A Course in Number Theory
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A Course in Number Theory

A Course in Number Theory


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About the Book

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.

Table of Contents:
1: Divisibility 2: Multiplicative Functions 3: Congruence Theory 4: Quadratic Residues 5: Algebraic Topics 6: Sums of Squares and Gauss Sums 7: Continued Fractions 8: Transcendental Numbers 9: Quadratic Forms 10: Genera and the Class Group 11: Partitions 12: The Prime Numbers 13: Two Major Theorems on the Primes 14: Diophantine Equations 15: Elliptic Curves: Basic Theory 16: Elliptic Curves: Further Results and Applications Answers and Hints to Problems Tables Bibliography Index to Notation General Index

Review :
`It is of interest both to students and teachers working in this field.' EMS Newsletter, No. 21, 1996 `An extremely demanding text for undergraduates, but well-suited for a mathematician who wants to learn some number theory.' American Mathematical Monthly


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Product Details
  • ISBN-13: 9780198523765
  • Publisher: Oxford University Press
  • Binding: Paperback
  • Height: 234 mm
  • No of Pages: 416
  • Spine Width: 23 mm
  • Width: 156 mm
  • ISBN-10: 0198523769
  • Publisher Date: 14 Sep 1995
  • Edition: Revised edition
  • Language: English
  • Returnable: N
  • Weight: 625 gr


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