A First Course in Coding Theory

Author: Raymond Hill

Publisher: Oxford University Press

ISBN: 9780198538035

Category: Computers

Page: 251

View: 9324


Algebraic coding theory is a new and rapidly developing subject, popular for its many practical applications and for its fascinatingly rich mathematical structure. This book provides an elementary yet rigorous introduction to the theory of error-correcting codes. Based on courses given by the author over several years to advanced undergraduates and first-year graduated students, this guide includes a large number of exercises, all with solutions, making the book highly suitable for individual study.

A Course in Group Theory

Author: J. F. Humphreys

Publisher: Oxford University Press on Demand

ISBN: 9780198534594

Category: Business & Economics

Page: 279

View: 8828


Each chapter ends with a summary of the material covered and notes on the history and development of group theory.

A First Course in Combinatorial Mathematics

Author: Ian Anderson

Publisher: Oxford University Press

ISBN: 9780198596738

Category: Science

Page: 134

View: 7080


The spirit and aim of this book is to present a compact introduction to the basic combinatorial tools - such as recurrence relations, generating functions, incidence matrices, and the inclusion-exclusion principle - that will give the reader a flavour of the distinctive characteristics of this attractive and increasingly important branch of mathematics. A studly of block designs is followed by a brief mention of applications to coding theory. In this new edition, Steiner triple systems are constructed and S(5,8,24) is obtained via the Golay code of length 24. The final chapter combines together the three combinatorial structures of the Leech lattice, the Golay codes, and Steiner systems. Also in this edition, an application of the marriage theorem to score sequences of tournaments has been included.

Introduction to Parallel Computing : A practical guide with examples in C

A practical guide with examples in C

Author: Wesley Petersen,Peter Arbenz

Publisher: OUP Oxford

ISBN: 9780191513619

Category: Computers

Page: 278

View: 8815


In the last few years, courses on parallel computation have been developed and offered in many institutions in the UK, Europe and US as a recognition of the growing significance of this topic in mathematics and computer science. There is a clear need for texts that meet the needs of students and lecturers and this book, based on the author's lecture at ETH Zurich, is an ideal practical student guide to scientific computing on parallel computers working up from a hardware instruction level, to shared memory machines, and finally to distributed memory machines. Aimed at advanced undergraduate and graduate students in applied mathematics, computer science, and engineering, subjects covered include linear algebra, fast Fourier transform, and Monte-Carlo simulations, including examples in C and, in some cases, Fortran. This book is also ideal for practitioners and programmers.

Noncommutative Rings and Their Applications

Author: Steven Dougherty,Alberto Facchini,Andre Gerard Leroy,Edmund Puczylowski,Patrick Sole

Publisher: American Mathematical Soc.

ISBN: 147041032X

Category: Mathematics

Page: 265

View: 1120


This volume contains the Proceedings of an International Conference on Noncommutative Rings and Their Applications, held July 1-4, 2013, at the Universite d'Artois, Lens, France. It presents recent developments in the theories of noncommutative rings and modules over such rings as well as applications of these to coding theory, enveloping algebras, and Leavitt path algebras. Material from the course ``Foundations of Algebraic Coding Theory``, given by Steven Dougherty, is included and provides the reader with the history and background of coding theory as well as the interplay between coding theory and algebra. In module theory, many new results related to (almost) injective modules, injective hulls and automorphism-invariant modules are presented. Broad generalizations of classical projective covers are studied and category theory is used to describe the structure of some modules. In some papers related to more classical ring theory such as quasi duo rings or clean elements, new points of view on classical conjectures and standard open problems are given. Descriptions of codes over local commutative Frobenius rings are discussed, and a list of open problems in coding theory is presented within their context.

Buildings, Finite Geometries and Groups

Proceedings of a Satellite Conference, International Congress of Mathematicians, Hyderabad, India, 2010

Author: N.S. Narasimha Sastry

Publisher: Springer Science & Business Media

ISBN: 1461407095

Category: Mathematics

Page: 344

View: 1475


This is the Proceedings of the ICM 2010 Satellite Conference on “Buildings, Finite Geometries and Groups” organized at the Indian Statistical Institute, Bangalore, during August 29 – 31, 2010. This is a collection of articles by some of the currently very active research workers in several areas related to finite simple groups, Chevalley groups and their generalizations: theory of buildings, finite incidence geometries, modular representations, Lie theory, etc. These articles reflect the current major trends in research in the geometric and combinatorial aspects of the study of these groups. The unique perspective the authors bring in their articles on the current developments and the major problems in their area is expected to be very useful to research mathematicians, graduate students and potential new entrants to these areas.

An Introduction to Discrete Mathematics and Formal System Specification

Author: D. C. Ince

Publisher: Oxford University Press


Category: Mathematics

Page: 349

View: 2180


This computer science textbook offers an introduction to the theory and practice of formal specification, defined as the use of discrete mathematics for describing the function of hardware and software systems. Formal specification plays a vital role, especially with regard to problem-free installation. Designed for students approaching the subject for the first time, this text develops all the required analytical and mathematical techniques. Numerous worked examples and exercises demonstrate actual software and computer systems. The book culminates with an introduction to "Z", a formal notation which is particularly useful for unambiguously specifying systems.

Wave theory and applications

Author: David Russell Bland

Publisher: Oxford University Press, USA

ISBN: 9780198596547

Category: Education

Page: 317

View: 9767


This textbook provides a modern introduction to wave theory and its applications to physical phenomena such as deep water waves, transmission lines, elasticity, and traffic flow. The author presents a broad coverage of the subject, including numerous exercises. Each of the main topics is described in detail with examples of their applications. These topics include the classical wave equation, dispersion, dissipation, interconnected waves, diffusive waves, and first and second order non-linear waves. The special attention paid to non-linear and elastic waves represents a major strength of the text, along with its inclusion of an entire chapter devoted to the use of characteristics and asymptotic expansions. Intended for advanced undergraduates, the book will also be of interest to instructors in mathematics, physics and engineering courses.