MATH 103: Number Theory

This course shall assume no experience of background in number theory of theoretical mathematics. The course introduces various strategies for composing mathematical proofs.

Number systems: natural numbers, integers, rational numbers, real numbers, complex numbers, the equivalence and the difference of cardinality between them, de Morvie’s theorem with application, hyperbolic ad logarithmic functions, introduction to number theory including divisibility, the Euclidean algorithm, GCD and LCM of 2 integers, fundamental theorem of arithmetic (UFT), properties of prime numbers, congruencies with applications, arithmetic functions, quadratic residues.

1. Kenneth H. Rosen, Elementary number theory and its applications, Addison-Wesley; 3 Sub edition (1999).

• http://www.math.sc.edu/~sumner/numbertheory/euclidean/euclidean.html