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 MATH4327: Topics in Probability IV

Department: Mathematical Sciences

MATH4327: Topics in 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) Complex Analysis II (MATH2011) and either: [Probability II (MATH2647)] OR [Stochastic Processes III (MATH3251)] OR [Markov Chains II (MATH2707) AND Analysis III (MATH3011)].

Corequisites

None

Excluded Combinations

None

Aims

To introduce one or two contemporary topics in probability theory and to develop and apply them.

Content

One or two of the following topics will run each year:
Random graphs and probabilistic combinatorics
Random walks in space
Geometric probability
Random matrix theory
Probability and phase transition
Conformally invariant probability
Interacting particle systems

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
Lectures	21	2 per week in Epiphany term; 1 in Easter term	1 hour	21
Problem classes	4	Fortnightly in Epiphany 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.