MTH3150 - Algebra and number theory II

On completion of this unit students will be able to:

1. Appreciate advanced concepts, algorithms and results in number theory;

2. Use Gaussian integers to find the primes expressible as a sum of squares;

3. Understand Diophantine equations, primitive roots and the quaternions - the best known skew field;

4. Appreciate many of the links between algebra and number theory;

5. Understand the most commonly occurring rings and fields: integers, integers modulo n, rationals, reals and complex numbers, more general structures such as algebraic number fields, algebraic integers and finite fields;

6. Perform calculations in the algebra of polynomials;

7. Use the Euclidean algorithm in structures other than integers;

8. Construct larger fields from smaller fields (field extensions);

9. Apply field theory to coding and cryptography.