Computational/Numerical linear algebra summer program [closed]

Feel free to close this question if it is inappropriate for the site. I am asking this since questions like these are accepted in math stack-exchange and math overflow.

I am a grad student and will be teaching a two week (12 hours) summer class on computational/numerical linear algebra for sophomores/juniors. Two questions popped up when I began preparing the material.

1. What are all the important things in computational/numerical linear algebra which should be taught in one week?
2. How to make the one week program productive? For instance, what sort of assignments should be provided.

For the first question, I came up with a quick and small list of material which I believe should be covered.

1. Different concepts related to a matrix like norm, row-space, column-space, null-space, rank, condition number etc.
2. Basic operations on matrices and their associated costs.
3. Solving linear systems.
4. Matrix decompositions ($LU$, $QR$, SVD,$XLX^{-1}$).
5. Least square, least norm and similar min/max problems.
6. Iterative techniques.
7. Using linear algebra packages (LAPACK, Eigen)
8. Some applications like solving differential equations, Fast Fourier Transform, Image processing etc.

The second question is a bit tricky for me and in some sense I am lost what I need to do, keeping in mind the class is for just $2$ weeks and is for students who will be in principle encountering the subject for the first time. I have attended summer schools in the past and some of them have been really good because of the kind of assignments that were given. I indeed learnt a lot from the summer schools because of good set of assignments.

1. Some simple theoretical questions based on norms, different associated spaces of the matrix etc.
2. MATLAB exercise to perform various decompositions using the built-in commands and solve systems using these decompositions and the time taken by different algorithms as a function of system size.
3. Assignments which highlight the difference in timing for dense and sparse matrix operations.
4. An application in image processing using MATLAB.
5. An assignment in C++ where they get to use the different C++ libraries.

I would appreciate a honest feedback on the above two fronts, especially on how to make the two week class productive. Also, if I have forgotten to take into account any other thing, please feel free to say so.

-
 Marvis, welcome to SciComp! The difficulty we've had in the past with a question like yours is that answers are going to be almost entirely opinion-based. These answers aren't well-suited to the Stack Exchange format. To see what I mean, see What core skills should every computational scientist have?, which generated a lot of discussion (especially in comments). – Geoff Oxberry♦ Jun 27 '12 at 17:47

closed as not constructive by Geoff Oxberry♦Jun 27 '12 at 17:48

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