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Discrete Mathematics

Proofs, Structures and Applications, Third Edition

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 progression from the basic mathematical ideas to the more sophisticated concepts examined later in the book. This edition preserves the philosophy of its predecessors while updating and revising some of the content. New to the Third Edition In the expanded first chapter, the text includes a new section on the formal proof of the validity of arguments in propositional logic before moving on to predicate logic. This edition also contains a new chapter on elementary number theory and congruences. This chapter explores groups that arise in modular arithmetic and RSA encryption, a widely used public key encryption scheme that enables practical and secure means of encrypting data. This third edition also offers a detailed solutions manual for qualifying instructors. Exploring the relationship between mathematics and computer science, this text continues to provide a secure grounding in the theory of discrete mathematics and to augment the theoretical foundation with salient applications. It is designed to help readers develop the rigorous logical thinking required to adapt to the demands of the ever-evolving discipline of computer science.

Exploring the relationship between mathematics and computer science, this text continues to provide a secure grounding in the theory of discrete mathematics and to augment the theoretical foundation with salient applications.

Pearls of Discrete Mathematics

Methods Used to Solve Discrete Math Problems Interesting examples highlight the interdisciplinary nature of this area Pearls of Discrete Mathematics presents methods for solving counting problems and other types of problems that involve discrete structures. Through intriguing examples, problems, theorems, and proofs, the book illustrates the relationship of these structures to algebra, geometry, number theory, and combinatorics. Each chapter begins with a mathematical teaser to engage readers and includes a particularly surprising, stunning, elegant, or unusual result. The author covers the upward extension of Pascal’s triangle, a recurrence relation for powers of Fibonacci numbers, ways to make change for a million dollars, integer triangles, the period of Alcuin’s sequence, and Rook and Queen paths and the equivalent Nim and Wythoff’s Nim games. He also examines the probability of a perfect bridge hand, random tournaments, a Fibonacci-like sequence of composite numbers, Shannon’s theorems of information theory, higher-dimensional tic-tac-toe, animal achievement and avoidance games, and an algorithm for solving Sudoku puzzles and polycube packing problems. Exercises ranging from easy to challenging are found in each chapter while hints and solutions are provided in an appendix. With over twenty-five years of teaching experience, the author takes an organic approach that explores concrete problems, introduces theory, and adds generalizations as needed. He delivers an absorbing treatment of the basic principles of discrete mathematics.

Through intriguing examples, problems, theorems, and proofs, the book illustrates the relationship of these structures to algebra, geometry, number theory, and combinatorics.

Discrete Mathematics with Proof

"Discrete mathematics has become increasingly popular in recent years due to its growing applications in the field of computer science. - Discrete Mathematics with Proof, Second Edition continues to facilitate an up-to-date understanding of this important topic, exposing readers to a wide range of modern and technological applications. Assuming only a basic background in calculus, Discrete Mathematics with Proof, Second Edition is an excellent book for mathematics and computer science courses at the undergraduate level. - It is also a valuable resource for professionals in various technical fields who would like an introduction to discrete mathematics."--Jacket.

- It is also a valuable resource for professionals in various technical fields who would like an introduction to discrete mathematics."--Jacket. Discrete Mathematics with Proof Eric Gossett Second Edition

Invitation to Discrete Mathematics

Invitation to Discrete Mathematics is an introduction and a thoroughly comprehensive text at the same time. A lively and entertaining style with mathematical precision and maturity uniquely combine into an intellectual happening and should delight the interested reader. A master example of teaching contemporary discrete mathematics, and of teaching science in general.

A clear and self-contained introduction to discrete mathematics for undergraduates and early graduates.

Discrete Mathematics With Combinatorics And Graph Theory

Discrete Mathematics is designed to serve as a textbook for a single-semester undergraduate course on the discrete and combinatorial mathematics. Beginning with a a lucid introduction to logic and set theory, the book goes on to cover matrix algebra, algebraic systems, coding theory, lattices and Boolean algebra, parts, and discrete probability A comprehensive chapter dedicated to graph theory makes it a complete undergraduate text on discrete mathematical structures.Written in an easy-to-understand manner, the book includes a large number of solved examples which illustrate problem-solving methodology. It contains an extensive set of exercises. Both solved and unsolved problems show a good gradation of difficulty levels. A summary at the end of each chapter reviews the key concepts discussed.

Beginning with a a lucid introduction to logic and set theory, the book goes on to cover matrix algebra, algebraic systems, coding theory, lattices and Boolean algebra, parts, and discrete probability A comprehensive chapter dedicated to ...

Computational Discrete Mathematics

Combinatorics and Graph Theory with Mathematica ®

This book was first published in 2003. Combinatorica, an extension to the popular computer algebra system Mathematica®, is the most comprehensive software available for teaching and research applications of discrete mathematics, particularly combinatorics and graph theory. This book is the definitive reference/user's guide to Combinatorica, with examples of all 450 Combinatorica functions in action, along with the associated mathematical and algorithmic theory. The authors cover classical and advanced topics on the most important combinatorial objects: permutations, subsets, partitions, and Young tableaux, as well as all important areas of graph theory: graph construction operations, invariants, embeddings, and algorithmic graph theory. In addition to being a research tool, Combinatorica makes discrete mathematics accessible in new and exciting ways to a wide variety of people, by encouraging computational experimentation and visualization. The book contains no formal proofs, but enough discussion to understand and appreciate all the algorithms and theorems it contains.

This book was first published in 2003.

Discrete Mathematics and Combinatorics

Discrete Mathematics and Combinatorics provides a concise and practical introduction to the core components of discrete mathematics, featuring a balanced mix of basic theories and applications. The book covers both fundamental concepts such as sets and logic, as well as advanced topics such as graph theory and Turing machines. The example-driven approach will help readers in understanding and applying the concepts. Other pedagogical tools - illustrations, practice questions, and suggested reading - facilitate learning and mastering the subject." -- Cover.

The book covers both fundamental concepts such as sets and logic, as well as advanced topics such as graph theory and Turing machines. The example-driven approach will help readers in understanding and applying the concepts.

Sejarah Islam lokal

History of Islam in Yogyakarta.

History of Islam in Yogyakarta.

Arkeologi Sejarah-Pemikiran Arab-Islam Vol. 4

Wacana keislaman hingga saat ini boleh dikatakan masih berkutat pada persoalan bagaimana Islam harus dipandang setelah agama tersebut berjalan lebih dari lima belas abad lamanya semenjak ia dilahirkan, dan sekarang ia sedang dihadapkan pada prestasi “pihak lain” dengan berbagai ke- ajaiban modernitasnya. Pandangan terhadap hal tersebut sangatlah penting, terutama di era belakangan ini. Sebagai sebuah komunitas, umat Islam memiliki keyakinan bahwa mereka adalah umat terbaik (khair al-ummah). Akan tetapi, pada saat yang sama mereka sedang berada dalam posisi “tidak ber- daya” menghadapi apa saja yang diluncurkan dari pihak lain yang oleh sebagian besar di antara mereka dianggap sebagai “musuh” yang tidak boleh didekati, dah bahkan justru harus diperangi dan dimusnahkan.

... dari bagaimana masing-masing kelompok tersebut memosisikan, menafsirkan,
memahami, dan mendudukkan teks dasar keagamaan Islam (Al-Qur'an dan as-
Sunnah) serta tradisi keagamaan Islam dalam kehidupan modern sekarang ini.

Action Research and New Media

Concepts, Methods, and Cases

Action research is now a well-documented and well-accepted research methodology. Moreover, it is especially appropriate in new media research, where innovation and change are continual, and where processes and outcomes are usually not predictable and often involve fuzzy and subjective human elements. This book offers a systematic, in-depth academic overview of the application of action research methods to the field of new media. In this space, it is the first publication of its kind in what is a new but rapidly growing field. The book is divided into two sections. Introducing the two key concepts, namely, new media and action research, the first section describes the underlying principles, processes, questions, methods and tools that are relevant to an action research approach to new media inquiry. This is followed by a deeper exploration of three advanced, innovative approaches to action research and new media: ethnographic, network, and anticipatory action research. The third and final section presents four case studies and their individual applications of action research in different new media contexts

As Brydon-Miller, Greenwood, and Maguire (2003) pointed out: 'action research
is a work in progress' (p. 11). Stringer (1999) commented that quite 'disparate'
histories of action research have been written by authors such as Kemmis and ...