This homework set is due Wednesday, February 1st, at the beginning of lecture, but feel free to turn it in earlier if possible.
Hilbert is one of the mathematicians I admire the most. I believe I first learned about him while in High School, through “Higher Geometry” by N.V. Efimov. My copy of Reid’s “Hilbert” is one of the first books I bought when I arrived in the States (in 1997).
Here is a link to the reprint in the Bulletin of the AMS of Mathematical Problems.
I would love to have a poster sized copy of the picture above. Springer sold them years ago, but now they seem impossible to find.
Ars Magna, “The Great Art”, by Gerolamo Cardano.
Here is Jeremy Ryder’s project from last term, on the Schoenberg functions. Here we have a space-filling continuous map whose coordinate functions and are nowhere differentiable.
The proof that are continuous uses the usual strategy, as the functions are given by a series to which Weierstrass -test applies.
The proof that is space filling is nice and short. The original argument can be downloaded here. A nice graph of the first few stages of the infinite fractal-like process that leads to the graph of can be seen in page 49 of Thim’s master thesis.