Undergraduate Programme and Module Handbook 2012-2013 (archived)
Module MATH3031: NUMBER THEORY III
Department: Mathematical Sciences
MATH3031:
NUMBER THEORY III
Type |
Open |
Level |
3 |
Credits |
20 |
Availability |
Available in 2012/13 and alternate years thereafter |
Module Cap |
None. |
Location |
Durham
|
Prerequisites
Corequisites
Excluded Combination of Modules
- Number Theory IV (MATH4211).
Aims
- To provide an introduction to Algebraic Number Theory (Diophantine
Equations and Ideal Theory).
Content
- Diophantine equations using elementary
methods.
- Unique factorization.
- Ideals.
- Euclidean rings.
- Fields.
- Algebraic integers.
- Quadratic fields and integers.
- The discriminant and integral bases.
- Factorization of ideals.
- The ideal class group.
- Units in quadratic fields.
Learning Outcomes
- By the end of the module students will: be able to solve
novel and/or complex problems in Number Theory.
- have a systematic and coherent understanding of theoretical
mathematics in the field of Number Theory.
- have acquired a coherent body of knowledge of these subjects
demonstrated through one or more of the following topic areas:
Euclidean rings, PID's, U uniqueness of Factorization.
- Algebraic Number Fields (especially Quadratic
fields).
- Applications to Diophantine equations.
- In addition students will have specialised mathematical
skills in the following areas which can be used with minimal guidance:
Abstract reasoning.
Modes of Teaching, Learning and Assessment and how these contribute to
the learning outcomes of the module
- Lectures demonstrate what is required to be learned and the
application of the theory to practical examples.
- Assignments for self-study develop problem-solving skills and
enable students to test and develop their knowledge and understanding.
- Formatively assessed assignments provide practice in the
application of logic and high level of rigour as well as feedback for
the students and the lecturer on students' progress.
- The end-of-year examination assesses the knowledge acquired
and the ability to solve predictable and unpredictable
problems.
Teaching Methods and Learning Hours
Activity |
Number |
Frequency |
Duration |
Total/Hours |
|
Lectures |
40 |
2 per week for 19 weeks and 2 in term 3 |
1 Hour |
40 |
|
Preparation and Reading |
|
|
|
160 |
|
Total |
|
|
|
200 |
|
Summative Assessment
Component: Examination |
Component Weighting: 100% |
Element |
Length / duration |
Element Weighting |
Resit Opportunity |
Examination |
three hour written examination |
100% |
|
Four written assignments to be assessed and
returned. Other assignments are set for self-study and complete solutions
are made available to students.
■ Attendance at all activities marked with this symbol will be monitored. Students who fail to attend these activities, or to complete the summative or formative assessment specified above, will be subject to the procedures defined in the University's General Regulation V, and may be required to leave the University