August 24, 2010

Lecture notes finished

Filed under: computer vision/machine vision/AI,education,mathematics,site,updates — Peter Saveliev @ 11:20 pm

It took me the whole summer but the lecture notes for Vector calculus are now online. They have been fully transcribed, edited, illustration added. There is certainly a lot of work left to make them more presentable, readable, etc. That will continue along with linking, internally and to the rest of the site. As a part of this work I’ll try to add something that I feel is missing – the discrete angle (image analysis, data analysis, etc).

The total number of articles has reached 446, with 1208 illustrations. There is some duplicate content but not a lot. The point is that one can take this material, rearrange it in a number of ways, and create various courses depending on the goals, or the audience, etc.

Still to come are the two courses I am teaching this fall: Calculus 1 and Differential Geometry. They will be transcribed some time next winter. More courses will continue to appear as a part of what I call my “fantasy math” project.

August 15, 2010

The topology of data and 3D image analysis: projects

Filed under: computer vision/machine vision/AI,education,mathematics,news — Peter Saveliev @ 1:58 pm

The summer is over and it’s time to report on some of the events. In the beginning of summer I made page for 3 potential NSF REU projects. These are the two that I ended up supervising:

The topic of the REU was computational science so the general goal was to do something new computationally while learning some math. So, we used and modified some existing software. The main idea of the first project is to use jPlex to compute dimensions of datasets while the main idea of the second was to use CHomP to compute the homology classes of 3D images along with their persistence. Ironically, jPlex computes persistent homology but lacks relative homology which had to be implemented. On the other hand, CHomP has relative homology but the persistence had to be implemented. These issues were mostly resolved. Unfortunately, in either case there wasn’t enough time to test the programs with real-life data.

To be continued…