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 MATH2151: PROBABILITY AND GEOMETRIC TOPOLOGY II
Department: Mathematical Sciences
MATH2151: PROBABILITY AND GEOMETRIC TOPOLOGY II
| Type | Level | Credits | Availability | Module Cap | Location |
|---|---|---|---|---|---|
| Open | 2 | 20 | Available in 2010/2011 | None. | Durham |
Pre-requisites
- Core A Mathematics (MATH1012) and Core B1 (MATH1051)
Corequisites
- None
Excluded Combinations
- Probability and Actuarial Mathematics II (MATH2161), Contours and Probability II (MATH2561), Codes and Probability II (MATH2571) and Codes and Geometric Topology II (MATH21411).
Aims
- To provide basic notions of two separate topics in mathematics with a view to study them in more depth in subsequent years.
Content
- Topic 1: Probability: Markov chains, random walks, real and complex generating functions, convergence in function space.
- Topic 2: Geometric topology: knots, surfaces, knot invariants.
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 the given topics.
- Have an awareness of the abstract concepts of theoretical mathematics in the field of the given topics.
- Have a knowledge and understanding of the major theories of these subjects demonstrated through one or more of the following topic areas: Probability: Markov Chains, random walks, real and complex generating functions, convergence in function space; Geometric topology: knots, surfaces, knot invariants.
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: Modelling.
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 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 | 38 | 2 per week | 1 Hour | 38 | |
| Tutorials | 10 | Fortnightly for 20 weeks | 1 Hour | 10 | Yes |
| Problems Classes | 10 | Fortnightly for 20 weeks | 1 Hour | 10 | |
| Preparation and Reading | 142 | ||||
| Total | 200 |
Summative Assessment
| Component | Component Weighting | Element | Length/Duration | Element Weighting | Resit Opportunity |
|---|---|---|---|---|---|
| Examination | 50% | end of year written examination | 1 hour 45 minutes | 100% | yes |
| Examination | 50% | end of year written examination | 1 hour 45 minutes | 100% | yes |
Formative Assessment
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.