Elementary Number Theory with Applications

by Thomas Koshy

2007 · Elsevier

This second edition updates the well-regarded 2001 publication with new short sections on topics like Catalan numbers and their relationship to Pascal's triangle and Mersenne numbers, Pollard rho factorization method, Hoggatt-Hensell identity. Koshy has added a new chapter on continued fractions. The unique features of the first edition like news of recent discoveries, biographical sketches of mathematicians, and applications--like the use of congruence in scheduling of a round-robin tournament--are being refreshed with current information. More challenging exercises are included both in the textbook and in the instructor's manual. Elementary Number Theory with Applications 2e is ideally suited for undergraduate students and is especially appropriate for prospective and in-service math teachers at the high school and middle school levels. * Loaded with pedagogical features including fully worked examples, graded exercises, chapter summaries, and computer exercises * Covers crucial applications of theory like computer security, ISBNs, ZIP codes, and UPC bar codes * Biographical sketches lay out the history of mathematics, emphasizing its roots in India and the Middle East

Hayekian Systems

by William N. Butos, Thomas J. McQuade

2023 · Taylor & Francis

The central theme in the work of F.A. Hayek was the problem of order in society, and his focus was epistemological: he was concerned with the constraints on knowledge, the problems associated with its distribution, the structures in which it inheres, and the implications of these issues for the understanding of social phenomena generally. But while his work has greatly improved our understanding of market processes, application to more complex social arrangements was not an unambiguous success. In seeking to progress beyond Hayek’s difficulties in formulating a more general theory of spontaneous order, this book fleshes out an analogy between social orders and the biological order detailed in Hayek’s The Sensory Order into a theory of adaptive systems. It focuses first on those aspects of the systems which enable them to learn about their environments, and then on the entrepreneurial processes which implement their anticipatory capabilities. The inclusion of anticipatory elements, inspired by the work of Robert Rosen, results in a theory of social orders which integrates many of the disparate findings of Austrian economists into a self-consistent conceptual framework and has applicability to other social arrangements such as firms and governments. Of particular interest is the interaction between the systems of science and government, an issue of significant current concern which is comprehensively explored here both theoretically and empirically. This book is essential reading for anyone interested in Hayek, Austrian economics, social theory, and the history of economic thought more broadly.