This is an archived handbook for a previous year. The current undergraduate and postgraduate handbooks can be viewed using the links above.
Undergraduate Handbook 2021-2022 (archived)
Module MATH4277: Discrete and Continuous Probability IV
Department: Mathematical Sciences
MATH4277: Discrete and Continuous Probability IV
| Type | Level | Credits | Availability | Module Cap | Location |
|---|---|---|---|---|---|
| Open | 4 | 10 | Not available in 2021/2022 | None. | Durham |
Pre-requisites
- Analysis in Many Variables II (MATH2031) AND Complex Analysis II (MATH2011) AND EITHER [Probability II (MATH2647)] OR [Stochastic Processes III (MATH3251)] OR [Markov Chains II (MATH22707) and Analysis III (MATH3011)]
Corequisites
- None
Excluded Combinations
- None
Aims
- To explore in depth fundamental probabilistic systems in both discrete and continuous settings, building on earlier probability courses.
Content
- Order statistics
- Coin tossing and trajectories of random walks
- Brownian motion
Learning Outcomes
Subject-specific Knowledge
- By the end of the module students will: be able to solve seen and unseen problems on the given topics.
- Have a knowledge and understanding of this subject demonstrated through an ability to analyse the behaviour of the probabilistic systems explored in the course.
- Reproduce theoretical mathematics concerning probabilistic systems at a level appropriate to Level 4, including key definitions and theorems.
Subject-specific Skills
- In addition students will have enhanced mathematical skills in the following areas: probabilistic intuition.
Key Skills
- Students will have basic mathematical skills in the following areas: problem solving, modelling, computation.
Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module
- Lecturing demonstrates the development of mathematical ideas into a coherent body of material, and how the theory is applied to practical examples.
- Four homework assignments provide formative assessment and feedback to guide students in the correct development of their knowledge and skills in preparation for the summative assessment.
- 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 | 21 | 2 per week in Michaelmas term; 1 in Easter term | 1 hour | 21 | |
| Problem Classes | 4 | Fortnightly in Michaelmas term | 1 hour | 4 | |
| Preparation and reading | 75 | ||||
| Total | 100 |
Summative Assessment
| Component | Component Weighting | Element | Length/Duration | Element Weighting | Resit Opportunity |
|---|---|---|---|---|---|
| Examination | 100% | Written examination | 2 hours | 100% |
Formative Assessment
Four 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.