Material to be
covered:
The goal of the present course is to give an introduction to the
subject and some of its methods. The topics covered will include
the fundamental theorem of arithmetic, Euclid's algorithm,
congruences, Diophantine problems, quadratic reciprocity,
arithmetic functions, and distribution of primes. If time allows,
we may also discuss some geometric methods, coming from lattice
point counting, such as Gauss's circle problem and Dirichlet
divisor problem, as well as some applications of Number Theory to
coding theory and cryptography.