based tools can be used to do scientific computations. A valuable text for computer science courses for scientists and engineers, this book should also prove useful to Mathematica users at all levels. Covering the latest release of Mathematica, the book includes useful tips and techniques to help even seasoned users.

Using basic category theory, this Element describes all the central concepts and proves the main theorems of theoretical computer science. Category theory, which works with functions, processes, and structures, is uniquely qualified to present the fundamental results of theoretical computer science. In this Element, readers will meet some of the deepest ideas and theorems of modern computers and mathematics, such as Turing machines, unsolvable problems, the P=NP question, Kurt Gödel's incompleteness theorem, intractable problems, cryptographic protocols, Alan Turing's Halting problem, and much more. The concepts come alive with many examples and exercises.

This book provides a valuable glimpse into discrete curvature, a rich new field of research which blends discrete mathematics, differential geometry, probability and computer graphics. It includes a v

Prepare for exams and succeed in your mathematics course with this comprehensive solutions manual! Featuring worked out-solutions to the problems in DISCRETE MATHEMATICS, 1st Edition, this manual show

This undergraduate-level describes the mathematics most needed in computer science. Bender and Williamson (both mathematics, U. of California, San Diego) cover Boolean functions and computer arithmeti

Written for a broad audience of students in mathematics, computer science, operations research, statistics, and engineering, this textbook presents a short, lively survey of several fascinating non-calculus topics in modern applied mathematics. Coverage includes probability, mathematical finance, graphs, linear programming, statistics, computer science algorithms, and groups. A key feature is the abundance of interesting examples not normally found in standard finite mathematics courses, such as options pricing and arbitrage, tournaments, and counting formulas. The author assumes a level of mathematical sophistication at the beginning calculus level, that is, students should have had at least a course in pre-calculus, and the added sophistication attained from studying calculus would be useful.

An introductory text for undergraduates majoring in mathematics, computer science, and related disciplines. The primary themes are the notions of proof, recursion, induction, modeling and algorithmic

For courses in discrete mathematics This title is part of the Pearson Modern Classics series. Pearson Modern Classics are acclaimed titles at a value price. Please visit www.pearsonhighered.com/m

This textbook for undergraduate mathematics, science, and engineering students introduces the theory and applications of discrete Fourier and wavelet transforms using elementary linear algebra, withou

This text for the first or second year undergraduate in mathematics, logic, computer science, or social sciences, introduces the reader to logic, proofs, sets, and number theory. It also serves as an

Data Structures Using C++ is designed to serve as a textbook for undergraduate engineering students of computer science and information technology as well as postgraduate students of computer applicat

Proceedings of the NATO Advanced Study Institute on Mathematics and Computer Science in Medical Imaging, held in Il Ciocco, Italy, September 21 - October 4, 1986

The logic and methodology of design is examined in this book from the perspective of computer science. Computers provide the context for this examination both by discussion of the design process for hardware and software systems and by consideration of the role of computers in design in general. The central question posed by the author is whether or not we can construct a theory of design. This book concentrates upon the relationship between design, mathematics and science and thus its audience must include designers and software designers as well as computer scientists.

Hungarian mathematics has always been known for discrete mathematics, including combinatorial number theory, set theory and recently random structures, and combinatorial geometry. The recent volume co

This survey of fundamental algebraic structures employs techniques applicable to mathematics, physics, engineering, and computer science. Topics include relations between groups and sets, the fundamen

The ?rst International Summer School on Theoretical Aspects of Computer Science was organized by the Institute for Studies in Theoretical Physics and Mathematics(IPM)inTehran,Iran. ProgramCommittee Co

Category theory has become increasingly important and popular in computer science, and many universities now have introductions to category theory as part of their courses for undergraduate computer scientists. The author is a respected category theorist and has based this textbook on a course given over the last few years at the University of Sydney. The theory is developed in a straightforward way, and is enriched with many examples from computer science. Thus this book meets the needs of undergradute computer scientists, and yet retains a level of mathematical correctness that will broaden its appeal to include students of mathematics new to category theory.

Based on the International Commission on Mathematical Instruction conference held in early 1987, this volume consists of a number of key papers presented by international authorities on the role of mathematics in applied subjects, such as engineering, computer science, and mathematical modelling. The importance of certain mathematical ideas, such as geometry and discrete mathematics is stressed, as well as the more classical methods. The book includes a long article by the editor synthesising some of the main themes and trends debated at the conference.

Discrete Mathematics: Essentials and Applications offers a comprehensive survey of the area, particularly concentrating on the basic principles and applications of Discrete Mathematics. This up-to-date text provides proofs of significance, keeping the focus on numerous relevant examples and many pertinent applications. Written in a simple and clear tone, the title features insightful descriptions and intuitive explanations of all complex concepts and ensures a thorough understanding of the subject matter.

This book surveys the mathematical and computational properties of finite sets of points in the plane, covering recent breakthroughs on important problems in discrete geometry, and listing many open problems. It unifies these mathematical and computational views using forbidden configurations, which are patterns that cannot appear in sets with a given property, and explores the implications of this unified view. Written with minimal prerequisites and featuring plenty of figures, this engaging book will be of interest to undergraduate students and researchers in mathematics and computer science. Most topics are introduced with a related puzzle or brain-teaser. The topics range from abstract issues of collinearity, convexity, and general position to more applied areas including robust statistical estimation and network visualization, with connections to related areas of mathematics including number theory, graph theory, and the theory of permutation patterns. Pseudocode is included for m

For courses in computer science and programming Starting Out with Java: From Control Structures through Data Structures provides a smooth introduction to programming with Java that moves fl

Discrete mathematics has been rising in prominence in the past fifty years, both as a tool with practical applications and as a source of new and interesting mathematics. The topics in discrete mathematics have become so well developed that it is easy to forget that common threads connect the different areas, and it is through discovering and using these connections that progress is often made. For over fifty years, Ron Graham has been able to illuminate some of these connections and has helped to bring the field of discrete mathematics to where it is today. To celebrate his contribution, this volume brings together many of the best researchers working in discrete mathematics, including Fan Chung, Erik D. Demaine, Persi Diaconis, Peter Frankl, Alfred W. Hales, Jeffrey C. Lagarias, Allen Knutson, Janos Pach, Carl Pomerance, N. J. A. Sloane, and of course, Ron Graham himself.

Wiley-Interscience Series in Discrete Mathematics and Optimization AdvisoryEditors: Ronald L. Graham, Jan Karel Lenstra, and Robert E. TarjanDiscrete mathematics, the study of finite structures, is on

Geometric algebra has established itself as a powerful and valuable mathematical tool for solving problems in computer science, engineering, physics, and mathematics. The articles in this volume, writ