1

I know that there already has been a thread here on Mathematics StackExchange roughly on the same topic: Best Sets of Lecture Notes and Articles (among others), but even there, I have not found the right sets of notes that work for me. In particular, I am looking for some adequate online maths notes which are written in English and touch upon ANY of the following topics (and not necessarily ALL):

  • Analysis (real, complex, functional, metric/normed vector/topological spaces and measure theory)
  • Algebra (abstract algebra, linear algebra and number theory)
  • Geometry (differential geometry of curves and surfaces and topology)

In particular, I am looking for some online notes which meet the following criteria:

  • Formal writing style: In particular, written in a formal Definition-Example-Result-Proof-Remark style, without any long verbose paragraphs in between, and definitely NOT written in the informal first-person conversational style.
  • Rigorous reasoning: In particular, does not skip too many steps in proofs or calculations. Also, clear and unambiguous notation is used.
  • Lively visual presentation: In particular, exposes the material in a visually distinct manner that is not hard on the eye (e.g. with reasonable spacing, coloured boxes and clear diagrams).

I have found many excellent sets of online math notes written in French which meet the above criteria right on the mark and I am satisfied with them, but as of yet I have found none written in English. It's fine if they don't meet the above criteria perfectly, but only as long as they do so adequately. If for reference, you are interested in the French online math notes that I have found and am satisfied with, then the following links may be useful:

I request your help.

  • I think asking for Algebra notes and Geometry notes and Analysis notes all in one question won't be well received here. Users of this site will suggest this should be three separate questions. Also I'll bet there is already a question somewhere on this site asking for recommended notes for at least one of these subjects. Probably all of them. – Mike Pierce Apr 12 '20 at 00:30
  • The sources you give are pretty good. It seems pretty hard to recommend a site of which you are not familiar. Are the given sources good but you want more or is there a problem with the sources? – John Douma Apr 12 '20 at 00:38
  • @MikePierce ; Thank you for your word of caution. Although it seems I have been misunderstood. I have re-edited my comment accordingly. I hope it helps. –  Apr 12 '20 at 00:57
  • @JohnDouma ; The links I have given are examples of the ones I am satisfied with, as indicated. In my question, I was wondering if there were any similar notes written in English and which touch upon ANY of the topics I mentioned. Every little bit helps, and I will be satisfied with anything I find adequate. –  Apr 12 '20 at 00:59
  • I have looked everywhere, even on other Math S.E. threads, but I found nothing of the type I am looking for (as indicated in my question). –  Apr 12 '20 at 01:02
  • without any long verbose paragraphs in between --- Interestingly, these are the aspects I was mostly interested in when I was in school, although of course at that time it was books in physical libraries. There were shelves and shelves of books on every conceivable topic, all of which mostly had the same main definitions and theorems and (to a lesser extent) examples, so it was often the case that the last thing I was looking for was yet another such book. Instead, I was often interested in explanations of the "big picture", historical comments, interesting tangential detours, etc. – Dave L. Renfro Apr 12 '20 at 18:11
  • @DaveL.Renfro ; I fully understand that you may prefer that style and I have nothing against you preferring it. I completely respect your viewpoint. But as far as I am concerned, that style has brought me nothing but a terrible academic experience and has consistently impeded my learning of mathematics, and to no end. As such, I have no interest in it whatsoever. –  Apr 13 '20 at 18:54

0 Answers0