This is an archived handbook for a previous year. The current undergraduate and postgraduate handbooks can be viewed using the links above.
Undergraduate Handbook 2016-2017 (archived)
Module MATH2617: Elementary Number Theory II
Department: Mathematical Sciences
MATH2617: Elementary Number Theory II
| Type | Level | Credits | Availability | Module Cap | Location |
|---|---|---|---|---|---|
| Open | 2 | 10 | Available in 2016/2017 | Durham |
Pre-requisites
- Calculus and Probability 1 (MATH1061) and Linear Algebra 1 (MATH1071).
Corequisites
- None.
Excluded Combinations
- None.
Aims
- To provide and introduction to the basics of number theory.
Content
- Review of basic features of integers.
- Congruences and modular arithmetic
- Quadratic reciprocity
- Diophantine equations
Learning Outcomes
Subject-specific Knowledge
- By the end of the module students will: be able to solve a range of predictable and unpredictable problems in Number Theory.
- have an awareness of the abstract concepts of theoretical mathematics in the field of Number Theory.
- have a knowledge and understanding of fundamental theories of these subjects demonstrated through one or more of the following topic areas: Fundamental theorem of arithmetic, modular arithmetic and chinese remainder theorem.
- Diophantine equations.
Subject-specific Skills
- In addition students will have the ability to undertake and defend the use of alternative mathematical skills in the following areas with minimal guidance: Abstract reasoning.
Key Skills
Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module
- Lecturing demonstrates what is required to be learned and the application of the theory to practical examples.
- Weekly/Fortnightly homework problems provide formative assessment to guide students in the correct development of their knowledge and skills.
- Tutorials provide active engagement and feedback to the learning process.
- 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 | 22 | 2 per week in Michaelmas and week 20 in Easter | 1 Hour | 22 | |
| Tutorials | 5 | Fortnightly for 10 weeks | 1 Hour | 5 | Yes |
| Problems Classes | 4 | Fortnightly in Michaelmas | 1 Hour | 4 | |
| Preparation and Reading | 69 | ||||
| Total | 100 |
Summative Assessment
| Component | Component Weighting | Element | Length/Duration | Element Weighting | Resit Opportunity |
|---|---|---|---|---|---|
| Examination | 100% | End of year written examination | 2 hours | 100% | Yes |
Formative Assessment
Fortnightly or Weekly written assignments.
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.