Number Theory
The number theory is one of the branches of pure mathematics, mainly studying the nature of the integer. Known as the "pure" mathematical field. Positive integer by the multiplication of the nature of the division, can be divided into prime number, combined, 1, prime number produced a lot of ordinary people can understand and unsolved problems, such as Goldbach conjecture, twin prime guess, etc. Many problems, although very formal in form, in fact, have to use a lot of hard mathematical knowledge. This field of research in a sense to promote the development of mathematics, gave birth to a large number of new ideas and new methods. In addition to studying the integer and prime numbers, the number theory also studies some numbers derived from integers (such as rational numbers) or some generalized integers (such as algebraic integers). The integer can be the solution of the equation (Diophantine equation). Some analytic functions (like Riemann ζ functions) include some integer, the nature of prime numbers, through these functions can also understand some of the number of problems. Through the number theory can also establish the relationship between real and rational numbers, and use the rational number to approximate the real number (Diophantine approximation). ...