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Other titles in the Springer Undergraduate Mathematics series:
Elementary Number Theory (Springer Undergraduate Mathematics Series)by Gareth A. Jones
Synopses & Reviews
An undergraduate-level introduction to number theory, with the emphasis on fully explained proofs and examples. Exercises, together with their solutions are integrated into the text, and the first few chapters assume only basic school algebra. Elementary ideas about groups and rings 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.
This is an elementary undergraduate level introduction to number theory, with carefully explained proofs and numerous exercises and worked examples. A feature of particular interest is a concise account of Fermat's 'Last Theorem' and its recent proof by Andrew Wiles.
Table of Contents
Preface.- Notes to the reader.- Divisibility.- Prime Numbers.- Congruences.- Congruences with prime modulus.- Euler's function.- The group of units.- Quadratic residues.- Arithmetic functions.- The Riemann zeta function.- Sums of squares.- Fermat's Last Theorem.- Appendix 1: Induction and well-ordering.- Appendix 2: Groups, rings and fields.- Appendix 3: Convergence.- Table of primes.- Solutions to excercises.- References.- Index of symbols.- Index of names.- Index.
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