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I am looking for resources to self study graduate-level maths which give similar experience as studying in a university. That usually involves

  • Lectures
  • Tutorial sessions
  • Homework assignments and their solutions

Because often the aims of a textbook is to accompany a course rather than teach from scratch, I am specifically looking for recorded courses and not for textbooks. I am also not looking for series of video lectures, as I find lectures without exercises only useful as a supplement to a full course. To give a few popular examples, there are some full courses at MIT open courseware - when you search for a course, you have the option to select that it should contain homework problems, video lectures, exams etc. There is also NPTEL, where most courses contain lectures and solved exercises.

Now for the not so well-known examples (probably because of the language), there are many full courses in Russian, from MSU and MIPT. Although they are not exactly "organized" as courses, all the materials for most courses are available.

So my question is, are there any other places where I can look for materials if I want to study a course properly, i.e. with lectures and problems to practice (either tutorial sessions or solved homework assignments)? I am looking mainly for graduate-level maths courses. I don't want to specify any particular topic, because it seems at this level learning resources are rather scarce. I would also like to point out that any language is welcome (I speak quite a few languages, and besides, I think automatic translation now works sufficiently well).

Edit: After a couple of comments, I want to further specify, that I am really looking for graduate maths courses, not calculus, simple probability and other introductory, "best-selling" courses offered by MOOCs. I am also not looking for textbooks, again, because textbooks, no matter how good, offer a different experience from a course as taught in university. And also, many people have the opinion that textbook exercises should have no solutions, unlike usual courses, where problem solving is discussed during tutorial sessions.

Rodion Zaytsev
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  • You can take a look at Edx! – Athanasios Paraskevopoulos Dec 28 '22 at 14:44
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    "Because often the aims of a textbook is to accompany a course rather than teach from scratch" : that has not been my experience. My experience has been that the challenge is to find the right textbook for you, on a particular area of Math. My experience has also been that about $80%$ of the learning takes place in the exercises, so you always want a book with many, many exercises. ...see next comment – user2661923 Dec 28 '22 at 14:49
  • Well I think Edx, Coursera and other such MOOCs are more about "buzzword" topics to attract more customers. I haven't really seen any advanced/fundamental math courses there. Perhaps I should have been more specific about that in my question - feel free to edit. – Rodion Zaytsev Dec 28 '22 at 14:49
  • MathSE is a great forum for filling the gap, on the exercises that you have trouble with. You have to remember to follow this protocol. ...see my next comment – user2661923 Dec 28 '22 at 14:50
  • @user2661923, agree, sometimes I can find appropriate textbooks, but I think it gets rarer as you shift towards more advanced stuff. I think for advanced courses there are rarely introductory textbooks which can replace a course on the subject. – Rodion Zaytsev Dec 28 '22 at 14:51
  • You can search MathSE for a particular subject, by searching under the tags reference-request &/or book-recommendation. Then, (for example), you can examine the Amazon reviews for a specific book. – user2661923 Dec 28 '22 at 14:51
  • Stanford has a few archived courses, though probably not at the level you want... – Andrew Dec 28 '22 at 14:51
  • Certainly more challenging to find the right textbook for you, on advanced stuff. However, judging by all of the reference-request and book-recommendation postings that I have seen on MathSE, that would still be my first try. – user2661923 Dec 28 '22 at 14:53
  • @user2661923 sure, but (rather unsurprisingly), I think there is a bias of recommending famous books, which may not be most appropriate. Besides quite often when people ask such a question they are told to just go through unsolved exercises and ask for hints here, which is way more pain than a typical university course. – Rodion Zaytsev Dec 28 '22 at 14:56
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    I have found that sometimes, for more advanced topics, if you know of a professor and you go to his her website, he-she sometimes puts his-her course on their website. So, you won't find the course or topic on edx, coursera but it's on the internet. Let me see if I can find some names for you. Also, I'm not a mathematician so I don't know if the ones associated with the name are advanced enough for you ? I'm more into applied math topics. – mark leeds Dec 28 '22 at 17:23
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    some names are goodman (courant ), george lowther, nicolas privault, mirand holmes cerfon, peter ireland and matt kerr. if you look these people up and then go to their website, you'll find some pretty interesting topics. – mark leeds Dec 28 '22 at 17:26
  • Yours is a curious viewpoint to me, as I've almost always found textbooks to be far more comprehensive than the courses they were used for. The only exceptions I can think of are highly specialized research topics (e.g. randomly selected examples from my posted answers: Example 1 and Example 2 and Example 3 and Example 4 and Example 5). (continued) – Dave L. Renfro Dec 28 '22 at 18:07
  • Indeed, it's difficult for me to think of a math topic suitable to base a graduate course on in which there is not a text or research monograph that could be used. I haven't given it much thought, so maybe other examples will occur to me, but off-hand the only thing I can think of that currently is lacking a suitable text or monograph is what I discuss in this answer. This book was partially intended for this purpose, but it hasn't (yet?) been completely finished. – Dave L. Renfro Dec 28 '22 at 18:14
  • @markleeds, thank you very much, this is indeed a very helpful suggestion! I think you make a very good point - it is exactly what I'm looking for, if a person posts their course and all the materials on a website, it does give a "classroom" experience! Of course it is difficult to find the names of these people, so I really appreciate those people you listed! – Rodion Zaytsev Dec 28 '22 at 19:36
  • @DaveL.Renfro, it is pretty much along the lines of the reason why I am specifically looking for "university"-type courses. Textbooks have indeed the goal of being comprehensive, whereas often the goal of a course is to introduce you to ideas and most essential topics, as there isn't time to cover everything. And I find that for me to get the most important results, I feel that I need to avoid being overwhelmed by a comprehensive textbook, which I find more suitable for a second review of the subject. – Rodion Zaytsev Dec 28 '22 at 19:41
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    @Rodion Zavtsev: I'm glad that you like the suggestion. Those names might not work for you but the way I find names is sort of by luck. Say I was googling for "Solving Backwards Difference Equations". Then, a lot of things will come up. But one might be a say a 10 page handout for a class. In that case, the name of the prof who made the handout might be on the handout or, better than that, the handout might be from the class itself !!!!. Good luck with your endeavor. – mark leeds Dec 29 '22 at 00:58
  • @markleeds, if you put your suggestion and method as an answer, I will gladly upvote it! (though I'm not sure it should be an accepted answer, as it seems that for my question there's no such thing). – Rodion Zaytsev Dec 29 '22 at 05:45
  • okay. thanks. I'll do that now. it's appreciated. – mark leeds Dec 30 '22 at 06:31

1 Answers1

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I have found that sometimes, for more advanced topics, if you know of a professor and you go to his her website, he-she sometimes puts his-her course on their website. So, you won't find the course or topic on edx, coursera but it's on the internet. Let me see if I can find some names for you. Also, I'm not a mathematician so I don't know if the ones associated with the name are advanced enough for you ? I'm more into applied math topics.

Some names are goodman (courant ), george lowther, nicolas privault, mirand holmes cerfon, peter ireland and matt kerr. if you look these people up and then go to the respective website, you'll find some pretty interesting topics.

Those names might not work for you but the way I find names is sort of by luck. Say I was googling for "Solving Backwards Difference Equations". Then, a lot of things will come up. But one might be a say a 10 page handout for a class. In that case, the name of the prof who made the handout might be on the handout or, better than that, the handout might be from the class itself !!!!. Good luck with your endeavor.

mark leeds
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