Number Theory (U01880)

? Credit Points : 20 ? SCQF Level : 10 ? Acronym : MAT-4-NTh

Course for final year students in Honours programmes in Mathematics.

Solving linear equations in integers, primes, Fundamental Theorem of Arithmetic, primitive roots, pseudoprimes, congruences, quadratic residues and reciprocity, arithmetical functions, representation of integers as sums of squares, p-adic numbers, rational points on conics and elliptic curves.

Entry Requirements

? Pre-requisites : MAT-3-NuR

Subject Areas

Home subject area

Specialist Mathematics & Statistics (Honours), (School of Mathematics, Schedule P)

Delivery Information

? Normal year taken : 4th year

? Delivery Period : Not being delivered

? Contact Teaching Time : 4 hour(s) per week for 11 weeks

All of the following classes

Type	Day	Start	End	Area
Lecture	Tuesday	09:00	09:50	KB
Lecture	Friday	09:00	09:50	KB

Summary of Intended Learning Outcomes

1. Ability to solve any linear equation in integers.
2. Ability to solve linear and quadratic congruences.
3. Familiarity with methods for writing an integer as a sum of two squares.
4. Ability to calculate with p-adic numbers.
5. Ability to find rational points on a conic.
6. Familiarity with methods of finding rational points on elliptic curves.
7. Appreciation of some analytic techinques in number theory.
8. Appreciation of some algebraic techinques in number theory.
9. Ability to construct a transcendental number.
10. Sense of wonderment at the beauty of the subject.