This is an archived handbook for a previous year. The current undergraduate and postgraduate handbooks can be viewed using the links above.
Undergraduate Handbook 2010-2011 (archived)
Module MATH3031: NUMBER THEORY III
Department: Mathematical Sciences
MATH3031: NUMBER THEORY III
| Type | Level | Credits | Availability | Module Cap | Location |
|---|---|---|---|---|---|
| Open | 3 | 20 | Available in 2010/2011 | None. | Durham |
Pre-requisites
- Linear Algebra II (MATH2021) and Algebra and Number Theory II (MATH2061).
Corequisites
- None.
Excluded Combinations
- 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
Subject-specific Knowledge
- 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.
Subject-specific Skills
- In addition students will have specialised mathematical skills in the following areas which can be used with minimal guidance: Abstract reasoning.
Key Skills
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 | Attendance Monitored |
|---|---|---|---|---|---|
| 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 | Component Weighting | Element | Length/Duration | Element Weighting | Resit Opportunity |
|---|---|---|---|---|---|
| Examination | 100% | Examination | three hour written examination | 100% |
Formative Assessment
Four written assignments to be assessed and returned. Other assignments are set for self-study and complete solutions are made available to students.
Students who do not attend monitored activities shown under Teaching Methods
and Learning Hours, or who fail to complete the summative or formative
assessment(s) specified above, may be subject to the Academic Progress
procedures defined in the University's General Regulation V, and may be
required to leave the University.