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.
E39 Language models and sequence modelling
Advanced pathE: Proposed extensionsplannedabout 100 h (planning estimate)
Planned: syllabus only, no teaching material yet. Nothing on this page can be studied; it describes what the course would cover.
Named in: Advanced applied mathematics pathway
Why this course
Needed to read any article on large language models with understanding.
Prerequisites
Concept-level units
Units follow the syllabus order, as a recommended sequence rather than a gate.
- Language as a probability distribution; perplexity and entropy
- n-grams to neural language models
- Pretraining objectives
- Decoding: greedy, beam, sampling, temperature
- Fine-tuning, instruction tuning and preference learning
- In-context learning
- Evaluation and benchmark contamination
- Limits: hallucination and calibration
Assessable outcome
Compute perplexity and sampling probabilities for a small model and explain what a benchmark number does and does not show.
Assessment design
- topic exercises
- mixed problem sets
- unseen proof or derivation problems
- cumulative examination
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.
- Jurafsky and Martin · Speech and Language Processing (free)
- Brown et al · Language models are few-shot learners (paper)
- Ouyang et al · Training language models to follow instructions with human feedback (paper)
Content record
- Version
- 0.0.0
- Review
- no review of any kind
- Provenance
- PROPOSED by the assistant on 4 Nov 2026 so that a person with a mathematics degree can read AI articles fluently; not in the owner's brief; APPROVED by the owner on 4 Nov 2026 as an elective; still needs a curriculum reviewer
- Known issues
- Approved as an elective on 4 Nov 2026; syllabus only, no lessons, candidate resources unverified, needs a curriculum reviewer.
- Type
- course
Bridges and laboratories
No bridge or laboratory is attached to this course yet.
You and this course
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