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Advanced Number Theory

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Advanced Number Theory, 9780486640235 (048664023X), Dover Publications, 1980
Eminent mathematician/teacher approaches algebraic number theory from historical standpoint. Demonstrates how concepts, definitions, theories have evolved during last 2 centuries. Abounds with numerical examples, over 200 problems, many concrete, specific theorems. Includes numerous graphs and tables.

The prerequisites for this book are the “standard” first-semester course in number theory (with incidental elementary algebra) and elementary calculus. There is no lack of suitable texts for these prerequisites (for example, An Introduction to the Theory of Numbers, by 1. Niven and H. S. Zuckerman, John Wiley and Sons, 1960, cari be cited as a book that introduces the necessary algebra as part of number theory). Usually, very little else cari be managed in that first semester beyond the transition from improvised combinatorial amusements of antiquity to the coherently organized background for quadratic reciprocity, which was achieved in the eighteenth Century.

The present text constitutes slightly more than enough for a secondsemester course, carrying the student on to the twentieth Century by motivating some heroic nineteenth-Century developments in algebra and analysis. The relation of this textbook to the great treatises Will necessarily be like that of a hisforical novel to chronicles. We hope that once the student knows what to seek he Will find “chronicles” to be as exciting as a “historical novel.”
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