Number Theory - 2019 entry

Number theory is a vast and fascinating field of mathematics, consisting of the study of the properties of whole numbers.  From this module, you will acquire a working knowledge of the main concepts of classical elementary number theory, together with some appreciation of modern computational techniques.

Prerequisite module: MTH1001 Structures, or equivalent

This course covers one of the oldest and most popular areas of mathematics, building on basic ideas and including modern applications. The dual objectives are to provide a solid foundation for further work in number theory, but also at the same time to give a self-contained interesting course suitable as an end in itself, with modern answers to ancient problems and modern applications of classical ideas. You will acquire a sound foundation in number theory from a modern perspective.

On successful completion of this module, you should be able to:

Module Specific Skills and Knowledge:

1 demonstrate a working knowledge of the main concepts of classical elementary number theory, together with some appreciation of modern computational techniques.

Discipline Specific Skills and Knowledge:

2 understand the role of Number Theory as a central topic in mathematics, and demonstrate an awareness of some of its modern applications;

3 comprehend a couple of useful techniques for the computation of integrals with complex methods.

Personal and Key Transferable/ Employment Skills and  Knowledge:

4 show enhanced problem-solving skills and ability to formulate your solutions as mathematical proofs;

5 reveal a fundamental knowledge of Number Theory from a modern perspective.

- divisibility, greatest common divisor;

- extended Euclidean algorithm, prime numbers and unique factorisation;

- congruences, Euler's and Wilson's theorems, Chinese Remainder Theorem;

- computational methods, primality testing, factorisation, RSA cryptosystem;

- primitive roots;

- quadratic residues and quadratic reciprocity;

- sums of two and four squares;

- Pythagorean triples;

- Fermat's Last Theorem for exponent four.

If a module is normally assessed entirely by coursework, all referred/deferred assessments will normally be by assignment.

If a module is normally assessed by examination or examination plus coursework, referred and deferred assessment will normally be by examination. For referrals, only the examination will count, a mark of 40% being awarded if the examination is passed. For deferrals, candidates will be awarded the higher of the deferred examination mark or the deferred examination mark combined with the original coursework mark.

ELE – http://vle.exeter.ac.uk

Reading list for this module: