These are problems from first year intro mathematics courses. For a lot of students these are mostly review from high school.
To me, a “university-level” problem is more like this:
Let W be an infinite-dimensional normed linear space over the real numbers. Use the Baire Category Theorem to show that if W is not countable-dimensional then W is not complete.
The above is a typical problem from the 3rd year real analysis course I took in the fall.
Man some hn posts bring the cringiest comments; please do tell us which school has functional analysis as a "typical" topic for juniors taking real analysis. Even if you're getting a second helping of real analysis by then, you're probably looking at Lebesgue integration on R and such, rather than general topological spaces.
I'll never understand why some people try to flex on an anonymous forum.
This is from PMATH 351 at University of Waterloo. Every pure math student takes the course in 3rd year. Lebesgue integration isn't covered until 4th year, though it is not restricted to R at that point.
I'm sorry you think my comment was intended to be a "flex". I was trying to make a point about university mathematics which is this: at university level students should be going beyond solving simple computational problems. Synthesizing a proof requires a higher level of understanding than the application of a standard problem-solving technique. See Bloom's taxonomy [1] for details.
To me, a “university-level” problem is more like this:
Let W be an infinite-dimensional normed linear space over the real numbers. Use the Baire Category Theorem to show that if W is not countable-dimensional then W is not complete.
The above is a typical problem from the 3rd year real analysis course I took in the fall.