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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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