Your programme is made up of credits, the total differs on programme to programme.
| Semester 1 Credit Value: | 10 |
| ECTS Credits: | 5.0 |
| European Credit Transfer System | |
To introduce a number of mathematical models that account for stochastic (random) variations that are often necessary to model real world phenomena. Key concepts of stochastic processes will be explored in various settings.
Module summary
When modelling real world systems through time, we may wish to model the uncertainty inherent in the system. Such models require an appropriate collection of random variables indexed through time. We will illustrate how stochastic processes can help us understand complex dynamical systems.
The first part of the module will involve a review of probability theory, particularly conditional probability. We will then introduce random walks and Markov chains. Birth-death models and queuing systems will also be explored.
Review of probability ideas: for instance, conditioning arguments. Gambling problems. Random walks. Markov chains: definition and examples, Chapman Kolmogorov equations, classification of states, notions of transience and recurrence, stationary distributions, simulation. Advanced topics may include: queueing, epidemic models.
| Category | Activity | Number | Length | Student Hours | Comment |
|---|---|---|---|---|---|
| Guided Independent Study | Assessment preparation and completion | 15 | 1:00 | 15:00 | Completion of in course assessments |
| Scheduled Learning And Teaching Activities | Lecture | 5 | 1:00 | 5:00 | Problem Classes |
| Scheduled Learning And Teaching Activities | Lecture | 2 | 1:00 | 2:00 | Revision Lectures |
| Scheduled Learning And Teaching Activities | Lecture | 20 | 1:00 | 20:00 | Formal Lectures |
| Guided Independent Study | Independent study | 58 | 1:00 | 58:00 | Preparation time for lectures, background reading, coursework review |
| Total | 100:00 |
Teaching methods are appropriate to allow students to develop a wide range of skills, from understanding basic concepts and facts to higher-order thinking. Lectures are used for the delivery of theory and explanation of methods, illustrated with examples, and for giving general feedback on marked work. Problem classes are used to help develop the students’ abilities at applying the theory to solving problems
The format of resits will be determined by the Board of Examiners
| Description | Length | Semester | When Set | Percentage | Comment |
|---|---|---|---|---|---|
| Written Examination | 120 | 1 | A | 80 | N/A |
| Description | Semester | When Set | Percentage | Comment |
|---|---|---|---|---|
| Prob solv exercises | 1 | M | 5 | Problem-solving exercises assessment |
| Prob solv exercises | 1 | M | 5 | Problem-solving exercises assessment |
| Prob solv exercises | 1 | M | 5 | Problem-solving exercises assessment |
| Prob solv exercises | 1 | M | 5 | Problem-solving exercises assessment |
A substantial formal unseen examination is appropriate for the assessment of the material in this module. The format of the examination will enable students to reliably demonstrate their own knowledge, understanding and application of learning outcomes. The assurance of academic integrity forms a necessary part of the programme accreditation.
Exam problems may require a synthesis of concepts and strategies from different sections, while they may have more than one ways for solution. The examination time allows the students to test different strategies, work out examples and gather evidence for deciding on an effective strategy, while carefully articulating their ideas and explicitly citing the theory they are using.
The coursework assignments allow the students to develop their problem solving techniques, to practise the methods learnt in the module, to assess their progress and to receive feedback; these assessments have a secondary formative purpose as well as their primary summative purpose.