Instructor

• Prof. Melvin Leok
  Office: APM 5763
  Email: mleok@math.ucsd.edu
  Office Hours: TBA

Target Audience

• This course is relevant to engineers, scientists, and mathematicians with an interest in the applications of topology to data science, dynamical systems, and computational simulations. The application areas addressed will be tailored to the interests of the course participants.

Course Description

• This course will survey computational techniques based on topology, including persistent homology, de Rham cohomology, and Morse theory, with applications to the physical sciences and engineering. Particular attention will be paid to the question of how one can efficiently compute these topological invariants in practical applications.

Announcements

• The resources below are password protected with the user name ma273b, and the password is the first 4 digits of:
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References

• Elementary Applied Topology, Robert Ghrist. [ Electronic Version ]
• Computational Homology, Tomasz Kaczynski, Konstantin Mischaikow, Marian Mrozek. [ Electronic Version ]
• Algebraic Topology, Allen Hatcher. [ Electronic Version ]
• Computational Topology: An Introduction, Herbert Edelsbrunner, John Harer. [ Electronic Version ]

Grading

• Your grade in the course is based on your project and your 20-minute project presentation during the last week of classes.
• The topic of your project should be decided in consultation with the instructor before the end of the first month of class.