Ideal for undergraduate and graduate students in pure mathematics, this new text introduces the central, fundamental topics in number theory, including: divisibility and multiplicative functions; congruence and quadratic residues; continued fractions, diophantine approximation and transcendence; partitions; and diophantine equations and elliptic curves. In addition, some more advanced results are given, such as the Gelfond-Schneider theorem, the prime number theorem, and the Mordell-Weil theorem. Based on twenty years of ...
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Ideal for undergraduate and graduate students in pure mathematics, this new text introduces the central, fundamental topics in number theory, including: divisibility and multiplicative functions; congruence and quadratic residues; continued fractions, diophantine approximation and transcendence; partitions; and diophantine equations and elliptic curves. In addition, some more advanced results are given, such as the Gelfond-Schneider theorem, the prime number theorem, and the Mordell-Weil theorem. Based on twenty years of teaching number theory, the approach is thoroughly classroom tested. Each chapter concludes with an extensive selection of sample problems, and an appendix contains hints, sketch solutions, and useful tables, making this the perfect self-contained tool for teaching and learning number theory.
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