Suggesting Rudin to an engineering or a programming student not already mathematically inclined is like offering a text in metallurgy or forest management to an apprentice lumberjack. They will learn nothing and give up in frustration almost immediately. Stewart calculus is plenty, and in some ways overkill.
I suspect it might work quite well in collaborative mathematics. Publish (internally, to your collaborators) when you get a new idea, have a rough sketch of a proof, find a plausible conjecture, think of a good way of presenting something, etc. Eventually, of course, you’d need to clean it all up and get the bugs out, but frequent informal known-buggy “releases” might be an excellent way to get from zero to a high-quality research paper.
That’s an interesting idea, although the discussion was about studying. I assume it can also be applied as a studying technique: Read small chunks of material and solve a lot of problems for feedback.
My point was that you cannot overlook the fundamentals.
Suggesting Rudin to an engineering or a programming student not already mathematically inclined is like offering a text in metallurgy or forest management to an apprentice lumberjack. They will learn nothing and give up in frustration almost immediately. Stewart calculus is plenty, and in some ways overkill.
I tend to jump straight into advanced when I really want to learn.
Maybe it works for you, but it is certainly not a common approach.
I disagree. There is no point in doing anything if you’re not trying to do it right.
Rudin is fundamental, which I find to be the only important thing. He is indeed difficult, but requires no prior knowledge of advanced math.
Maybe I’m wrong, but I think it’s worth trying.
Tell that to Zuckerberg, a big fan of RERO.
Perhaps RERO is the right way to develop software, but it will fail you in math.
I suspect it might work quite well in collaborative mathematics. Publish (internally, to your collaborators) when you get a new idea, have a rough sketch of a proof, find a plausible conjecture, think of a good way of presenting something, etc. Eventually, of course, you’d need to clean it all up and get the bugs out, but frequent informal known-buggy “releases” might be an excellent way to get from zero to a high-quality research paper.
That’s an interesting idea, although the discussion was about studying. I assume it can also be applied as a studying technique: Read small chunks of material and solve a lot of problems for feedback.
My point was that you cannot overlook the fundamentals.