This course covers several mathematical techniques that are frequently used in complex systems science. The techniques are covered in independent units, taught by different instructors. Each unit has its own prerequisites. Note that this course is meant to introduce students to various important techniques and to provide illustrations of their application in complex systems. A given unit is not meant to offer complete coverage of its topic or substitute for an entire course on that topic.
The units included during this offering of the course are:
(1) Introduction to differential equations (David Feldman)
(2) Ordinary differential equations (ODEs) and numerical ODE solvers (Liz Bradley)
(3) Functions and iteration (David Feldman)
(4) Maximum entropy methods (Simon DeDeo)
(5) Random Walks (Sid Redner)
(6) Vector and matrix algebra (Anthony Rhodes)
(7) Introduction to information theory (Seth Lloyd)
(8) Game Theory I - Static Games (Justin Grana)
(9) Game Theory II - Dynamic Games (Justin Grana)
(10) Introduction to Renormalization (Simon DeDeo)
(11) Fundamentals of Machine Learning (Artemy Kolchinsky)
(12) Introduction to Computation Theory (Josh Grochow)
(13) Fundamentals of NetLogo (Bill Rand)
Other units to be developed over time.