Discrete Structures With Contemporary Applications

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Discrete Structures with Contemporary Applications

Alexander Stanoyevitch
Discrete Structures with Contemporary Applications Book PDF

Author : Alexander Stanoyevitch
Publisher : Chapman and Hall/CRC
Page : 0 pages
File Size : 48,9 Mb
Release : 2011-01-19
Category : Computers
ISBN : 1439817685

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Discrete Structures with Contemporary Applications by Alexander Stanoyevitch Pdf

Reflecting many of the recent advances and trends in this area, Discrete Structures with Contemporary Applications covers the core topics in discrete structures as well as an assortment of novel applications-oriented topics. The applications described include simulations, genetic algorithms, network flows, probabilistic primality tests, public key cryptography, and coding theory. A modern and comprehensive introduction to discrete structures With clear definitions and theorems and carefully explained proofs, this classroom-tested text presents an accessible yet rigorous treatment of the material. Numerous worked-out examples illustrate key points while figures and tables help students grasp the more subtle and difficult concepts. "Exercises for the Reader" are interspersed throughout the text, with complete solutions included in an appendix. In addition to these, each section ends with extensive, carefully crafted exercise sets ranging from routine to nontrivial; answers can be found in another appendix. Most sections also contain computer exercises that guide students through the process of writing their own programs on any computing platform. Accommodates various levels of computer implementation Although the book highly encourages the use of computing platforms, it can be used without computers. The author explains algorithms in ordinary English and, when appropriate, in a natural and easy-to-understand pseudo code that can be readily translated into any computer language. A supporting website provides an extensive set of sample programs.

Discrete Mathematics

Rowan Garnier,John Taylor
Discrete Mathematics Book PDF

Author : Rowan Garnier,John Taylor
Publisher : Taylor & Francis
Page : 847 pages
File Size : 47,7 Mb
Release : 2009-11-09
Category : Computers
ISBN : 9781439812815

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Discrete Mathematics by Rowan Garnier,John Taylor Pdf

Taking an approach to the subject that is suitable for a broad readership, Discrete Mathematics: Proofs, Structures, and Applications, Third Edition provides a rigorous yet accessible exposition of discrete mathematics, including the core mathematical foundation of computer science. The approach is comprehensive yet maintains an easy-to-follow prog

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 : 41,7 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.

Introduction to Cryptography with Mathematical Foundations and Computer Implementations

Alexander Stanoyevitch
Introduction to Cryptography with Mathematical Foundations and Computer Implementations Book PDF

Author : Alexander Stanoyevitch
Publisher : CRC Press
Page : 646 pages
File Size : 51,7 Mb
Release : 2010-08-09
Category : Computers
ISBN : 9781439817636

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Introduction to Cryptography with Mathematical Foundations and Computer Implementations by Alexander Stanoyevitch Pdf

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.

Contemporary Trends in Discrete Mathematics

Ronald L. Graham
Contemporary Trends in Discrete Mathematics Book PDF

Author : Ronald L. Graham
Publisher : American Mathematical Soc.
Page : 412 pages
File Size : 52,6 Mb
Release : 1999-01-01
Category : Mathematics
ISBN : 0821885812

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Contemporary Trends in Discrete Mathematics by Ronald L. Graham Pdf

Discrete mathematics stands among the leading disciplines of mathematics and theoretical computer science. This is due primarily to its increasing role in university curriculae and its growing importance in applications ranging from optimization to molecular biology. An inaugural conference was held cooperatively by DIMATIA and DIMACS to focus on the versatility, width, and depth of current progress in the subject area. This volume offers a well-balanced blend of research and survey papers reflecting the exciting, attractive topics in contemporary discrete mathematics. Discussed in the book are topics such as graph theory, partially ordered sets, geometrical Ramsey theory, computational complexity issues and applications.

Modern Algebra and Discrete Structures

R. F. Lax
Modern Algebra and Discrete Structures Book PDF

Author : R. F. Lax
Publisher : Pearson
Page : 0 pages
File Size : 47,8 Mb
Release : 1991
Category : Algebra
ISBN : 0060438789

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Modern Algebra and Discrete Structures by R. F. Lax Pdf

This text offers students clarity and instructors flexibility. Its thorough coverage of applications, algorithms, and examples, and its inclusion of many proofs explain and reinforce the material. Its traditional organization makes it a suitable text for several courses. Attention to contemporary topics such as key cryptosystems and coding theory makes the text current. It is flexible enough to be used for courses in applied algebra or modern (abstract) algebra.

Discrete Mathematics and Graph Theory

K. Erciyes
Discrete Mathematics and Graph Theory Book PDF

Author : K. Erciyes
Publisher : Springer Nature
Page : 345 pages
File Size : 53,5 Mb
Release : 2021-01-28
Category : Computers
ISBN : 9783030611156

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Discrete Mathematics and Graph Theory by K. Erciyes Pdf

This textbook can serve as a comprehensive manual of discrete mathematics and graph theory for non-Computer Science majors; as a reference and study aid for professionals and researchers who have not taken any discrete math course before. It can also be used as a reference book for a course on Discrete Mathematics in Computer Science or Mathematics curricula. The study of discrete mathematics is one of the first courses on curricula in various disciplines such as Computer Science, Mathematics and Engineering education practices. Graphs are key data structures used to represent networks, chemical structures, games etc. and are increasingly used more in various applications such as bioinformatics and the Internet. Graph theory has gone through an unprecedented growth in the last few decades both in terms of theory and implementations; hence it deserves a thorough treatment which is not adequately found in any other contemporary books on discrete mathematics, whereas about 40% of this textbook is devoted to graph theory. The text follows an algorithmic approach for discrete mathematics and graph problems where applicable, to reinforce learning and to show how to implement the concepts in real-world applications.

Graph Theory, Combinatorics and Algorithms

Martin Charles Golumbic,Irith Ben-Arroyo Hartman
Graph Theory Combinatorics and Algorithms Book PDF

Author : Martin Charles Golumbic,Irith Ben-Arroyo Hartman
Publisher : Springer Science & Business Media
Page : 296 pages
File Size : 43,6 Mb
Release : 2006-03-30
Category : Mathematics
ISBN : 9780387250366

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Graph Theory, Combinatorics and Algorithms by Martin Charles Golumbic,Irith Ben-Arroyo Hartman Pdf

Graph Theory, Combinatorics and Algorithms: Interdisciplinary Applications focuses on discrete mathematics and combinatorial algorithms interacting with real world problems in computer science, operations research, applied mathematics and engineering. The book contains eleven chapters written by experts in their respective fields, and covers a wide spectrum of high-interest problems across these discipline domains. Among the contributing authors are Richard Karp of UC Berkeley and Robert Tarjan of Princeton; both are at the pinnacle of research scholarship in Graph Theory and Combinatorics. The chapters from the contributing authors focus on "real world" applications, all of which will be of considerable interest across the areas of Operations Research, Computer Science, Applied Mathematics, and Engineering. These problems include Internet congestion control, high-speed communication networks, multi-object auctions, resource allocation, software testing, data structures, etc. In sum, this is a book focused on major, contemporary problems, written by the top research scholars in the field, using cutting-edge mathematical and computational techniques.

Teaching and Learning Discrete Mathematics Worldwide: Curriculum and Research

Eric W. Hart,James Sandefur
Teaching and Learning Discrete Mathematics Worldwide Curriculum and Research Book PDF

Author : Eric W. Hart,James Sandefur
Publisher : Springer
Page : 276 pages
File Size : 44,8 Mb
Release : 2017-12-09
Category : Education
ISBN : 9783319703084

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Teaching and Learning Discrete Mathematics Worldwide: Curriculum and Research by Eric W. Hart,James Sandefur Pdf

This book discusses examples of discrete mathematics in school curricula, including in the areas of graph theory, recursion and discrete dynamical systems, combinatorics, logic, game theory, and the mathematics of fairness. In addition, it describes current discrete mathematics curriculum initiatives in several countries, and presents ongoing research, especially in the areas of combinatorial reasoning and the affective dimension of learning discrete mathematics. Discrete mathematics is the math of our time.' So declared the immediate past president of the National Council of Teachers of Mathematics, John Dossey, in 1991. Nearly 30 years later that statement is still true, although the news has not yet fully reached school mathematics curricula. Nevertheless, much valuable work has been done, and continues to be done. This volume reports on some of that work. It provides a glimpse of the state of the art in learning and teaching discrete mathematics around the world, and it makes the case once again that discrete mathematics is indeed mathematics for our time, even more so today in our digital age, and it should be included in the core curricula of all countries for all students.

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 : 52,5 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.

Introduction to Combinatorics

Walter D. Wallis,John C. George
Introduction to Combinatorics Book PDF

Author : Walter D. Wallis,John C. George
Publisher : CRC Press
Page : 424 pages
File Size : 41,8 Mb
Release : 2016-12-12
Category : Mathematics
ISBN : 9781498777636

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Introduction to Combinatorics by Walter D. Wallis,John C. George Pdf

What Is Combinatorics Anyway? Broadly speaking, combinatorics is the branch of mathematics dealing with different ways of selecting objects from a set or arranging objects. It tries to answer two major kinds of questions, namely, counting questions: how many ways can a selection or arrangement be chosen with a particular set of properties; and structural questions: does there exist a selection or arrangement of objects with a particular set of properties? The authors have presented a text for students at all levels of preparation. For some, this will be the first course where the students see several real proofs. Others will have a good background in linear algebra, will have completed the calculus stream, and will have started abstract algebra. The text starts by briefly discussing several examples of typical combinatorial problems to give the reader a better idea of what the subject covers. The next chapters explore enumerative ideas and also probability. It then moves on to enumerative functions and the relations between them, and generating functions and recurrences., Important families of functions, or numbers and then theorems are presented. Brief introductions to computer algebra and group theory come next. Structures of particular interest in combinatorics: posets, graphs, codes, Latin squares, and experimental designs follow. The authors conclude with further discussion of the interaction between linear algebra and combinatorics. Features Two new chapters on probability and posets. Numerous new illustrations, exercises, and problems. More examples on current technology use A thorough focus on accuracy Three appendices: sets, induction and proof techniques, vectors and matrices, and biographies with historical notes, Flexible use of MapleTM and MathematicaTM

Discrete Mathematics

László Lovász,József Pelikán,Katalin Vesztergombi
Discrete Mathematics Book PDF

Author : László Lovász,József Pelikán,Katalin Vesztergombi
Publisher : Springer Science & Business Media
Page : 344 pages
File Size : 51,5 Mb
Release : 2006-05-10
Category : Mathematics
ISBN : 9780387217772

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Discrete Mathematics by László Lovász,József Pelikán,Katalin Vesztergombi Pdf

Aimed at undergraduate mathematics and computer science students, this book is an excellent introduction to a lot of problems of discrete mathematics. It discusses a number of selected results and methods, mostly from areas of combinatorics and graph theory, and it uses proofs and problem solving to help students understand the solutions to problems. Numerous examples, figures, and exercises are spread throughout the book.

Discrete Mathematics and Its Applications

Kenneth H. Rosen
Discrete Mathematics and Its Applications Book PDF

Author : Kenneth H. Rosen
Publisher : McGraw-Hill
Page : 0 pages
File Size : 43,5 Mb
Release : 2018-05
Category : Computer science
ISBN : 125967651X

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Discrete Mathematics and Its Applications by Kenneth H. Rosen Pdf

A precise, relevant, comprehensive approach to mathematical concepts...

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 : 54,8 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.

Foundations of Combinatorics with Applications

Edward A. Bender,S. Gill Williamson
Foundations of Combinatorics with Applications Book PDF

Author : Edward A. Bender,S. Gill Williamson
Publisher : Courier Corporation
Page : 738 pages
File Size : 48,6 Mb
Release : 2013-01-18
Category : Mathematics
ISBN : 9780486151502

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Foundations of Combinatorics with Applications by Edward A. Bender,S. Gill Williamson Pdf

This introduction to combinatorics, the foundation of the interaction between computer science and mathematics, is suitable for upper-level undergraduates and graduate students in engineering, science, and mathematics. The four-part treatment begins with a section on counting and listing that covers basic counting, functions, decision trees, and sieving methods. The following section addresses fundamental concepts in graph theory and a sampler of graph topics. The third part examines a variety of applications relevant to computer science and mathematics, including induction and recursion, sorting theory, and rooted plane trees. The final section, on generating functions, offers students a powerful tool for studying counting problems. Numerous exercises appear throughout the text, along with notes and references. The text concludes with solutions to odd-numbered exercises and to all appendix exercises.