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 content has been reworked and improved, this edition continues to cover many algorithms that arise in cryptography and error-control codes. New to the Second Edition A CD-ROM containing an (...) interactive version of the book that is powered by Scientific Notebook®, a mathematical word processor and easy-to-use computer algebra system New appendix that reviews prerequisite topics in algebra and number theory Double the number of exercises Instead of a general study on finite groups, the book considers finite groups of permutations and develops just enough of the theory of finite fields to facilitate construction of the fields used for error-control codes and the Advanced Encryption Standard. It also deals with integers and polynomials. Explaining the mathematics as needed, this text thoroughly explores how mathematical techniques can be used to solve practical problems. About the Authors Darel W. Hardy is Professor Emeritus in the Department of Mathematics at Colorado State University. His research interests include applied algebra and semigroups. Fred Richman is a professor in the Department of Mathematical Sciences at Florida Atlantic University. His research interests include Abelian group theory and constructive mathematics. Carol L. Walker is Associate Dean Emeritus in the Department of Mathematical Sciences at New Mexico State University. Her research interests include Abelian group theory, applications of homological algebra and category theory, and the mathematics of fuzzy sets and fuzzy logic. (shrink)

It’s a commonplace that Federal Reserve chairman Ben Bernanke draws his policies from Milton Friedman and Anna Schwartz’s A Monetary History of the United States. With that in mind, this article establishes five points. First, contrary to conventional wisdom, Friedman and Schwartz merely insinuate their claim the Fed caused the Depression in MH. Second, their criticisms of Fed policy during the Depression, which turn on its refusal to adopt open market purchases, repudiate Friedman’s famed libertarianism and market fundamentalism. Third, Friedman (...) and Schwartz don’t refute the practical objections of bankers who opposed OMPs in the 1930s. Consequently, Bernanke’s policies for addressing the financial crisis risk doing precisely what Friedman’s targets warned against—encouraging financial speculation without addressing problems of unemployment. Fourth, Friedman and Schwartz’s prescriptions entail a neoliberal, not a libertarian, state, one governed by technocrats and answerable to financial markets. Finally, what accounts for and unifies Friedman’s contradictions is the beneficiary—finance. (shrink)

This is an EXACT reproduction of a book published before 1923. This IS NOT an OCR'd book with strange characters, introduced typographical errors, and jumbled words. This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our (...) continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. (shrink)

The species concept is one of the oldest and most fundamental in biology. And yet it is almost universally conceded that no satisfactory definition of what constitutes a species has ever been proposed. The present article is devoted to an attempt to review the status of the problem from a methodological point of view. Since the species is one of the many taxonomic categories, the question of the nature of these categories in general needs to be entered into.

The aim of this paper is on the one hand to remind the Western reader of some aporias of Chinese antiquity, and on the other hand to show that a logic of sorts or of types similar to that which has been proposed to explain the relation between categories (in the mathematical sense of the term) and logic brings much light on these aporias. This should be contrasted with older traditional explanations using conventional syllogistics or feeling satised with too simple (...) explanations such as the confusion between inclusion and identity. The article is based on preceding papers of the Author, but stresses the basic unity of the solutions which were proposed there. (shrink)

Arabic scholarship and literature flourished during the Mamlūk period, and scholars and students from across the Muslim world were drawn to Cairo and Damascus. This led to opportunities for travel, education, and employment, yet these opportunities were available almost exclusively to men. In Syria and Egypt, and most of the medieval world, women’s involvement in travel, education, and public life, was often restricted. However, there were exceptions, including the prolific writer and poet ʿĀʾisha al-Bāʿūniyya (d. 1517). As a woman, she (...) crossed a number of social and cultural borders in order to enter into the domain of religious scholarship and literary production. Drawing from historical and biographical sources, and especially from ʿĀʾisha al-Bāʿūniyya’s writings, I examine her social and intellectual background, her travels and scholarly interactions in order to highlight some of the social trends and intellectual forces at work in the late Mamlūk period. (shrink)