This volume, written by his friends, collaborators and students, is offered to the memory of Paul Tunin. Most of the papers they contributed discuss subjects related to his own fields of research. The wide range of topics reflects the versatility of his mathematical activity. His work has inspired many mathematicians in analytic number theory, theory of functions of a complex variable, interpolation and approximation theory, numerical algebra, differential equations, statistical group theory and theory of graphs. Beyond the influence of his deep and important results he had the exceptional ability to communicate to others his enthusiasm for mathematics. One of the strengths of Turan was to ask unusual questions that became starting points of many further results, sometimes opening up new fields of research. We hope that this volume will illustrate this aspect of his work adequately. Born in Budapest, on August 28, 1910, Paul Turan obtained his Ph. D. under L. Fejer in 1935. His love for mathematies enabled him to work even under inhuman circumstances during the darkest years of the Second World War. One of his major achievements, his power sum method originated in this period. After the war he was visiting professor in Denmark and in Princeton. In 1949 he became professor at the Eotvos Lorand University of Budapest, a member of the Hungarian Academy of Sciences and a leading figure of the Hungarian mathematical community.

This text provides a detailed presentation of the main results for infinite products, as well as several applications. The target readership is a student familiar with the basics of real analysis of a single variable and a first course in complex analysis up to and including the calculus of residues. The book provides a detailed treatment of the main theoretical results and applications with a goal of providing the reader with a short introduction and motivation for present and future study. While the coverage does not include an exhaustive compilation of results, the reader will be armed with an understanding of infinite products within the course of more advanced studies, and, inspired by the sheer beauty of the mathematics. The book will serve as a reference for students of mathematics, physics and engineering, at the level of senior undergraduate or beginning graduate level, who want to know more about infinite products. It will also be of interest to instructors who teach courses that involve infinite products as well as mathematicians who wish to dive deeper into the subject. One could certainly design a special-topics class based on this book for undergraduates. The exercises give the reader a good opportunity to test their understanding of each section.

This book is an introduction to the theory of rings and modules that goes beyond what one normally obtains in a graduate course in abstract algebra. In addition to the presentation of standard topics in ring and module theory, it also covers category theory, homological algebra and even more specialized topics like injective envelopes and proj

A journal of statistics emphasizing the statistical study of biological problems. Papers contain original theoretical contributions of direct or potential value in applications.

Table of Integrals, Series, and Products provides information pertinent to the fundamental aspects of integrals, series, and products. This book provides a comprehensive table of integrals. Organized into 17 chapters, this book begins with an overview of elementary functions and discusses the power of binomials, the exponential function, the logarithm, the hyperbolic function, and the inverse trigonometric function. This text then presents some basic results on vector operators and coordinate systems that are likely to be useful during the formulation of many problems. Other chapters consider inequalities that range from basic algebraic and functional inequalities to integral inequalities and fundamental oscillation and comparison theorems for ordinary differential equations. This book discusses as well the important part played by integral transforms. The final chapter deals with Fourier and Laplace transforms that provides so much information about other integrals. This book is a valuable resource for mathematicians, engineers, scientists, and research workers.

Hopkins collects the work of 35 instructors who share their innovations and insights about teaching discrete mathematics at the high school and college level. The book's 9 classroom-tested projects, including building a geodesic dome, come with student handouts, solutions, and notes for the instructor. The 11 history modules presented draw on original sources, such as Pascal's "Treatise on the Arithmetical Triangle," allowing students to explore topics in their original contexts. Three articles address extensions of standard discrete mathematics content. Two other articles explore pedagogy specifically related to discrete mathematics courses: adapting a group discovery method to larger classes, and using logic in encouraging students to construct proofs.