Mathematics (faster route) BSc/MSci
4H: Measure Theory and Probability MATHS4116
- Academic Session: 2026-27
- School: School of Mathematics and Statistics
- Credits: 10
- Level: Level 4 (SCQF level 10)
- Typically Offered: Semester 1
- Available to Visiting Students: Yes
- Collaborative Online International Learning: No
- Curriculum For Life: No
Short Description
This course introduces measure theory in a rigorous way and explores some applications to probability theory. Both of these are core mathematical disciplines. In addition, the knowledge of probability theory provided in this course is essential basis for further courses in mathematical finance.
Timetable
17 x 1 hr lectures and 6 x 1 hr tutorials in a semester
Excluded Courses
Probability STATS4060
Co-requisites
None
Assessment
Assessment
90% Examination, 10% Coursework.
Main Assessment In: April/May
Course Aims
The aim of this course is to introduce students to measure theory in a rigorous way, and explore some applications to probability theory.
Intended Learning Outcomes of Course
By the end of this course students will be able to:
Demonstrate knowledge of the central definitions and facts of measure theory and probability theory and use these to solve problems of a numerical or logical nature. In particular, students will be able to
■ Explain the notion of and give definitions of measure space and probability space and list their basic properties.
■ Integrate simple positive measurable functions, positive measurable functions, and general L1 -functions and derive properties of integrals this way.
■ State and apply the monotone convergence theorem, dominated convergence theorem, and the Fubini theorem.
■ Determine whether two or more random variables are independent.