Discrete Mathematics And Algebraic Structures

Author : Stephan Foldes
Publisher : John Wiley & Sons
Page : 362 pages
File Size : 48,9 Mb
Release : 2011-02-14
Category : Mathematics
ISBN : 9781118031438

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Fundamental Structures of Algebra and Discrete Mathematics by Stephan Foldes Pdf

Introduces and clarifies the basic theories of 12 structural concepts, offering a fundamental theory of groups, rings and other algebraic structures. Identifies essentials and describes interrelationships between particular theories. Selected classical theorems and results relevant to current research are proved rigorously within the theory of each structure. Throughout the text the reader is frequently prompted to perform integrated exercises of verification and to explore examples.

Author : Larry J. Gerstein
Publisher : W H Freeman & Company
Page : 413 pages
File Size : 50,5 Mb
Release : 1987-01-01
Category : Algebra, Abstract.
ISBN : 0716718049

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Discrete Mathematics and Algebraic Structures by Larry J. Gerstein Pdf

Provides a brief but substantial introduction to ideas, structures and techniques in discrete mathematics and abstract algebra. It addresses many of the common mathematical needs of students in mathematics and computer science at undergraduate level.

Author : Ken Levasseur,Al Doerr
Publisher : Lulu.com
Page : 254 pages
File Size : 45,8 Mb
Release : 2017-05-15
Category : Electronic
ISBN : 9781105618987

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Applied Discrete Structures - Part 2- Algebraic Structures by Ken Levasseur,Al Doerr Pdf

Applied Discrete Structures, Part II - Algebraic Structures, is an introduction to groups, monoids, vector spaces, lattices, boolean algebras, rings and fields. It corresponds with the content of Discrete Structures II at UMass Lowell, which is a required course for students in Computer Science. It presumes background contained in Part I - Fundamentals. Applied Discrete Structures has been approved by the American Institute of Mathematics as part of their Open Textbook Initiative. For more information on open textbooks, visit http: //www.aimath.org/textbooks/. This version was created using Mathbook XML (https: //mathbook.pugetsound.edu/) Al Doerr is Emeritus Professor of Mathematical Sciences at UMass Lowell. His interests include abstract algebra and discrete mathematics. Ken Levasseur is a Professor of Mathematical Sciences at UMass Lowell. His interests include discrete mathematics and abstract algebra, and their implementation using computer algebra systems.

Author : Sriraman Sridharan,R. Balakrishnan
Publisher : CRC Press
Page : 320 pages
File Size : 46,7 Mb
Release : 2019-07-30
Category : Mathematics
ISBN : 9780429942624

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Discrete Mathematics by Sriraman Sridharan,R. Balakrishnan Pdf

Conveying ideas in a user-friendly style, this book has been designed for a course in Applied Algebra. The book covers graph algorithms, basic algebraic structures, coding theory and cryptography. It will be most suited for senior undergraduates and beginning graduate students in mathematics and computer science as also to individuals who want to have a knowledge of the below-mentioned topics. Provides a complete discussion on several graph algorithms such as Prims algorithm and Kruskals algorithm for sending a minimum cost spanning tree in a weighted graph, Dijkstras single source shortest path algorithm, Floyds algorithm, Warshalls algorithm, Kuhn-Munkres Algorithm. In addition to DFS and BFS search, several applications of DFS and BFS are also discussed. Presents a good introduction to the basic algebraic structures, namely, matrices, groups, rings, fields including finite fields as also a discussion on vector spaces and linear equations and their solutions. 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.

Author : K. D. Joshi
Publisher : New Age International
Page : 768 pages
File Size : 53,7 Mb
Release : 1989
Category : Mathematics
ISBN : 8122401201

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Foundations of Discrete Mathematics by K. D. Joshi Pdf

This Book Is Meant To Be More Than Just A Text In Discrete Mathematics. It Is A Forerunner Of Another Book Applied Discrete Structures By The Same Author. The Ultimate Goal Of The Two Books Are To Make A Strong Case For The Inclusion Of Discrete Mathematics In The Undergraduate Curricula Of Mathematics By Creating A Sequence Of Courses In Discrete Mathematics Parallel To The Traditional Sequence Of Calculus-Based Courses.The Present Book Covers The Foundations Of Discrete Mathematics In Seven Chapters. It Lays A Heavy Emphasis On Motivation And Attempts Clarity Without Sacrificing Rigour. A List Of Typical Problems Is Given In The First Chapter. These Problems Are Used Throughout The Book To Motivate Various Concepts. A Review Of Logic Is Included To Gear The Reader Into A Proper Frame Of Mind. The Basic Counting Techniques Are Covered In Chapters 2 And 7. Those In Chapter 2 Are Elementary. But They Are Intentionally Covered In A Formal Manner So As To Acquaint The Reader With The Traditional Definition-Theorem-Proof Pattern Of Mathematics. Chapters 3 Introduces Abstraction And Shows How The Focal Point Of Todays Mathematics Is Not Numbers But Sets Carrying Suitable Structures. Chapter 4 Deals With Boolean Algebras And Their Applications. Chapters 5 And 6 Deal With More Traditional Topics In Algebra, Viz., Groups, Rings, Fields, Vector Spaces And Matrices.The Presentation Is Elementary And Presupposes No Mathematical Maturity On The Part Of The Reader. Instead, Comments Are Inserted Liberally To Increase His Maturity. Each Chapter Has Four Sections. Each Section Is Followed By Exercises (Of Various Degrees Of Difficulty) And By Notes And Guide To Literature. Answers To The Exercises Are Provided At The End Of The Book.

Author : G. Shanker Rao
Publisher : New Age International
Page : 43 pages
File Size : 47,6 Mb
Release : 2007-12-31
Category : Mathematical ability
ISBN : 9788122426694

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Discrete Mathematical Structures by G. Shanker Rao Pdf

About the Book: This text can be used by the students of mathematics and computer science as an introduction to the fundamentals of discrete mathematics. The book is designed in accordance with the syllabi of B.E., B. Tech., MCA and M.Sc. (Computer Science) prescribed in most of the universities of India. Each chapter is supplemented with a number of worked example as well as a number of problems to be solved by the students. This would help in a better understanding of the subject. Contents: Mathematical Logic Set Theory Relations Functions and Recurrence Relations Boolean Algebra Logic Gates Elementary Combinatorics Graph Theory Algebraic Structures Finite State Machines

Author : Ken Levasseur,Al Doerr
Publisher : Lulu.com
Page : 574 pages
File Size : 54,9 Mb
Release : 2012-02-25
Category : Applied mathematics
ISBN : 9781105559297

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Applied Discrete Structures by Ken Levasseur,Al Doerr Pdf

Applied Discrete Structures, is a two semester undergraduate text in discrete mathematics, focusing on the structural properties of mathematical objects. These include matrices, functions, graphs, trees, lattices and algebraic structures. The algebraic structures that are discussed are monoids, groups, rings, fields and vector spaces. Website: http: //discretemath.org Applied Discrete Structures has been approved by the American Institute of Mathematics as part of their Open Textbook Initiative. For more information on open textbooks, visit http: //www.aimath.org/textbooks/. This version was created using Mathbook XML (https: //mathbook.pugetsound.edu/) Al Doerr is Emeritus Professor of Mathematical Sciences at UMass Lowell. His interests include abstract algebra and discrete mathematics. Ken Levasseur is a Professor of Mathematical Sciences at UMass Lowell. His interests include discrete mathematics and abstract algebra, and their implementation using computer algebra systems.

Author : Sriraman Sridharan,R. Balakrishnan
Publisher : CRC Press
Page : 314 pages
File Size : 47,7 Mb
Release : 2019-07-30
Category : Mathematics
ISBN : 9780429942631

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Discrete Mathematics by Sriraman Sridharan,R. Balakrishnan Pdf

Conveying ideas in a user-friendly style, this book has been designed for a course in Applied Algebra. The book covers graph algorithms, basic algebraic structures, coding theory and cryptography. It will be most suited for senior undergraduates and beginning graduate students in mathematics and computer science as also to individuals who want to have a knowledge of the below-mentioned topics. Provides a complete discussion on several graph algorithms such as Prims algorithm and Kruskals algorithm for sending a minimum cost spanning tree in a weighted graph, Dijkstras single source shortest path algorithm, Floyds algorithm, Warshalls algorithm, Kuhn-Munkres Algorithm. In addition to DFS and BFS search, several applications of DFS and BFS are also discussed. Presents a good introduction to the basic algebraic structures, namely, matrices, groups, rings, fields including finite fields as also a discussion on vector spaces and linear equations and their solutions. 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.

Author : Anonim
Publisher : Elsevier
Page : 379 pages
File Size : 52,6 Mb
Release : 2011-08-26
Category : Mathematics
ISBN : 0080867731

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Linear and Combinatorial Optimization in Ordered Algebraic Structures by Anonim Pdf

Linear and Combinatorial Optimization in Ordered Algebraic Structures

Author : Juerg Kohlas
Publisher : Springer Science & Business Media
Page : 274 pages
File Size : 40,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781447100096

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Information Algebras by Juerg Kohlas Pdf

Information usually comes in pieces, from different sources. It refers to different, but related questions. Therefore information needs to be aggregated and focused onto the relevant questions. Considering combination and focusing of information as the relevant operations leads to a generic algebraic structure for information. This book introduces and studies information from this algebraic point of view. Algebras of information provide the necessary abstract framework for generic inference procedures. They allow the application of these procedures to a large variety of different formalisms for representing information. At the same time they permit a generic study of conditional independence, a property considered as fundamental for knowledge presentation. Information algebras provide a natural framework to define and study uncertain information. Uncertain information is represented by random variables that naturally form information algebras. This theory also relates to probabilistic assumption-based reasoning in information systems and is the basis for the belief functions in the Dempster-Shafer theory of evidence.

Author : Ellis L. Johnson,Bernhard H. Korte,P. L. Hammer
Publisher : Unknown
Page : 453 pages
File Size : 45,5 Mb
Release : 1977
Category : Mathematical optimization
ISBN : OCLC:4277334

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Annals of Discrete Mathematics by Ellis L. Johnson,Bernhard H. Korte,P. L. Hammer Pdf

Author : R.E. Burkard,R.A. Cuninghame-Green,U. Zimmermann
Publisher : Elsevier
Page : 380 pages
File Size : 54,9 Mb
Release : 1984-01-01
Category : Mathematics
ISBN : 0080872069

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Algebraic and Combinatorial Methods in Operations Research by R.E. Burkard,R.A. Cuninghame-Green,U. Zimmermann Pdf

For the first time, this book unites different algebraic approaches for discrete optimization and operations research. The presentation of some fundamental directions of this new fast developing area shows the wide range of its applicability. Specifically, the book contains contributions in the following fields: semigroup and semiring theory applied to combinatorial and integer programming, network flow theory in ordered algebraic structures, extremal optimization problems, decomposition principles for discrete structures, Boolean methods in graph theory and applications.

Author : UDAY SINGH RAJPUT
Publisher : PHI Learning Pvt. Ltd.
Page : 400 pages
File Size : 46,6 Mb
Release : 2012-05-26
Category : Mathematics
ISBN : 9788120345898

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ADVANCED DISCRETE MATHEMATICS by UDAY SINGH RAJPUT Pdf

Written in an accessible style, this text provides a complete coverage of discrete mathematics and its applications at an appropriate level of rigour. The book discusses algebraic structures, mathematical logic, lattices, Boolean algebra, graph theory, automata theory, grammars and recurrence relations. It covers the important topics such as coding theory, Dijkstra’s shortest path algorithm, reverse polish notation, Warshall’s algorithm, Menger’s theorem, Turing machine, and LR(k) parsers, which form a part of the fundamental applications of discrete mathematics in computer science. In addition, Pigeonhole principle, ring homomorphism, field and integral domain, trees, network flows, languages, and recurrence relations. The text is supported with a large number of examples, worked-out problems and diagrams that help students understand the theoretical explanations. The book is intended as a text for postgraduate students of mathematics, computer science, and computer applications. In addition, it will be extremely useful for the undergraduate students of computer science and engineering.

Author : B. Mikolajczak
Publisher : Elsevier
Page : 401 pages
File Size : 40,7 Mb
Release : 1991-01-14
Category : Mathematics
ISBN : 0080867847

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Algebraic and Structural Automata Theory by B. Mikolajczak Pdf

Automata Theory is part of computability theory which covers problems in computer systems, software, activity of nervous systems (neural networks), and processes of live organisms development. The result of over ten years of research, this book presents work in the following areas of Automata Theory: automata morphisms, time-varying automata, automata realizations and relationships between automata and semigroups. Aimed at those working in discrete mathematics and computer science, parts of the book are suitable for use in graduate courses in computer science, electronics, telecommunications, and control engineering. It is assumed that the reader is familiar with the basic concepts of algebra and graph theory.

Author : James L. Hein
Publisher : Jones & Bartlett Learning
Page : 758 pages
File Size : 42,9 Mb
Release : 2003
Category : Computers
ISBN : 0763722103

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Discrete Mathematics by James L. Hein Pdf

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.