View source for 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)

== 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 [http://ocw.mit.edu/courses/mathematics/18-085-computational-science-and-engineering-i-fall-2008/syllabus/ here] with complete recorded lectures [http://ocw.mit.edu/courses/mathematics/18-085-computational-science-and-engineering-i-fall-2008/video-lectures/  here].