Math 574 -- Introduction to Computational Topology (Spring 2012)
Topology studies how a shape or object is connected. In the past few years, there has been an increased interest in the development and use of topological methods for solving various problems in science and engineering. This new line of study is called Computational Topology or Applied Algebraic Topology. Computational topology combines topological results with efficient computational tools to analyze data and solve problems in many fields -- computer graphics and image analysis, sensor networks, clustering, robotics, genetics, protein biochemistry, geography, and many more.
This course will present an introductory, self-contained overview of computational topology. There are no prerequisites, but mathematical sophistication at the senior undergraduate level and some familiarity with the use of computer packages such as MATLAB are expected. We will cover basic concepts from a number of areas of mathematics, such as abstract algebra, algebraic topology, and optimization. We will also look at algorithms and data structures, and efficient software for analyzing the topology of point sets and shapes, often posing questions in an optimization framework.
We will not follow any particular book, and will rely mostly on handouts and class notes. Material from several recent (and not-so recent) papers will also be covered. Since the main goal of this course is to expose the audience to this interdisciplinary research area, evaluation will be done through homeworks (around five assignments of moderate length) and a course project. No exams will be given.
Topics covered, and lecture
Video streams of lectures (from AMS)
|Tuesday, Jan 10:||The email id for this course is wsucomptopo AT gMaiL d0t com|
|Office hours will be held via Skype at the ID: wsucomptopo.|
|Wednesday, Jan 18:||Due to the snow closure, the class will NOT meet on Thursday, Jan 19.|
|Monday, Feb 6:||Zomorodian's book is available online now through the WSU Libraries (as an E-book).|
|Friday, Feb 24:||Edelsbrunner and Harer is available in Owen Library Reference (under Math 574).|
Project-- Due on Thursday, May 3.
Tutorial from Mathworks page Another
guide to MATLAB from UBC CS.
TetGen and TetView
Files for the pyramid example: node face
M-Edit (another visualization tool - Windows executable available)
Applied and Computational Topology @ Stanford
Lecture notes by Robert Ghrist
Intro to Computational Topology by Afra Zomorodian (@ Dartmouth)