I'm looking for some ideas for longer and more research type problems to do in real analysis. The coursework we get is not very demanding and it would be nice to have some longer and harder projects to do on the side. At the moment i have background in basic real analysis, (limits and sequences, differentiation and continuity, integration, sequences of functions and series), linear algebra, and basic set theory and construction and the axioms of real/rational/natural numbers, but as i'm studying and intend to study more all the time, any suggestions about more advanced topics are also highly appreciated and would give something to work towards and do later on. Something that would require a bit more time and effort and looking into, something a bit more researchier than proving specific limits and differentiation rules.
2026-03-26 11:05:37.1774523137
Any good undergrad analysis research problems?
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How about the problem of finding a function which is differentiable, but whose derivative is not continuous?
You could look it up, and there's a standard example ($f(x)=\begin{cases}x^2\sin(1/x),x\gt0\\0,x\le0\end{cases}$, I believe).
But in addition to studying it, maybe you could look for other examples.