Self Paced

Mathematics for Complex Systems (Complexity Explorer)

This tutorial 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 tutorial 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 tutorial includes units designed for beginning math students (those who have completed at least one year of high-school algebra but not calculus) and for more advanced math students (see individual units for prerequisites). These units are listed below, along with the tentative dates on which they will be available. If you are enrolled in this tutorial, you will receive notification by email whenever a new unit is available. Students can complete the entire tutorial or are free to follow any of the units independently.

Units for beginning math students (prerequisite: at least one year of high-school algebra):

- Functions and iteration (David Feldman: Excerpts from Dave's Dynamical Systems course)

- Introduction to differential equations (David Feldman: Excerpts from Dave's Dynamical Systems course)

- Vector and matrix algebra (Anthony Rhodes, April, 2015)

- Introduction to logarithms (Melanie Mitchell; 2015)

- Basic probability, combinatorics, and statistical distributions (TBD)

- Introduction to information theory (Jim Crutchfield; 2015)

Units for more advanced math students:

- Ordinary differential equations (Liz Bradley: Excerpts from Liz's Nonlinear Dynamics course; Prerequisite: Calculus)

- Maximum entropy methods (Simon DeDeo; Prerequisite: Calculus, Basic Probability; April, 2015)

- Bayesian inference and Bayesian networks (Melanie Mitchell; Prerequisite: Basic probability; 2015)

- Introduction to stochastic processes (Prerequisites: Calculus, basic probability; 2015 )

- Critical phenomena (Prerequisite: Calculus, basic probability; 2015)

- Renormalization methods (Prerequisite: Calculus; 2015)