What are some basic skills for calculus? Find my list here.
What are some basic skills for calculus? Find my list here.
Stackexchange is a great place to ask questions and practice writing math. See my profile here.
Would you like me to give a similar talk at your institution online? Email me!
· The Coarea Inequality, undergraduate math seminar, Pitt, (virtual) Oct 6, 2020. Slides Zoom Talk
· Hausdorff measures, the ultimate collection of measuring cups: Undergraduate Math Seminar, University of Pittsburgh, Fall 2019
· Derivatives in Multivariable Calculus: Undergraduate Math Seminar, University of Pittsburgh, Spring 2019
· The Beautiful Math Behind Calculus 3: Undergraduate Math Seminar, University of Pittsburgh, Spring 2017
· Mathematics Gives Us a Language: Undergraduate Math Seminar, University of Pittsburgh, Spring 2015
Express every rational number in binary system. (Forcing strict monotonicity we can assume every number has a unique expression as a string of 0's and 1's.) Why wouldn't applying the Cantor's diagonal argument end up proving that the set of rational numbers is also uncountable?!
The sets (0,1] and (0,1) has the same cardinality, seen by simple set theory lemmas, so there exists a bijective map between them. Construct an explicit example of such a bijection. (Anecdote: As an undergraduate I did find one and it was one of those aha moments that changed the way I thought about infinity!)
Let $f:R \to R$ be a differentiable at every point. If $f'(0) >0$, then is it guaranteed that the function is increasing in some open neighborhood $(-e,e)$ of $0$ for some positive $e$?
Is the sum of the inverses of the prime numbers convergent? 1/2+1/3+1/5+1/7+1/11+1/13+ ...
Why won't applying the diagonal argument also prove that the rational numbers are also uncountable?! (or will it?)