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.

Talks at undergraduate-level seminars.

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

A list of interesting questions at undergraduate level

  1. 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?!

  2. 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!)

  3. 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 $e$?

  4. Is the sum of the inverses of the prime numbers convergent? 1/2+1/3+1/5+1/7+1/11+1/13+ ...

  5. Why won't applying the diagonal argument also prove that the rational numbers are also uncountable?! (or will it?)