# Unit information: Further Topics In Probability 4 in 2021/22

Unit name Further Topics In Probability 4 MATHM0018 20 M/7 Teaching Block 2 (weeks 13 - 24) Dr. Balazs Not open MATH20008 Probability 2, MATHM6204 Martingale Theory with Applications (3 or 4) None School of Mathematics Faculty of Science

## Description including Unit Aims

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.

Unit description

This course deals with probabilistic methods and with various analytic tools used and exploited in probability theory. It builds on the rigorous foundations given in the Martingale Theory with Applications unit and proceeds to prove some of the key theorems of probability: the Weak and Strong Laws of Large Numbers and the Central Limit Theorem. The analytic tools introduced in a probabilistic context are: generating functions, Fourier transforms, weak convergence of probability measures, and fine analysis thereof.

Relation to other units

MATH20008 Probability 2 and MATH36204 or MATHM6204 Martingale Theory with Applications (3 or 4) are prerequisites. MATH34000 Measure Theory and Integration and MATH20006 Metric Spaces are recommended.

## Intended Learning Outcomes

To gain profound understanding of the basic notions and techniques of probabilistic and analytic methods in probability theory. In particular: generating functions, Fourier-transforms, weak convergence of probability measures. Special emphasis will be on various “down-to-earth” applications of the mathematical theory.

## Teaching Information

The unit will be taught through a combination of

• synchronous online and, if subsequently possible, face-to-face lectures
• asynchronous online materials, including narrated presentations and worked examples
• guided asynchronous independent activities such as problem sheets and/or other exercises
• synchronous weekly group problem/example classes, workshops and/or tutorials
• synchronous weekly group tutorials
• synchronous weekly office hours

## Assessment Information

80% Timed, open-book 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 you fail this unit and are required to resit, reassessment is by a written examination in the August/September Resit and Supplementary exam period.

## Resources

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. MATHM0018).

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.