Worksheets written for middle/high schoolers (i.e. stuff I wrote for math club when I ran it, c.a. late 2016/early 2017):
- An introduction to sum notation with practice problems.
- A worksheet on deriving the cubic formula. The answers are below in the "papers" section.
- An introduction to mathematical induction with practice problems.
- Problems relating to king chickens (introducing graph theory in a fun way).
- Further explorations into king chickens.
Papers understandable by high schoolers (i.e. mostly stuff I wrote in high school):
- Pre-Calc level: Intuitive construction of dot and cross products, and determinants
- AP Calc BC level: An introduction to the gamma function and further explorations. It's a rather dense article (after all it's from two years of work, building from the gamma function, to the reflection and multiplication formulas to Stirling's formula to Bertrand's postulate). But I'm confident that a strong AP Calc student will be able to work through it. The arguments are certainly not rigorous by any means, but I think an AP Calc student will understand them and be convinced by them.
- Algebra II/Precalculus level: Derivation of the cubic formula.
- Linear Algebra level(?): Using linear algebra to understand a rudimentary version of Google search.
- Linear Algebra level(?): Different applications of linear algebra (a theoretical one of how to "exponentiate" matrices and a practical one of finding an explicit formula for the Fibonacci numbers).
Papers from college but perhaps understandable by an ambitious high schooler:
- Calc III level: Thoughts/worksheet(?) on different definitions of differentiability in higher dimensions.
- Calc III++ level (real analysis?): An introduction to measure theory (a project inspired by probability theory). Again, pretty dense and difficult. But this was one of my favorites to create; I learned a lot by writing it and I hope it will serve as a good guide to anybody learning real analysis in the future.
Email danrui@uw.edu if you have ideas about stuff I could put here!