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This textbook is an introduction to algebra via examples. The book moves from properties of integers, through other examples, to the beginnings of group theory. Applications to public key codes and to error correcting codes are emphasised. These applications, together with sections on logic and finite state machines, make the text suitable for students of computer science as well as mathematics students. Attention is paid to historical development of the mathematical ideas. This second edition contains new material on mathematical reasoning skills and a new chapter on polynomials has been added. The book was developed from first-level courses taught in the UK and USA. These courses proved successful in developing not only a theoretical understanding but also algorithmic skills. This book can be used at a wide range of levels: it is suitable for first- or second-level university students, and could be used as enrichment material for upper-level school students.
Revised and updated version of popular textbook. New sections and numerous problems.
Algebraic geometry is introduced, with particular attention given to projective curves, rational functions and divisors. The construction of algebraic geometric codes is given, and the Tsfasman-Vladut-Zink result mentioned above it discussed."--BOOK JACKET.
Using mathematical tools from number theory and finite fields, Applied Algebra: Codes, Ciphers, and Discrete Algorithms, Second Edition presents practical methods for solving problems in data security and data integrity. It is designed for an applied algebra course for students who have had prior classes in abstract or linear algebra. While the con
This unique book explains the basic issues of classical and modern cryptography, and provides a self contained essential mathematical background in number theory, abstract algebra, and probability--with surveys of relevant parts of complexity theory and other things. A user-friendly, down-to-earth tone presents concretely motivated introductions to these topics. More detailed chapter topics include simple ciphers; applying ideas from probability; substitutions, transpositions, permutations; modern symmetric ciphers; the integers; prime numbers; powers and roots modulo primes; powers and roots for composite moduli; weakly multiplicative functions; quadratic symbols, quadratic reciprocity; pseudoprimes; groups; sketches of protocols; rings, fields, polynomials; cyclotomic polynomials, primitive roots; pseudo-random number generators; proofs concerning pseudoprimality; factorization attacks finite fields; and elliptic curves. For personnel in computer security, system administration, and information systems.
In science, industry, public administration and documentation centers large amounts of data and information are collected which must be analyzed, ordered, visualized, classified and stored efficiently in order to be useful for practical applications. This volume contains 50 selected theoretical and applied papers presenting a wealth of new and innovative ideas, methods, models and systems which can be used for this purpose. It combines papers and strategies from two main streams of research in an interdisciplinary, dynamic and exciting way: On the one hand, mathematical and statistical methods are described which allow a quantitative analysis of data, provide strategies for classifying objects or making exploratory searches for interesting structures, and give ways to make comprehensive graphical displays of large arrays of data. On the other hand, papers related to information sciences, informatics and data bank systems provide powerful tools for representing, modelling, storing and retrieving facts, data and knowledge characterized by qualitative descriptors, semantic relations, or linguistic concepts. The integration of both fields and a special part on applied problems from biology, medicine, archeology, industry and administration assure that this volume will be informative and useful for theory and practice.
"The United States Code is the official codification of the general and permanent laws of the United States of America. The Code was first published in 1926, and a new edition of the code has been published every six years since 1934. The 2012 edition of the Code incorporates laws enacted through the One Hundred Twelfth Congress, Second Session, the last of which was signed by the President on January 15, 2013. It does not include laws of the One Hundred Thirteenth Congress, First Session, enacted between January 2, 2013, the date it convened, and January 15, 2013. By statutory authority this edition may be cited "U.S.C. 2012 ed." As adopted in 1926, the Code established prima facie the general and permanent laws of the United States. The underlying statutes reprinted in the Code remained in effect and controlled over the Code in case of any discrepancy. In 1947, Congress began enacting individual titles of the Code into positive law. When a title is enacted into positive law, the underlying statutes are repealed and the title then becomes legal evidence of the law. Currently, 26 of the 51 titles in the Code have been so enacted. These are identified in the table of titles near the beginning of each volume. The Law Revision Counsel of the House of Representatives continues to prepare legislation pursuant to 2 U.S.C. 285b to enact the remainder of the Code, on a title-by-title basis, into positive law. The 2012 edition of the Code was prepared and published under the supervision of Ralph V. Seep, Law Revision Counsel. Grateful acknowledgment is made of the contributions by all who helped in this work, particularly the staffs of the Office of the Law Revision Counsel and the Government Printing Office"--Preface.