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I've noticed that there are very few Massive Online Open Course (MOOCs) that cover the core college math curriculum, for example

  • Basic integral and differential calculus
  • ODE
  • PDE
  • Linear Algebra
  • Abstract Algebra
  • Probability
  • Statistics
  • Combinatorics
  • Symbolic logic
  • Complex Variables
  • Real Analysis

Anyone care to speculate what are the factors involved that make these bread-and-butter topics so much harder to MOOC-size or less easier to motivate professors to produce than Introduction to Water and Climate or Cybersecurity Fundamentals? I.e. it seems that specialized niche topics receive far more pedagogical energy than basic ones. But I know as a student that I would very much appreciate having the core fundamental topics available in MOOC form.

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I feel that this is heavily driven by the job-market. Topics in academic mathematics do not possess the necessary buzzword status to make MOOCs profitable. Very few job postings ever ask for competency in abstract algebra, real and complex analysis, basic calculus, etc. Many job postings want machine learning, "big data," "artificial intelligence," virtual reality, etc.

When a MOOC advertises its wares, very few people are going to click on an ad that tells them they can learn abstract algebra and category theory. A MOOC teaching Python and "data science" intrigues a number of people who believe that if they can just learn a little Python, all of the sudden Facebook will pay them $150k a year to do data science.

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First, as @DC 541 has already pointed out, the audience for relatively advanced math courses is much smaller than the audience for business and software courses, so why would somebody go to the effort?

Second, while having the lectures available for streaming is very nice, the real meat of any upper division math course is going to be the homework and exam problems. For more computational courses it's possible to set up sophisticated automated graders that essentially run a bunch of unit tests on the submitted code. I don't think grading proofs can be automated in the same way.

That means grading the homework is going to be a bottleneck. If you were to employ an army of TAs to grade a thousand real analysis homework assignments it would cost a fortune. MOOCS have tried to get around this for some subjects using a published rubric and grading by peers. I'm not convinced it works very well, and I've never seen it used for a math course.

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    I've been in advanced MOOCs with peer grading and it actually is fun and works rather well.
    – Lars Ericson
    Commented Dec 18, 2018 at 21:48
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    Also I don't think grad schools for example do a very good job of screening people's math skills (for remedial purposes, not acceptance). I think it would be an interesting and fun challenge to write an automated grading system that "interviewed" a person and posed various problems to automatically assess their competency in a variety of math skills.
    – Lars Ericson
    Commented Dec 18, 2018 at 21:50
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    I happen to work in a quantitative area and we have to do this every other day: assess the math skills of job candidates. If you can do that online automatically, you can teach core advanced math skills online automatically.
    – Lars Ericson
    Commented Dec 18, 2018 at 21:50
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    @LarsEricson: The upper division math courses aren't quantitative courses at all. They are courses fundamentally about logic, not about quantities.
    – Alexander Woo
    Commented Dec 19, 2018 at 0:52
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    @scaaahu see here for example. I don't think KRyan 's suggestion is impossible, just not very useful for helping students who are pretty new to human readable proofs, let alone formal languages for writing proofs.
    – Charles E. Grant
    Commented Dec 19, 2018 at 4:16

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