Recently I’ve been doing a lot of relatively advanced mathematics. Since most kids are off from school, I don’t have much work. In many ways this is a blessing; while I love tutoring, it has become exhausting in recent weeks. I’ve needed a break for a while now, and those last few days were becoming […]
A Breath of Fresh Air
In an attempt to make sincere progress on Rudin’s Principles of Mathematical Analysis this coming spring, I’ve decided to give myself a challenge; over the next 10 or so weeks I’ll attempt to answer and write up solutions to every problem in Rosenlicht’s book Introduction to Analysis. To do this, I’ll hopefully complete a chapter […]
Set Theory in October
The leaves are changing. Fog settles in the morning and lifts as day breaks, allowing sunlight to scatter across gold and orange leaves. The Hudson Valley is so beautiful this time of year. It makes me happy to be alive, to be thinking and working and experiencing all of this. Days blur into one another. […]
Derivative of the Natural Number Power Function
Yesterday I saw a video exploring fractional derivatives. That is, derivatives not of fractional exponents, but derivatives of functions midway between the first and second derivative, second and third, and so on. This topic got me thinking about how one goes about finding the nth derivative of a power function, which led me to write […]
Tommy Benjamin 