58勛圖

MT5866 Probability Theory

Academic year

2026 to 2027 Semester 1

Further information on which modules are specific to your programme.

Key module information

SCOTCAT credits

15

The Scottish Credit Accumulation and Transfer (SCOTCAT) system allows credits gained in Scotland to be transferred between institutions. The number of credits associated with a module gives an indication of the amount of learning effort required by the learner. European Credit Transfer System (ECTS) credits are half the value of SCOTCAT credits.

SCQF level

SCQF level 11

The Scottish Credit and Qualifications Framework (SCQF) provides an indication of the complexity of award qualifications and associated learning and operates on an ascending numeric scale from Levels 1-12 with SCQF Level 10 equating to a Scottish undergraduate Honours degree.

Planned timetable

12 noon Mondays (weeks 2, 4, 7, 9, 11), Tuesdays and Thursdays

This information is given as indicative. Timetable may change at short notice depending on room availability.

Module description

This module will develop probability theory in a rigorous manner to access some of the big theorems of the subject, such as the laws of large numbers, the central limit theorem, and the martingale convergence theorem. The module will have the flavour of mathematical analysis, but there are applications across the mathematical sciences in areas such as statistics, game theory, statistical physics and mathematical biology.

Relationship to other modules

Pre-requisites

BEFORE TAKING THIS MODULE YOU MUST PASS MT2504 AND PASS MT3502

Assessment pattern

2-hour Written Examination = 100%

Re-assessment

Oral examination = 100%

Learning and teaching methods and delivery

Weekly contact

2.5 lectures (x 10 weeks), 1 tutorial (x 10 weeks)

Intended learning outcomes

  • Understand the rigorous foundations of probability theory on a finite or continuous sample space.
  • Understand key properties of random variables, including expectations and notions of convergence of sequences of random variables.
  • Apply important techniques in probability theory such as inequalities, moments, and characteristic functions.
  • Appreciate and apply some of the major theorems of probability such as the laws of large numbers, the martingale convergence theorems, the central limit theorem and the renewal theorem, along with careful proofs of such results.