| Unit name | Further Topics In Probability 3 |
|---|---|
| Unit code | MATH30006 |
| Credit points | 20 |
| Level of study | H/6 |
| Teaching block(s) |
Teaching Block 2 (weeks 13 - 24) |
| Unit director | Professor. Balazs |
| Open unit status | Not open |
| Pre-requisites |
Applied Probability 2 (MATH21400). Measure Theory and Integration (MATH34000) would be useful but is not essential. |
| Co-requisites |
None. |
| School/department | School of Mathematics |
| Faculty | Faculty of Science |
Unit aims
To outline, discuss, and prove with full mathematical rigour some of the key results in classical probability theory; with special emphasis on applications.
General Description of the Unit
This course deals with various analytic tools used and exploited in probability theory. Various modes of convergence of random variables (almost surely, weak, in probability, in Lp and in distribution) and the connections between them are presented. The key theorems are the Weak and Strong Laws of Large Numbers and the Central Limit Theorem. The analytic tools are: generating functions, Laplace- and Fourier transforms and fine analysis thereof.
Further information is available on the School of Mathematics website: http://www.maths.bris.ac.uk/study/undergrad/
Learning Objectives
To gain profound understanding of the basic notions and techniques of analytic methods in probability theory. In particular: generating functions, Laplace- and Fourier-transforms. To gain insight and familiarity with the various notions of convergence in the theory of random variables (in probability, almost sure, L^p, in distribution). Special emphasis will be on various “down-to-earth” applications of the mathematical theory.
Lectures supported by problem sheets and solution sheets.
80% Examination and 20% Coursework
Instructor’s lecture notes and problem sheets
