Mathematics is the queen of the sciences—and number theory is the queen of mathematics.
Introduction
Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. German mathematician Carl Friedrich Gauss (1777–1855) said, “Mathematics is the queen of the sciences—and number theory is the queen of mathematics.” Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example, rational numbers), or defined as generalizations of the integers (for example, algebraic integers).
Contents
Analytical Number Theory
Prime Distribution
Arithmetic Functions
Riemann Zeta-Function
Dirichlet’s Theorem
Algebraic Number Theory
Congruent Classes
Quadratic Reciprocity
Diophantine Equations