# Master Level Math Course Subject Suggestions

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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 $\mathcal{R}^N$ [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