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Author: Jason J. Molitierno
Publisher: CRC Press
ISBN: 1439863393
Category : Computers
Languages : en
Pages : 423
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Book Description
On the surface, matrix theory and graph theory seem like very different branches of mathematics. However, adjacency, Laplacian, and incidence matrices are commonly used to represent graphs, and many properties of matrices can give us useful information about the structure of graphs.Applications of Combinatorial Matrix Theory to Laplacian Matrices o
Author: Jason J. Molitierno
Publisher: CRC Press
ISBN: 1439863393
Category : Computers
Languages : en
Pages : 423
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Book Description
On the surface, matrix theory and graph theory seem like very different branches of mathematics. However, adjacency, Laplacian, and incidence matrices are commonly used to represent graphs, and many properties of matrices can give us useful information about the structure of graphs.Applications of Combinatorial Matrix Theory to Laplacian Matrices o
Author: Richard A. Brualdi
Publisher: Cambridge University Press
ISBN: 0521865654
Category : Mathematics
Languages : en
Pages : 26
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Book Description
A natural sequel to the author's previous book Combinatorial Matrix Theory written with H. J. Ryser, this is the first book devoted exclusively to existence questions, constructive algorithms, enumeration questions, and other properties concerning classes of matrices of combinatorial significance. Several classes of matrices are thoroughly developed including the classes of matrices of 0's and 1's with a specified number of 1's in each row and column (equivalently, bipartite graphs with a specified degree sequence), symmetric matrices in such classes (equivalently, graphs with a specified degree sequence), tournament matrices with a specified number of 1's in each row (equivalently, tournaments with a specified score sequence), nonnegative matrices with specified row and column sums, and doubly stochastic matrices. Most of this material is presented for the first time in book format and the chapter on doubly stochastic matrices provides the most complete development of the topic to date.
Author: San Ling
Publisher: CRC Press
ISBN: 1420079476
Category : Computers
Languages : en
Pages : 333
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Book Description
The reach of algebraic curves in cryptography goes far beyond elliptic curve or public key cryptography yet these other application areas have not been systematically covered in the literature. Addressing this gap, Algebraic Curves in Cryptography explores the rich uses of algebraic curves in a range of cryptographic applications, such as secret sh
Author: Gary L. Mullen
Publisher: CRC Press
ISBN: 1439873828
Category : Computers
Languages : en
Pages : 1048
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Book Description
Poised to become the leading reference in the field, the Handbook of Finite Fields is exclusively devoted to the theory and applications of finite fields. More than 80 international contributors compile state-of-the-art research in this definitive handbook. Edited by two renowned researchers, the book uses a uniform style and format throughout and
Author: Walter D. Wallis
Publisher: CRC Press
ISBN: 1498777627
Category : Mathematics
Languages : en
Pages : 311
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Book Description
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
Author: Anthony Bonato
Publisher: CRC Press
ISBN: 1351814761
Category : Mathematics
Languages : en
Pages : 372
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Book Description
Graph Searching Games and Probabilistic Methods is the first book that focuses on the intersection of graph searching games and probabilistic methods. The book explores various applications of these powerful mathematical tools to games and processes such as Cops and Robbers, Zombie and Survivors, and Firefighting. Written in an engaging style, the book is accessible to a wide audience including mathematicians and computer scientists. Readers will find that the book provides state-of-the-art results, techniques, and directions in graph searching games, especially from the point of view of probabilistic methods. The authors describe three directions while providing numerous examples, which include: • Playing a deterministic game on a random board. • Players making random moves. • Probabilistic methods used to analyze a deterministic game.
Author: Richard E. Klima
Publisher: CRC Press
ISBN: 1439872414
Category : Computers
Languages : en
Pages : 558
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Book Description
Easily Accessible to Students with Nontechnical Backgrounds In a clear, nontechnical manner, Cryptology: Classical and Modern with Maplets explains how fundamental mathematical concepts are the bases of cryptographic algorithms. Designed for students with no background in college-level mathematics, the book assumes minimal mathematical prerequisites and incorporates student-friendly Maplets throughout that provide practical examples of the techniques used. Technology Resource By using the Maplets, students can complete complicated tasks with relative ease. They can encrypt, decrypt, and cryptanalyze messages without the burden of understanding programming or computer syntax. The authors explain topics in detail first before introducing one or more Maplets. All Maplet material and exercises are given in separate, clearly labeled sections. Instructors can omit the Maplet sections without any loss of continuity and non-Maplet examples and exercises can be completed with, at most, a simple hand-held calculator. The Maplets are available for download at www.radford.edu/~npsigmon/cryptobook.html. A Gentle, Hands-On Introduction to Cryptology After introducing elementary methods and techniques, the text fully develops the Enigma cipher machine and Navajo code used during World War II, both of which are rarely found in cryptology textbooks. The authors then demonstrate mathematics in cryptology through monoalphabetic, polyalphabetic, and block ciphers. With a focus on public-key cryptography, the book describes RSA ciphers, the Diffie–Hellman key exchange, and ElGamal ciphers. It also explores current U.S. federal cryptographic standards, such as the AES, and explains how to authenticate messages via digital signatures, hash functions, and certificates.
Author: Miklos Bona
Publisher: CRC Press
ISBN: 1439850526
Category : Computers
Languages : en
Pages : 478
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Book Description
A Unified Account of Permutations in Modern CombinatoricsA 2006 CHOICE Outstanding Academic Title, the first edition of this bestseller was lauded for its detailed yet engaging treatment of permutations. Providing more than enough material for a one-semester course, Combinatorics of Permutations, Second Edition continues to clearly show the usefuln
Author: Pierre-Loic Meliot
Publisher: CRC Press
ISBN: 1498719139
Category : Mathematics
Languages : en
Pages : 683
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Book Description
Representation Theory of Symmetric Groups is the most up-to-date abstract algebra book on the subject of symmetric groups and representation theory. Utilizing new research and results, this book can be studied from a combinatorial, algorithmic or algebraic viewpoint. This book is an excellent way of introducing today’s students to representation theory of the symmetric groups, namely classical theory. From there, the book explains how the theory can be extended to other related combinatorial algebras like the Iwahori-Hecke algebra. In a clear and concise manner, the author presents the case that most calculations on symmetric group can be performed by utilizing appropriate algebras of functions. Thus, the book explains how some Hopf algebras (symmetric functions and generalizations) can be used to encode most of the combinatorial properties of the representations of symmetric groups. Overall, the book is an innovative introduction to representation theory of symmetric groups for graduate students and researchers seeking new ways of thought.
Author: Jurgen Bierbrauer
Publisher: CRC Press
ISBN: 148229981X
Category : Computers
Languages : en
Pages : 539
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Book Description
This book is designed to be usable as a textbook for an undergraduate course or for an advanced graduate course in coding theory as well as a reference for researchers in discrete mathematics, engineering and theoretical computer science. This second edition has three parts: an elementary introduction to coding, theory and applications of codes, and algebraic curves. The latter part presents a brief introduction to the theory of algebraic curves and its most important applications to coding theory.
