How does the process of collaboration in math work ? Do mathematicians like to share their problems ? Can I do this by e-mail ? How to ask mathematicians if they want to collaborate in a math project ? I'm still learning more advanced math but these are questions I had in mind and didn't know...
I'd like a list of math papers that are useful not for the content but for teaching how to do math, that is, math research papers that teach how to come up with new mathematical ideas.
A person told me that doing math research independently (alone) is very difficult, because the findings of someone who is not interacting with the experts in a given field of study will most likely not be "novel", that is, they would have already been published before. Is that true ? Can the...
Most published math papers are answers to open questions posed by the authors of the papers, right? So why is this problem that the paper responds to is never explicit in the text by the authors? Would not that be an important thing since it would save time for other mathematicians not to waste...
Why is it difficult to find really challenging vector analysis problems (problems about Green's, Stokes' and Gauss' theorems in a Calculus 3 course) in Calculus books? Most of the problems are elementary, at least that's the impression I have(I could be wrong). Is it really difficult to...
Is it possible to learn to prove limits by the formal definition without doing a course of real analysis? I'm not talking about just following the model that the Calculus books give, what I want is to understand the why of all the steps in formally proving the limit, to understand the why to use...
How to know if a surface is closed ? Surfaces such as x^(2/3) + y^(2/3) + z^2 = 1 or x^6 + y^6 + z^6 = 1. Is there a way to know if these surfaces are closed ( without the help of a computer program) ? Is there a general way to know if a surface is closed ? What about curves ? How to know if a...
I don't know if there's anyone here from China, but I'll make this question the same way. I'd like to know if the Chinese books of Mathematics and Physics at undergraduate and graduate level are good (that is, if these books contain many challenging problems)?
I have a question about mathematics at the research level. How difficult is it to formulate new open problems in mathematics? For example, can a master's student create such problems? And a doctoral student? Or are only experienced mathematicians able to do this? Does this depend on the research...
I know this can be a silly question but it's a curiosity of mine and I have no idea what the answer is, so I'll ask anyway. The question is: How many open problems and conjectures are there in Mathematics currently ? I'm sure nobody knows the exact number but an approximation would be nice...
Is it true that some problems from Putnam and IMC have connections to Mathematics at the research level and it's necessary to use techniques at that level to solve them ? If so, could someone give me examples of Real Analysis problems of this type ?
But I think that sometimes it's necessary to prove a new theorem or lemma in order to solve a problem or exercise. Is this true ? I think this occurs mainly in math competitions.
Is it possible to deduce theorems besides those in the books of mathematics (I'm talking about consecrated subjects such as Calculus and Real Analysis, for example)? Again, my question is not at the research level. My question is at the undergraduate level. And if so, why are the Calculus books...