Under construction. This area is a framework being built: most courses have no teaching material yet, and things may change or break. Private self-study. Not an official programme and not recognised by any ministry or school. No qualification, mark or document is issued, and “years 1 to 3” and “advanced” are names of study paths only.
G03 Graduate probability
Advanced pathG: Advanced sharedplannedabout 160 h (planning estimate)
Draft lectures and exercises are available for this course. They were written by AI and checked by a second AI; no person has reviewed them yet. Use them as a study aid, not as an authority.
Named in: Advanced pure mathematics pathway; Advanced applied mathematics pathway
Why this course
Probability with measure theory: conditional expectation, convergence and martingales.
Prerequisites
Concept-level units
Units follow the syllabus order, as a recommended sequence rather than a gate.
- Probability spaces
- Conditional expectation
- Modes of convergence
- Laws of large numbers
- Martingales
- Weak convergence and central limits
Assessable outcome
Reason about random variables using measure-theoretic probability.
Assessment design
- deeper problem sets
- reconstruction of an unfamiliar argument
- advanced source reading
- cumulative examination or substantial project
cumulative; uses spaced retrieval
Resources
Every title here is candidate, unverified unless marked verified. Titles were suggested while planning. Nobody has checked that they exist, what they cost or how they are licensed.
- Durrett · Probability: Theory and Examples
Content record
- Version
- 0.0.0
- Review
- no review of any kind
- Provenance
- catalogue imported from the owner brief of 29 Oct 2026; no teaching content authored
- Known issues
- none recorded
- Type
- course
Bridges and laboratories
No bridge or laboratory is attached to this course yet.
You and this course
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