[throwawaymath]

The University of Illinois at Urbana-Champaign offers a wide variety of mathematics courses online for self-paced study[1]. The courses range from 100 - 400 level. 100 - 300 level courses confer undergraduate course credit at UIUC, whereas 400 level courses are eligible for graduate credit. (Note that you are not enrolled as a degree-seeking student in a mathematics program, you're simply taking courses online).

You have 16 weeks from the date of registration to complete each course. The courses themselves have weekly homework, two midterms and a final. You must find an eligible proctor to complete the midterms and final in person, but otherwise you need not go anywhere. Each course costs about $1500 - 2000. The lectures for each unit are video recordings of lectures in the corresponding course onsite at UIUC. There is also a certificate you can earn, but it's primarily focused on completion of lower-level courses.[2] Your homeworks are graded (with feedback) by a lecturer or math TA at the university. There are also remote office hours available.

UIUC is probably the highest caliber mathematics program which offers something like this. It's generally difficult to find a top ~20 math university willing to support online, self-paced study for credit. The ones which do offer such a system are usually very expensive[3] or predominantly focus on lower-level courses like a simple calculus sequence.

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1. https://netmath.illinois.edu

2. https://netmath.illinois.edu/academics/certificate-program

3. https://cvn.columbia.edu/program/columbia-university-applied...