This is a course on the mathematics and applications of infinite random matrices. Students will learn about the tools such as the Free Probability used to characterize infinite random matrices. Our emphasis will be on exploring known connections between these tools (such as the combinatorial aspects of free probability) and discovering new connections (such as between multivariate orthogonal polynomials and free cumulants of free probability).

**Assessment**

This course does not involve any written exams. Students need to answer 5 assignment questions to complete the course, the answers will be in the form of written work in pdf or word. Students can write the answers in their own time. Each answer needs to be 200 words (1 Page). Once the answers are submitted, the tutor will check and assess the work.

**Certification**

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Course Credit: MIT

### Course Curriculum

Histogramming | 00:05:00 | ||

Experiments with the Classical Ensembles | 00:10:00 | ||

The Stieltjes Transform Based Approach | 00:10:00 | ||

Tridiagonal Matrices, Orthogonal Polynomials and the Classical Random Matrix Ensembles | 00:05:00 | ||

Essentials of Finite Random Matrix Theory | 00:30:00 | ||

Numerical Methods in Random Matrices | 00:10:00 | ||

Project Ideas | 00:05:00 | ||

Assessment | |||

Submit Your Assignment | 00:00:00 | ||

Certification | 00:00:00 |

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