UCL modules
General
- List of modules, they update it each year
- Prerequisite structure, not updated yet but still informative
- Timetable, you have to create your own timetable, not updated ofc
Prerequisites
- Mathematical Methods 2
- MA100 and MT of MA212 except
- Triple integrals
- Line integrals
- Scalar potential
- Independence of path
- Green's Theorem
- Computational Methods 2
- Into to numerical stability
- LU, SVD decomposition
- Interpolation of functions
- Numerical integration
- Analysis 4
- Mostly overlaps with MA203 except
- Weierstrass Approximation Theorem
- Arzela-Ascoli Theorem
- Contraction Mapping Theorem
- Picard-Lindelof Theorem (relation to ODEs)
- Point-set topology bits and pieces
- Algebra 3
- This is basically LT of MA212
- Has a bit more theory on linear forms
- Algebra 4
- Mostly overlaps with MA211 except
- Automorphism groups
- Semi-direct product, group actions
- Finite multiplicative subgroup of a field is cyclic
- Field extensions in more detail
Modules
- Functional Analysis, LT, requires Analysis 4
Algebraic Topology, LT, requires Algebra 3, cancelled for 2020/21- Commutative Algebra, LT, requires Algebra 4
- Differential Geometry, LT, requires Mathematical Methods 2
- Numerical Methods, MT, requires Mathematical Methods 2 and Computational Methods 2
- Galois Theory, MT, requires Algebra 4
- Lie Groups and Lie Algebras, MT, requires Algebra 3
- Measure Theory, MT, requires Analysis 4
Miscellaneous
Here are some bits from my original email to Irini (she said that it's absolutely okay with her and only worries about the timetable clashes).
This one is about Functional Analysis
As far as I understand, methods of functional analysis are heavily used in theoretical machine learning (such as this). This sentiment is also reinforced whenever I talk with academics in this field.
This one about Algebraic Topology
20/06/2020I find the Topological Data Analysis and related ideas very interesting and I would very much like to have a head start to pursue this more in graduate school. The introduction to https://math.hawaii.edu/~yury/papers/probpers.pdf was very informative to me, it seems that persistance homology really is a valid basis for statistical theory. I've also found introduction and conclusion to https://arxiv.org/pdf/1901.02034.pdf very interesting.