Undergraduate Course: Number Theory (MATH10026)
Course Outline
| School |
School of Mathematics |
College |
College of Science and Engineering |
| Course type |
Standard |
Availability |
Available to all students |
| Credit level (Normal year taken) |
SCQF Level 10 (Year 4 Undergraduate) |
Credits |
20 |
| Home subject area |
Mathematics |
Other subject area |
Specialist Mathematics & Statistics (Honours) |
| Course website |
http://student.maths.ed.ac.uk |
|
|
| Course description |
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 |
Students MUST have passed:
Numbers & Rings (MATH10023)
|
Co-requisites |
|
| Prohibited Combinations |
|
Other requirements |
None
|
| Additional Costs |
None |
Course Delivery Information
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.
|
Assessment Information
| Examination only. |
| Please see Visiting Student Prospectus website for Visiting Student Assessment information |
Special Arrangements
| Not entered |
Contacts
| Course organiser |
Dr Liam O'Carroll
Tel: (0131 6)50 5070
Email: L.O'Carroll@ed.ac.uk |
Course secretary |
Ms Jennifer Marshall
Tel: (0131 6)50 5048
Email: Jennifer.Marshall@ed.ac.uk |
|
copyright 2010 The University of Edinburgh -
1 September 2010 6:18 am
|
University Homepage