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Greengoose's maths notes
2026-04-09 under construction today...
This is a reference I'm putting together as part of my notes for my maths degree. It doesn't need an introduction right now because there isn't anything here yet.
I ought to redo this contents page soon.
It's possible I'll structure this as a set of "courses", each with (probably insufficient) information for you to learn a certain topic.
Style & structure of these notes
Each page is about either a specific mathematical object, or a theorem.
For a mathematical object, the sections tend to include:
- Definition - what the thing is, and any relevant notation.
- Construction - a formal construction (rare).
- Criterion - equivalent necessary & sufficient criteria that are useful for proving that you have an example of the thing.
- Properties - sometimes split into "basic" and "interesting".
- Types - classifying various kinds of this object.
- Examples - common examples. This section tends to be badly used; I should also add examples of proofs in "Criterion"... Maybe this should be moved to a <details> under the definition.
- Related theorems
- See also - related concepts; also disambiguation (maybe disambiguation should go at the top?).
For a theorem, the sections tend to include:
- Statement - the conditions and result of the theorem.
- Proof - a proof of the theorem
- Corollaries - immediate consequences of the theorem
- Examples
- See also
This site could probably benefit from some CSS, but I can't be bothered with that at the moment - it's perfectly usable as it is.
Pages by subject
- miscellaneous - set theory and other essentials
- algebra - group theory, linear algebra, rings & modules
- topology
- geometry
All pages, alphabetically
