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(Please let me know if I am posting this in the right place, or if there are better tags I could use.)

Is there an educational platform like Webassign or OLI (Open Learning Initiative) that you don't need to be in a class to use? Also, are there any that offer upper level and/or grad level math? The first question is more important than the second, but please answer the second if you can.

These platforms give a bunch of multiple choice and/or free response problems. When you are wrong, some of them tell you what is wrong about your answer without giving away the correct answer. They also have multiple versions of the same type of question or set of questions to practice with.

So, if you know of any websight or app (fee required or not) that does any of this where you don't need to be in a college class to do the exercises, can you please let me know?

Although, if you know of one where you only have to enroll in a MOOC (Massive Open Online Course), (like EdX, Coursera, Kahn Academy, Udacity, MITOpenCourseware) can you please let me know?

Edit: In case there is any confusion about what types of classes I'm talking about, the most common class that would indicate the level I'm talking about would be abstract algebra (AKA modern algebra). It doesn't necessarily have to include abstract algebra, but it would be the most likely indicator.

The ambiguous ones (as indicators) would be linear algebra, discrete math, and number theory (as these are commonly taught at community colleges, meaning lower division). But, please share any site that offers these.

There is a long list of (not so ambiguous) upper level (and especially grad level) classes, e.g. modern analysis (AKA real analysis), complex analysis, functional analysis, numerical analysis, numerical linear algebra, differential geometry, algebraic geometry, topology, algebraic topology, differential topology, logic, set theory, combinatorics, graph theory, probability theory, and I'll just include category theory for the sake of wishful thinking

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    $\begingroup$ Wrt the second question: imo, a defining characteristic of upper division courses is the shift away from repetition and multiple choice questions towards proofs and open ended questions. I think your best bet is to just sit down with a good textbook (maybe find a mentor or friends to help you). $\endgroup$
    – user596778
    Nov 11, 2020 at 5:49
  • $\begingroup$ @JetChung Thanks for the input! I am by no means new to upper division courses (as I have taken a bunch of grad level courses in math). I have found that I learn much more quickly this way. DataCamp was the first to get my to realize this with coding, statistics, machine learning, etc. I have also been taking classes that I never did formally, and these websites have have been so much better than the books at refreshing me on stuff that I haven't seen in years. $\endgroup$
    – user3146
    Nov 13, 2020 at 0:40
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    $\begingroup$ For most of those graduate level classes, most students would be at a level where they can more or less check their own proofs. And even if they need a teacher/tutor to check their proofs, certainly no automated system today is capable of it. $\endgroup$
    – Mark S.
    Nov 13, 2020 at 2:05
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    $\begingroup$ Terry Tao does have MC quizzes on some of the classes you're asking about: scherk.pbworks.com/w/page/14864181/FrontPage. $\endgroup$
    – user596778
    Nov 13, 2020 at 18:14
  • $\begingroup$ @MarkS. Thanks for the input. Again, I am by no means a stranger to proof-based classes (upper division and grad). This wouldn't need to involve a proof checker (though those do exist). Even if it involved only the computation problems from proof-based books (like integrating over a Dirac delta generalized function from functional analysis or how many Cayley diagrams are there of the quaternions), that would be a great tool. There are even upper division texts that are not proof-based (like "Visual Group Theory") that could have something to effect of what I'm talking about to accompany it. $\endgroup$
    – user3146
    Nov 17, 2020 at 22:01

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I would reccomend you register for MathXL under self-study.

A wide array of Pearson published Math textbooks have MathXL content.

This includes textbooks for post-secondary level courses up to Differential Equations and Linear Algebra. No higher level courses, unfortunately.

You can register here: https://www.pearsonmylabandmastering.com/northamerica/mathxl/students/get-registered/index.html

You will have to pay for access though. Just like enrolled students need to beyond a trial period.

I personally find MathXL far more comprehensive than WebAssign and am using it for self-study while taking Calculus II.

Another reccomendation is Zybooks online textbooks, if you are looking for an online interactive textbook. However they do not provide a drill evironment like MathXL. Again nothing for higher level courses.

https://www.zybooks.com/

Edit:

I thought you might be interested in reasorces for the basic set of undergraduate math courses (Calculus I-III + Differential Equations and Linear Algebra). If you want similar reasouces beyond that level I have no idea.

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    $\begingroup$ Thanks for the input! I will definitely check these out. If you come across any that include strictly upper division course (please see my edit), then please let me know (with an update or edit or whatever else). $\endgroup$
    – user3146
    Nov 13, 2020 at 0:42
  • $\begingroup$ Sorry I misinterpeted what you meant by Upper level Math courses. Since you said and/or Grad level I assumed by Upper Level you included the basic set of Undergraduate Math courses (Calculus I-III + Linear Algebra & Differential Equations). Beyond those fundementals I don't know if there are any similar reasouces. In his comment Jet Chung gives good reasoning why this might be (more focus on proofs ect.). $\endgroup$
    – Gordon
    Nov 13, 2020 at 1:11

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