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DRPS : Course Catalogue : School of Mathematics : Mathematics

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 https://info.maths.ed.ac.uk/teaching.html Taught in Gaelic? No
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
Information for Visiting Students
Pre-requisites None
Displayed in Visiting Students Prospectus? Yes
Course Delivery Information
Not being delivered
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.
Special Arrangements
None
Additional Information
Academic description Not entered
Syllabus Not entered
Transferable skills Not entered
Reading list Not entered
Study Abroad Not entered
Study Pattern Not entered
Keywords NTh
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
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copyright 2011 The University of Edinburgh - 31 January 2011 7:59 am