Cong Zhou
Teaching:
Unified Calculus & Analytic Geometry IV (Math 264). pdf file of syllabus. Lecture notes: [Charpter 15 part 1], [Charpter 15 part 2], [Charpter 16], [Charpter 17]
Elementary Differential Equations (Math 353). pdf file of syllabus. Lecture notes: [Chapter 1 & 2], [Chapter 4], [Chapter 7]
Free probability theory is an advanced field of mathematics. It lies between several branches of mathematics and may not be directly mentioned in the most common classifications of mathematical fields. If one were to categorize free probability theory, it could be considered an advanced interdisciplinary field among probability theory, mathematical statistics, abstract algebra (especially operator algebra), and mathematical physics. This field is a relatively new branch of mathematics, primarily used to study the properties of random variables defined in non-commutative probability spaces, especially when these random variables satisfy the so-called 'freeness' condition. The applications of free probability theory are wide-ranging, including but not limited to quantum physics, large-scale random matrix theory, and signal processing.