There are many excellent sources on the topic of continuous nowhere differentiable functions. Johan Thim’s Master thesis, written under the supervision of Lech Maligranda, is available online, here, but feel free to use any other sources you find relevant.
As a final project for the course, please choose an example of a continuous nowhere differentiable function, either from Thim’s thesis or elsewhere, and write a note on who it is due to and what the function is, together with complete proofs of continuity and nowhere differentiability. Feel free to add additional information you consider relevant for context.
Contact me (by email) as soon as you have chosen the example you will work on, to avoid repetitions; I will add your name and the chosen example to the list below as I hear from you.
Please take this project very seriously (in particular, do not copy details from books or papers, I want to see your own version of the details as you work through the arguments). Feel free to ask for feedback as you work on it; in fact, asking for feedback is a good idea. Do not wait until the last minute. At the end, it would be nice to make at least some of the notes available online, please let me know when you turn it in whether you grant me permission to host your note on this blog.
The project is due Wednesday, December 14, by noon, but feel free (and encouraged) to turn it in earlier.
List of projects:
- Diana Kruse: Bolzano function.
- Jesse Tillotson: Weierstrass function.
- Erron Kearns: Katsuura function.
- David Sanchez: Peano function.
- Shehzad Ahmed: Faber functions.
- Chip Roth: McCarthy function.
- Jeremy Ryder: Schoenberg functions.