| Unit name | Martingale Theory with Applications 4 |
|---|---|
| Unit code | MATHM0045 |
| Credit points | 20 |
| Level of study | M/7 |
| Teaching block(s) |
Teaching Block 1 (weeks 1 - 12) |
| Unit director | Professor. Balazs |
| Open unit status | Not open |
| Units you must take before you take this one (pre-requisite units) |
MATH20008 Probability 2 |
| Units you must take alongside this one (co-requisite units) |
None |
| Units you may not take alongside this one |
None |
| School/department | School of Mathematics |
| Faculty | Faculty of Science |
Unit aims
To lay foundations for further studies in probability theory. To stimulate through theory and examples, an interest and appreciation of the power of the elegant method of martingales in probability theory.
Unit description
First, rigorous foundations and essential tools of probability theory are introduced; various modes of convergence of random variables (almost sure, L^p, in probability, weak) and the connections between them are presented. We then turn to the theory of martingales which is of fundamental importance to probability theory, statistics, and mathematical finance. This unit is a concise introduction of the basic concepts, results and examples of this powerful and elegant theory.
Relation to other units
Probability 2 has introduced Martingales, but only covers the most basic of results, mostly without rigorous proofs. This unit will prove most of the results in a rigorous measure-theoretic fashion, and will be essential for students who wish to go on to study post-graduate level probability theory. In particular, students will find the understanding of material in this unit very helpful in other related units, such as Financial Mathematics and Further Topics in Probability (for which this unit is a prerequisite).
To gain insight and familiarity with the various techniques and notions of convergence in the theory of random variables (in probability, almost sure, L^p, in distribution). To gain an understanding of martingales, and to be able to formulate problems in probability/statistics theory in terms of martingales. Students will also gain more experience in writing proofs, thus laying the foundation for future studies in probability theory at advanced undergraduate and postgraduate levels.
The unit will be taught through a selection of lectures, online materials, independent activities such as problem sheets and other exercises, problem classes, support sessions and office hours.
80% Timed examination 20% Coursework.
Raw scores on the examinations will be determined according to the marking scheme written on the examination paper. The marking scheme, indicating the maximum score per question, is a guide to the relative weighting of the questions. Raw scores are moderated as described in the Undergraduate Handbook.
If this unit has a Resource List, you will normally find a link to it in the Blackboard area for the unit. Sometimes there will be a separate link for each weekly topic.
If you are unable to access a list through Blackboard, you can also find it via the Resource Lists homepage. Search for the list by the unit name or code (e.g. MATHM0045).
How much time the unit requires
Each credit equates to 10 hours of total student input. For example a 20 credit unit will take you 200 hours
of study to complete. Your total learning time is made up of contact time, directed learning tasks,
independent learning and assessment activity.
See the University Workload statement relating to this unit for more information.
Assessment
The Board of Examiners will consider all cases where students have failed or not completed the assessments required for credit.
The Board considers each student's outcomes across all the units which contribute to each year's programme of study. For appropriate assessments, if you have self-certificated your absence, you will normally be required to complete it the next time it runs (for assessments at the end of TB1 and TB2 this is usually in the next re-assessment period).
The Board of Examiners will take into account any exceptional circumstances and operates
within the Regulations and Code of Practice for Taught Programmes.
