Fourier analytic applications to number theory

In this paper we give expositions of Roth's theorem, Weyl's inequality and Vinogradov's three-primes theorem. In the proofs, we will frequently use exponential sums and more specifically the discrete Fourier transform. In the proof of Vinogradov's three-primes theorem we will use Hardy and Littlewood's circle method. This paper is intended to be self-contained and will hopefully be readable to someone with little background in the area.Science, Faculty ofMathematics, Department ofGraduat