Master Level Math Course Subject Suggestions

Contents that we need in the Math course (just a list for now, we can talk about priorities afterwards):

Course Abbreviations

Use upper case letters for strong dependency, lower case letters for optional / nice-to-have.

IA = image analysis
CV = computer vision 3D
RM = Robotic Manipulation
AA (to be added by Rolo) = Algorithms (the advanced course, not the introductory one)

Semi-structured list, should evolve based on feedback...

Some applications of linear algebra [IA, CV, RM]
- least squares [IA, CV]
- basic matrix decompositions [IA, CV, RM]
- singular value decomposition [rm]
Multivariate Calculus [IA, CV, RM]
systems of ODEs and difference equations
basic (analytical) geometry [IA, CV, RM]
- parameterised curves on <math>\mathcal{R}^N</math> [IA, CV, RM]
- tangent, curvature, line integrals, reparameterization [IA, CV, RM]
- 3D Coordinate Frames (spatial affine transforms) [CV, RM]
optimization
- Lagrangian [rm]
- numerical methods, convergence, stability, error
  - root finding (Newton-Raphson)
  - interpolation and approximation (B-splines, least squares) [cv]
  - maybe numerical differentiation and integration [IA, CV, rm]
overview of probability theory and statistics [IA, CV]
- distributions: uniform, normal, ... [IA, CV]
- moments and descriptors: mean, variance, median, quartiles, histogram features... [ia, cv]
- hypotheses, tests, design of experiments
- a glimpse of Bayesian inference
signal analysis [IA, CV]
- Fourier [IA, CV]
- Laplace, Z-transform
- linear systems [IA, CV]
- signal models (redundancy / link wrt interpolation and approximation?) [IA, CV]

Things to mention, without going into depth

Inspiration can be drawn from here with complete recorded lectures here.