Online Courses open to all [closed]

There are various online courses happening around the world. I feel that it will be beneficial to have a website just like https://mathseminars.org/ and http://dermenjian.com/seminars/, but for courses happening online that are open to all. But even if such a website is not made, I am requesting for people to make a list of courses (ongoing, upcoming, or finished and archived) which will be/are accessible to anyone with a good internet connection (e.g, available on Youtube, etc.).

For example, Ravi Vakil is taking a (pseudo-)course titled Algebraic Geometry In the time of Covid, Richard Borcherds is posting videos on YouTube on Algebraic Geometry, Commutative algebra.

Solution 1:

(I edited the question to allow archived courses, as all ongoing/upcoming courses that are recorded will eventually stop running. Hopefully this is OK)

The Mathematical Sciences Research Institute currently has no graduate summer school courses running, but has some courses archived. I didn't check them all, but here are some examples:

Gaps between Primes and Analytic Number Theory

These courses will give students a full overview of the results of Zhang and Maynard on gaps between primes, and will provide them will a clear understanding of the tools involved. This will make accessible a significant part of modern analytic number theory. The lecturers will also make sure to include, within their course, examples and discussions going further than is strictly required to understand the proofs of Zhang and Maynard, e.g., in the direction of automorphic forms and the Riemann Hypothesis over finite fields.

Incompressible Fluid Flows at High Reynolds Number

The purpose of this two week workshop is to introduce graduate students to state-of-the-art methods and results in mathematical fluid dynamics. In the first week, we will discuss the mathematical foundations and modern analysis aspects of the Navier-Stokes and Euler equations. In the second week, we will run two courses concurrently on the topics of inviscid limits and hydrodynamic stability. Specifically, one course will focus on boundary layers in high Reynolds number flows and the Prandtl equations while the other will focus on mixing and connections to turbulence. Through the lectures and associated problem sessions, the students will learn about a number of new analysis tools and principles of fluid mechanics that are not always taught in a graduate school curriculum.

Recent topics on well-posedness and stability of incompressible fluid and related topics

The purpose of the workshop is to introduce graduate students to fundamental results on the Navier-Stokes and the Euler equations, with special emphasis on the solvability of its initial value problem with rough initial data as well as the large time behavior of a solution. These topics have long research history. However, recent studies clarify the problems from a broad point of view, not only from analysis but also from detailed studies of orbit of the flow.

Polynomial Method

In the past eight years, a number of longstanding open problems in combinatorics were resolved using a new set of algebraic techniques. In this summer school, we will discuss these new techniques as well as some exciting recent developments.

These four courses have recorded lectures and the first even has exercises; the second has exercises and notes. There are other courses on the site but not all of them have videos: e.g. Commutative Algebra and its Interaction with Algebraic Geometry does not.

Solution 2:

How about MIT OpenCourseWare - Mathematics?

The list there includes undergraduate and graduate courses on various mathematical topics, both pure and applied.