Number Theory

This course is an elementary introduction to number theory with no algebraic prerequisites. Topics covered include primes, congruences, quadratic reciprocity, diophantine equations, Arithmetic functions, Lagrange's four-squares theorem and partitions.

1. To be able to write down formal Mathematical proofs
2. To be able to explain elementary results on distributions of prime numbers
3. To be able to apply number-theoretic techniques to simply computations.
4. To be able to describe properties of some special number theorectic functions and their growth rates
5. To be able to explain properties of numbers of some special forms
6. To be able to describe complete solutions of some special Diophantine equations and to be able to explain insolvability of some special nonlinear Diophantine equations.
7. To be able to explain the proof of Lagrange's four squares theorem .
8. To be able to explain basic theory of partitions.