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.
G02 Functional analysis
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
Banach and Hilbert spaces and operators; the graduate analysis core.
Prerequisites
- Required
- G01 Measure & integration, B08 Linear algebra II: abstract structure, B13 Real analysis II: metric & multivariable analysis
- Recommended
- none
- Can be taken at the same time
- none
- Everything required, transitively (12 courses)
- B01, B02, B03, B04, B06, B08, B09, B13, B15, F01, F02, G01
- Courses that require this one
- P11, P13, A06, A15
Concept-level units
Units follow the syllabus order, as a recommended sequence rather than a gate.
- Normed and Banach spaces
- Hilbert spaces
- Bounded operators
- Duality
- Core functional-analysis theorems
- Spectral and compact-operator examples
Assessable outcome
Prove and apply operator and completeness results in suitable function spaces.
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.
- Kreyszig
- MIT functional analysis
- Lax later
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
- Elementary Banach/Hilbert topics can precede measure theory; an Lp-based sequence needs G01 first. Reviewer to refine.
- Type
- course
Bridges and laboratories
- Bridge: Elementary Banach/Hilbert before measure theory planned Elementary parts can precede G01; Lp-based functional analysis needs integration first. Reviewer decision.
You and this course
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