Overview

This textbook covers with the main topics in number theory as taught in universities throughout the world. Number theory deals mainly with properties of integers and rational numbers; it is not an organized theory in the usual sense, but a vast collection of individual topics and results, with some coherent sub-theories and a long list of unsolved problems. Nine main areas of the subject are treated: (i) divisibility and multiplicative functions; (ii) congruences and quadratic residues; (iii) the basics of algebraic numbers and sums of squares; (iv) continued fractions, diophantine approximations and transcendence; (v) quadratic forms; (vi) partitions; (vii) the prime numbers; (viii) diophantine equations; and (ix) elliptic curves (this part has been considerably extended for this edition). The increased use of computers in number theory is reflected in many sections (with much greater emphasis in this edition). Some results of a more advanced nature are also given, including the Gelfond-Schneider theorem, the prime number theorem, and the Mordell-Weil theorem. The latest work on fermat's last theorem is also breifly discussed. Each chapter ends with a collection of problems; hints or sketch solutions are given at the end of the book, together with various useful tables.

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9780198523765

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<br> This excellent book on number theory is detailed and readable. If the appropriate chapters are selected, it is suitable for upper-undergraduate and graduate levels..... The book contains excellent problems, a bibliography, and many references to computer applications. Rose's second edition can serve as a good textbook or a fine reference book and can be used for independent study by anyone interested in learning number theory. --The Mathematics Teacher<br> The book nicely presented central areas of numbers theory. --Dr. Jurgen Hurrelbrink, Louisiana State University--Baton Rouge<br> An extremely demanding text for undergraduates, but well-suited for a mathematician who wants to learn some number theory. --American Mathematical Monthly<br> The author shows an impeccable taste in his choice of topics and gives a lot of historical discussion, making this book a pleasant one to browse, and a great text on which to base a first undergraduate number theory course . . . . It should giv

<br> This excellent book on number theory is detailed and readable. If the appropriate chapters are selected, it is suitable for upper-undergraduate and graduate levels..... The book contains excellent problems, a bibliography, and many references to computer applications. Rose's second edition can serve as a good textbook or a fine reference book and can be used for independent study by anyone interested in learning number theory. --The Mathematics Teacher<p><br> The book nicely presented central areas of numbers theory. --Dr. Jurgen Hurrelbrink, Louisiana State University--Baton Rouge<p><br> An extremely demanding text for undergraduates, but well-suited for a mathematician who wants to learn some number theory. --American Mathematical Monthly<p><br> The author shows an impeccable taste in his choice of topics and gives a lot of historical discussion, making this book a pleasant one to browse, and a great text on which to base a first undergraduate number theory course . . . . It should give students a tantalizing glimpse into a beautiful area of number theory, and inspire them to further explore the subject. --Mathematical Reviews<p><br>

This excellent book on number theory is detailed and readable. If the appropriate chapters are selected, it is suitable for upper-undergraduate and graduate levels..... The book contains excellent problems, a bibliography, and many references to computer applications. Rose's second edition can serve as a good textbook or a fine reference book and can be used for independent study by anyone interested in learning number theory. --The Mathematics Teacher<br> The book nicely presented central areas of numbers theory. --Dr. Jurgen Hurrelbrink, Louisiana State University--Baton Rouge<br> An extremely demanding text for undergraduates, but well-suited for a mathematician who wants to learn some number theory. --American Mathematical Monthly<br> The author shows an impeccable taste in his choice of topics and gives a lot of historical discussion, making this book a pleasant one to browse, and a great text on which to base a first undergraduate number theory course . . . . It should give students a tantalizing glimpse into a beautiful area of number theory, and inspire them to further explore the subject. --Mathematical Reviews<br>

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