Undergraduate Course: Essentials in Analysis and Probability (MATH10047)
|School||School of Mathematics
||College||College of Science and Engineering
|Credit level (Normal year taken)||SCQF Level 10 (Year 4 Undergraduate)
||Availability||Available to all students
|Summary||The central topic of this course is measure theory. Measure theory is the foundation for advanced topics in Analysis and Probability.
The course will cover many of the following topics:
Random events, sigma-algebras, monotone classes.
Measurable spaces, random variables - measurable functions.
Measures, probability measures, signed measures.
Borel sets in R^d, Lebesgue measure. Caratheodory extension theorem.
Sequences of events and random variables, Borel-Cantelli lemma.
Distributions of random variables. Independence of random variables.
Integral of measurable functions - mathematical expectation,.
Moments of random variables, L_p spaces.
Convergence concepts of measurable functions.
Limit theorems for integrals.
Weak and strong laws of large numbers.
Completeness of L_p spaces.
Conditional expectation and conditional distribution of random variables.
Information for Visiting Students
|High Demand Course?
Course Delivery Information
|Academic year 2017/18, Available to all students (SV1)
|Learning and Teaching activities (Further Info)
Lecture Hours 22,
Seminar/Tutorial Hours 5,
Summative Assessment Hours 2,
Programme Level Learning and Teaching Hours 2,
Directed Learning and Independent Learning Hours
|Assessment (Further Info)
|Additional Information (Assessment)
||Coursework 5%, Examination 95%
||Hours & Minutes
|Main Exam Diet S1 (December)||MATH10047 Essentials in Analysis and Probability||2:00|
On completion of this course, the student will be able to:
- To provide the students with the basic notions and results from measure theory and integration, motivating them by fundamental concepts of probability theory.
- To prepare a firm ground for further studies in analysis, in modern probability theory and in their applications.
- To provide students with further experience in constructing proofs for previously unseen results.
|Course organiser||Dr Pieter Blue
Tel: (0131 6)50 5076
|Course secretary||Mrs Alison Fairgrieve
Tel: (0131 6)50 5045