Elementary Number Theory
By: by Gareth A. Jones, J. Mary Jones
Contributors: Jones, J. Mary
Series: Springer Undergraduate Mathematics Series, 1615-2085; Springer undergraduate mathematics series
Publisher: Springer London; Imprint; Springer
Published: 1998
Place of publication: London
Language: eng
Format: [electronic resource] /
Number of pages: 306
ISBN-13: 9781447106135
Subjects: Mathematics; 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.
Table of contents: title: Preface; title: Notes to the reader; title: Divisibility; title: Prime Numbers; title: Congruences; title: Congruences with prime modulus; title: Euler's function; title: The group of units; title: Quadratic residues; title: Arithmetic functions; title: The Riemann zeta function; title: Sums of squares; title: Fermat's Last Theorem; title: Appendix 1: Induction and well-ordering; title: Appendix 2: Groups, rings and fields; title: Appendix 3: Convergence; title: Table of primes; title: Solutions to excercises; title: References; title: Index of symbols; title: Index of names; title: Index.