Elementary number theory
By: Gareth A. Jones and J. Mary Jones.
Contributors: Jones, J. Mary 1946-
Series: Springer undergraduate mathematics series
Publisher: Springer
Published: 1998
Place of publication: London; New York
Language: eng
Number of pages: 301
Subjects: Number theory
Description: This book gives an undergraduate-level introduction to Number Theory, with the emphasis on fully explained proofs and examples; exercises (with solutions) are integrated into the text. The first few chapters, covering divisibility, prime numbers and modular arithmetic, assume only basic school algebra, and are therefore suitable for first or second year students as an introduction to the methods of pure mathematics. Elementary ideas about groups and rings (summarised in an appendix) are then used to study groups of units, quadratic residues and arithmetic functions with applications to enumeration and cryptography. The final part, suitable for third-year students, uses ideas from algebra, analysis, calculus and geometry to study Dirichlet series and sums of squares; in particular, the last chapter gives a concise account of Fermat's Last Theorem, from its origin in the ancient Babylonian and Greek study of Pythagorean triples to its recent proof by Andrew Wiles.
Notes: Includes bibliographical references (p. 289-290) and indexes.