# Master Level Math Course Subject Suggestions

From ISLAB/CAISR

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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)

## Math Topics

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

- Principal theorem proving techniques
- by complete induction
- by contradiction

## Remarks

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