Fall 2013      MATH:7450 (22M:305) Topics in Topology: Scientific and Engineering Applications of Algebraic Topology

Instructor:  Dr. Isabel K. Darcy
Email: idarcybiomath AT gmail.com


While other ideas are welcome (for example, creating your own software or teaching material), most projects will focus on analyzing data. We will use a variety of software to perform topological data analysis including MAPPER, JAVAPLEX, PHOM, and DIONYSUS.

PHOM is an R package for calculating persistent homology and can run on Windows, Mac, and Linux. Both PHOM and R are freeware. Instructions on how to install R can be found in the R manual. More elementary instructions (specific to this course) will be made available. The software R is used in both industry and in undergraduate education due to the mathematical power of this freeware. It can also be linked to C, C++, and Fortran code.

While everyone should be able to run the freeware PHOM, the software MAPPER and JAVAPLEX both require access to matlab. Dionysus is a C++ library for computing persistent homology and cohomology. If you are taking this course for credit, you will have access to both matlab and C++.

If you are collaborating with someone, you should decide as a group at the beginning of the semester how the work will be divided and what you would like to accomplish. I will not require that you finish all (or even most parts), but your collaborators can. The following is one potential project outline, but you may follow any journal format you prefer. Note that while the ideal paper would include all of the following, even published papers do not include all (or even most) of the following. You and your collaborators will need to decide what to include. Writing an article that is almost ready for submitting for publication to a good journal (or developing good software or creating sufficient teaching material or etc.) will be sufficient for earning an A in this class.

NOTE: Even published papers do not include all (or even most) of the following. You and your collaborators will need to decide what to include.

  1. Abstract.
  2. Introduction: Briefly introduce the problem, techniques, and outline the paper. Try to use as few technical terms as possible (or reference section where defined).
  3. Background
  4. Results
  5. Discussion
  6. Conclusion
  7. Acknowledgement
  8. Author contribution
  9. Funding sources and conflicts of interest
  10. References

If you prefer to write software, there are many potential projects. One example (as suggested by Rama Kunapuli) would be to write a Sage interface to call the R subroutines in PHOM as well as the C++ subroutines in Dionysus.