Mathematics for Complex Systems

This course is offered through ComplexityExplorer — you can add it to your Accredible profile to organize your learning, find others learning the same thing and to showcase evidence of your learning on your CV with Accredible's export features.

Course Date: 29 September 2014 to 30 June 2015 (9 weeks)

Price: free

Course Summary

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.   

Estimated Workload: 4-8 hours per week


When does the course start? September 29, 2014

When does it end? June 30, 2015

Who is the instructor? This course has several instructors; see the course description page.

How much does it cost? Nothing. The course is completely free.

How is the course funded? The course is funded by the Santa Fe Institute (SFI) through a grant from the John Templeton Foundation, and by donations from users.   In order to support future courses, we will be asking for small, voluntary donations to cover the costs of developing and providing those courses.

Who is the intended audience and what are the prerequisites? This course is intended for people who want to gain familiarity with, or review, mathematical topics important for understanding complex systems.   Each of the units has its own pre-requisites:  some are for people with no more than high-school algebra, and some are for more advanced students. 

How does the course work? Each unit consists of a series of short videos, with each video corresponding to subtopics of the unit's main topic. The course website leads you through the videos in order, allowing you to skip or repeat videos as you desire. You can watch these videos at your own pace and in any order you desire; once posted, they will remain available throughout the course.  The videos are interspersed with short exercises and quizzes, designed to test your understanding of the material covered in the previous video.  At the end of each units there is a test (graded automatically).

How long does the course last? Through June 30, 2015.   As each unit is relatively independent, you may want to cover only those units most relevant to your particular interests, and you can do so in any order.  During this first offering of the course, the units are being developed as the course proceeds and will be added one by one during the course period.  The videos and other course material will stay online after the course ends. 

What about exercises and quizzes? Many videos are followed by a short exercises or quiz that you can do online and that is graded automatically. These exercises and quizzes won’t count towards your final grade; their purpose is to allow you to try out simulations, to see how well you have understood the material in the video, and to see what you might need to review.

What about the tests? Each unit will be followed by a test.  You will take the tests online, and they will be graded automatically.  You may use any of the course materials while taking the test, but we request that you do not consult other people or the Web for answers to test questions. 

How is the course graded? Your score for each unit is the score you received on the end-of-unit test.    This course does not have a total "course grade". 

Will I receive a certificate for completing this course?  No, this course does not provide a certificate.

Is there a required textbook? No textbook is required.  The lectures will be complemented by numerous suggested readings that will be listed in the Supplementary Materials page on the course site. 

Do I have to enroll to take the course?   Yes, you need to enroll in order to access any of the course materials.  However, enrollment is easy, quick, and free!

How do I enroll? Go to, then to Online Courses, and click the “Enroll” button next to this course. You will be guided through the short enrollment process.

Can I enroll after the course begins? Yes, you may enroll at any time during the course period. 

How much time does the course require?  This depends entirely on which units you work on; different units will have different levels of difficulty. 

What are the rules on collaboration with other people? You are free, and encouraged, to discuss anything with anyone!  The course website hosts an online forum for students to discuss the course material. However, we ask that the end-of-unit tests be taken entirely on your own, without collaboration with others. Of course, we are relying on the honor system for our students to abide by these rules.

Can I get university credit for this course? No, not at this time. It is possible that in the future we may be able to partner with colleges and universities so as to offer our courses for credit, but there is currently no mechanism for this.

What is this Forum you've been talking about? The course website hosts a forum in which course participants can post questions, answers, and otherwise discuss the course materials. Questions posted to this forum will be answered by the instructors, teaching assistants, and/or other students.

Will there be any other kind of social networking for participants? We hope to help organize local "Meetups" via our course Forum for course participants who would like to meet in person.

How do I get the videos to play at a faster rate (e.g., 2x)?  Our videos are streamed through YouTube.  You can opt in on YouTube for their html5 player, which allows you to speed up or slow down videos.  To opt in, go to

Can I download the videos directly, rather than watching them via YouTube?  Yes, just click on the "Download" button that appears in the Summary view of the Lectures page.   We will also make all the videos for each unit available as zip files on the Supplementary Materials page. 

Will the videos and other course material be available after the course ends?  Yes.  After the course ends it will be on our "Archived Courses" list, under "Online Courses".  You will be able to access all parts of the course except for the discussion forum.  You also won't be able to submit any tests when the course is not in session. 

What if I have more questions? Please address any other questions you have to


  1. Ordinary Differential Equations (David Feldman and Liz Bradley)
  2. Vector and Matrix Algebra
  3. Probability, Combinatorics, and Statistical Distributions
  4. Bayesian Inference and Bayesian Networks (Melanie Mitchell)
  5. Introduction to Information Theory
  6. Introduction to Stochastic Processes
  7. Phase Transitions
  8. Maximum Entropy Methods (Simon DeDeo)
  9. Renormalization Methods (Simon DeDeo)

Course Workload

4-8 hours per week

Review course:

Please sign in to review this course.

Similar Courses

{{ }} {{ }}


{{course.start_date | date:'MMM d'}} — {{ course.end_date | date:'MMM d'}}   ({{ course.time_until_course_starts }} ,   length: {{ course.length_in_weeks }} weeks) Self-paced — no deadlines    
${{ course.price }} p/mfree


Course Activity & Community

Be the first Accredible user to join this course!

uploaded {{ feed_item.model.caption || feed_item.model.url || feed_item.model.file_file_name }} for the course {{ }} — {{ feed_item.time_ago }}

{{ }} {{ comment.text | truncate: (comment.length || comment_display_length) }}   read more hide

{{ comment.time_ago }}

started the course {{ }} — {{ feed_item.time_ago }}
followed {{ }} — {{ feed_item.time_ago }}
followed thier friend {{ }} — {{ feed_item.time_ago }}
{{ feed_item.model.text }} (on the course {{ }}) — {{ feed_item.time_ago }}

{{ }} {{ comment.text | truncate: (comment.length || comment_display_length) }}   read more hide

{{ comment.time_ago }}