Undergraduate Programme and Module Handbook 2020-2021 (archived)
Module MATH2647: PROBABILITY II
Department: Mathematical Sciences
MATH2647: PROBABILITY II
| Type | Open | Level | 2 | Credits | 10 | Availability | Available in 2020/21 | Module Cap | Location | Durham |
|---|
Prerequisites
- (Calculus I (MATH1061) and Probability I (MATH1597)) and Linear Algebra I (MATH1071) and Analysis I (MATH1051) [the latter may be a co-requisite].
Corequisites
- Analysis I (MATH1051) unless taken before.
Excluded Combination of Modules
- None
Aims
- To reinforce the knowledge of Probability gained at Level 1 and provide a firm foundation for modules in this area in higher years.
Content
- Infinite collections of events.
- Sequences of random variables and their convergence.
- Generating functions.
- Markov chains.
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: Markov Chains, random walks, real and complex generating functions, convergence in function space.
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 | |
|---|---|---|---|---|---|
| Lectures | 22 | 2 per week in Michaelmas and in first week of Easter | 1 Hour | 22 | |
| Tutorials | 5 | Fortnightly in Michaelmas and one in Easter | 1 Hour | 5 | ■ |
| Problems Classes | 4 | Fortnightly in Michaelmas | 1 Hour | 4 | |
| Preparation and Reading | 69 | ||||
| Total | 100 |
Summative Assessment
| Component: Examination | Component Weighting: 90% | ||
|---|---|---|---|
| Element | Length / duration | Element Weighting | Resit Opportunity |
| End of year written examination | 2 hours | 100% | Yes |
| Component: Continuous Assessment | Component Weighting: 10% | ||
| Element | Length / duration | Element Weighting | Resit Opportunity |
| Fortnightly or Weekly written assignments. | 100% | ||
Formative Assessment:
■ 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