Provides an introduction to linear codes including cyclic codes. Presents a description of private key cryptosystems as also a discussion on public key cryptosystems such as RSA, ElGamal and Miller-Rabin. Finally, the Agrawal-KayalSaxena algorithm AKS Algorithm for testing if a given positive integer is prime or not in polynomial time is presented- the first time in a textbook.
Two distinguished features of the book are: Illustrative examples have been presented throughout the book to make the readers appreciate the concepts described. Answers to all even-numbered exercises in all the chapters are given. Through contributions from leading experts, this handbook provides a comprehensive introduction to the underlying theory and methodologies, as well as the various applications of approximation algorithms and metaheuristics. Volume 1 of this two-volume set deals primarily with methodologies and traditional applications.
It includes restriction, relaxation, local ratio, approximation schemes, randomization, tabu search, evolutionary computation, local search, neural networks, and other metaheuristics. It also explores multi-objective optimization, reoptimization, sensitivity analysis, and stability.
Traditional applications covered include: bin packing, multi-dimensional packing, Steiner trees, traveling salesperson, scheduling, and related problems. Volume 2 focuses on the contemporary and emerging applications of methodologies to problems in combinatorial optimization, computational geometry and graphs problems, as well as in large-scale and emerging application areas. It includes approximation algorithms and heuristics for clustering, networks sensor and wireless , communication, bioinformatics search, streams, virtual communities, and more.
About the Editor Teofilo F. Gonzalez is a professor emeritus of computer science at the University of California, Santa Barbara. He completed his Ph. He is known for his highly cited pioneering research in the hardness of approximation; for his sublinear and best possible approximation algorithm for k-tMM clustering; for introducing the open-shop scheduling problem as well as algorithms for its solution that have found applications in numerous research areas; as well as for his research on problems in the areas of job scheduling, graph algorithms, computational geometry, message communication, wire routing, etc.
The 40 revised full papers presented together with 5 invited papers were carefully reviewed and selected from submissions. The papers provide original research results in fundamental aspects of computer science as well as reports from the frontline of software technology and theoretical computer science. A broad variety of current topics from the theory of computing are addressed, ranging from software science, programming theory, systems design and analysis, formal methods, mathematical logic, mathematical foundations, discrete mathematics, combinatorial mathematics, complexity theory, and automata theory to theoretical computer science in general.
Download Discrete Mathematics In The Schools books , This book provides teachers of all levels with a great deal of valuable material to help them introduce discrete mathematics into their classrooms. Download Teaching Computing books , Teaching can be intimidating for beginning faculty. Some graduate schools and some computing faculty provide guidance and mentoring, but many do not. Often, a new faculty member is assigned to teach a course, with little guidance, input, or feedback.
The book serves as a practical, easy-to-use resource, covering a wide range of topics in a collection of focused down-to-earth chapters. Download Discrete Mathematics And Computing books , 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. The 38 revised full papers presented together with 7 invited papers were carefully reviewed and selected from submissions. Those In Chapter 2 Are Elementary. Each Chapter Has Four Sections. The 46 revised full papers presented were carefully reviewed and selected from 99 submissions. They focus on most recent and innovative trends in this broad area, ranging from distance education to collaborative learning, from interactive learning environments to the modelling of STEM Science, Technology, Mathematics, Engineering curricula.
Exercises are included in each chapter, and additional information is provided in two appendices and an accompanying Web site. Only a basic knowledge of linear algebra and calculus is required. Skip to content Home Search results for: programming foundations discrete mathematics. Author : R. Author : Peter A. Author : Ronald L. Author : Teofilo F. Author : V. By the end of the course, you should be able to make the leap from theory to using discrete math in practice: saving time and resulting in code that's cleaner and easier to maintain in the long run.
Learn how to use discrete mathematics to become a better programmer. Find out about the role of math in programming, and how to use discrete math to analyze and manipulate data, test logic, and visualize solutions. Mathematical Foundations of Computer Science, Volume I is the first of two volumes presenting topics from mathematics mostly discrete mathematics which have proven relevant and useful to computer science.
This volume treats basic topics, mostly of a set-theoretical nature sets, functions and relations, partially ordered sets, induction, enumerability, and diagonalization and illustrates the usefulness of mathematical ideas by presenting applications to computer science. Readers will find useful applications in algorithms, databases, semantics of programming languages, formal languages, theory of computation, and program verification. The material is treated in a straightforward, systematic, and rigorous manner.
The volume is organized by mathematical area, making the material easily accessible to the upper-undergraduate students in mathematics as well as in computer science and each chapter contains a large number of exercises. The volume can be used as a textbook, but it will also be useful to researchers and professionals who want a thorough presentation of the mathematical tools they need in a single source.
In addition, the book can be used effectively as supplementary reading material in computer science courses, particularly those courses which involve the semantics of programming languages, formal languages and automata, and logic programming. 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 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.
From the exciting history of its development in ancient times to the present day, Introduction to Cryptography with Mathematical Foundations and Computer Implementations provides a focused tour of the central concepts of cryptography. Rather than present an encyclopedic treatment of topics in cryptography, it delineates cryptographic concepts in chronological order, developing the mathematics as needed.
Written in an engaging yet rigorous style, each chapter introduces important concepts with clear definitions and theorems. Numerous examples explain key points while figures and tables help illustrate more difficult or subtle concepts. Each chapter is punctuated with "Exercises for the Reader;" complete solutions for these are included in an appendix. Carefully crafted exercise sets are also provided at the end of each chapter, and detailed solutions to most odd-numbered exercises can be found in a designated appendix.
The computer implementation section at the end of every chapter guides students through the process of writing their own programs. A supporting website provides an extensive set of sample programs as well as downloadable platform-independent applet pages for some core programs and algorithms. As the reliance on cryptography by business, government, and industry continues and new technologies for transferring data become available, cryptography plays a permanent, important role in day-to-day operations.
This self-contained sophomore-level text traces the evolution of the field, from its origins through present-day cryptosystems, including public key cryptography and elliptic curve cryptography. The first book devoted exclusively to quantitative graph theory, Quantitative Graph Theory: Mathematical Foundations and Applications presents and demonstrates existing and novel methods for analyzing graphs quantitatively.
Incorporating interdisciplinary knowledge from graph theory, information theory, measurement theory, and statistical technique.
This book, in its Second Edition, provides the basic concepts and applications of discrete mathematics and graph theory. The book is aimed at undergraduate students of computer science and engineering, and information technology. It is also suitable for undergraduate and postgraduate students of computer science, mathematics and computer applications.
The book exposes the students to fundamental knowledge in: - Mathematical logic, tautology and normal forms - Elementary set theory, functions and their relations - Algebraic structure, binary operation, group theory and homomorphism - Theory of permutations and combinations, binomial and multinomial theorems - Recurrence relations and methods of solving them - Graph theory, spanning tree, Eulerian and Hamiltonian circuits and isomorphism Key Features Includes a large number of worked-out problems for sound understanding of the concepts.
Gives a quiz section at the end of each chapter to help students prepare for the competitive examinations.
0コメント