This day was sort of our attempt to introduce the things that would be necessary later in our trainings - namely, series, induction, the binomial theorem, logarithms, and trigonometry! It didn’t go nearly as well as planned; in particular, we did a poor job emphasizing the definitions of trig functions when explaining them, and this led to a lot of misunderstanding by the end that we sort of had to try and clear up. Otherwise, it went OK. Particularly notable was the part where we printed out and played with a slide rule.
This went near-perfectly! We talked about the connection between velocity and slope, and then somewhat formally expressed this. We then used this definition of the derivative to derive and apply a bunch of really useful rules for taking derivatives. We also used the binomial theorem and a proof by induction to prove the power rule in two separate ways in a somewhat crappy competition. Finally, we practiced by finding some derivatives.
We hope to keep solving cool problems and showing interesting things about math in general. By the end of this weekend, we’ll be mostly done with derivatives, and by the end of the trainings in general we’ll have done integrals and Taylor series’ as well, essentially covering (the particularly important parts of) Calculus BC.