Following the meeting yesterday I have added an example of a not continuous function that has continuous partial derivatives 

https://drive.google.com/drive/folders/0BzUXUMab8u_ZRFNnYmxtQ0FDc1E?usp=sharing

also try to answer the following questions:

Consider the regression one slide under the optimization directory

1.  What is the VC dimension of M?   

2.  For a given continuous function construct a neural network that approximate it?

3.  A m*n matrix A  defines a function from R^m to R^n by the multiplication Ax, x in R^n.   What is the Jacobian of A?   

We'll continue today the optimization thread starting with least square for regression - https://drive.google.com/drive/folders/0BzUXUMab8u_ZRFNnYmxtQ0FDc1E

Monte Carlo slide for today's meeting - https://drive.google.com/drive/folders/0BzUXUMab8u_ZU0h3ZEc5Z2VrMm8

link correction

Use this link - https://drive.google.com/drive/folders/0BzUXUMab8u_ZRFFMNmExeno3bWc

Distance, distance between sets and linkage algorithm are introduced here - https://drive.google.com/file/d/0BzUXUMab8u_Zb0lPZ0ZLeDJIaVU/view?usp=sharing