Elementary Methods in Number Theory

ISBN-13: 9781475773927 / Angielski / Miękka / 2013 / 514 str.

Melvyn B. Nathanson

Opis

This basic introduction to number theory is ideal for those with no previous knowledge of the subject. The main topics of divisibility, congruences, and the distribution of prime numbers are covered. Of particular interest is the inclusion of a proof for one of the most famous results in mathematics, the prime number theorem. With many examples and exercises, and only requiring knowledge of a little calculus and algebra, this book will suit individuals with imagination and interest in following a mathematical argument to its conclusion.

Spis treści

A First Course in Number Theory.- Divisibility and Primes.- Congruences.- Primitive Roots and Quadratic Reciprocity.- Fourier Analysis on Finite Abelian Groups.- The abc Conjecture.- Divisors and Primes in Multiplicative Number Theory.- Arithmetic Functions.- Divisor Functions.- Prime Numbers.- The Prime Number Theorem.- Primes in Arithmetic Progressions.- Three Problems in Additive Number Theory.- Waring’s Problem.- Sums of Sequences of Polynomials.- Liouville’s Identity.- Sums of an Even Number of Squares.- Partition Asymptotics.- An Inverse Theorem for Partitions.

O autorze

Preliminary Text. Do not use. "Elementary Methods in Number Theory" is divided into two parts. The first part is a basic introduction to elementary number theory for students with no previous knowledge of the subject. The main topics are divisibility, congruences, and the distribution of prime numbers. The second part of the book is an introduction to three classical problems in additive number theory. The book contains many examples and exercises. The only prerequisites for this book are a little calculus and algebra, and the imagination and perseverance to follow a mathematical argument.