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 <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


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