The CA for Math 229 is Daishi Kiyohara.
If you find a mistake, omission, etc., please let me know by e-mail.
The orange ball marks our current location in the course.
For an explanation of the background pattern, skip ahead to the end of the page.
These online lecture notes use MathJax. You might have to change browser for the formulas to look right. Safari seems to work.
September 2 and 9:
plan.pdf and
intro.pdf:
administrivia, AI matters, and “philosophy”/examples;
The dictum “Much have I learned from my teachers, more from my colleagues, and most of all from my students” is from Tractate Taanit 7a of the Babylonian Talmud, quoting Rabbi Hanina.
[also: which if any of 8675309, 6060842, 6654321, and 7184981043 is prime, and how surprised might you be if one of them is prime, or half of a prime pair? Thanks to Jordan Ellenberg and David Farmer for noting the prime and prime pair respectively. (Turns out that I had already seen the twin-prime observation in the mouse-over text for xkcd comic #1047: Approximations.)]
[See also:
OEIS Sequence A006880
${} = \pi(10^n)$ for $0 \leq n \leq 22$.
The sequence $\{p_n\} = 2, 3, 5, 7, 11, \ldots$ itself is
#40.
The subsequence I put on the board is
$$
2, 3, 5, 7, 11, 13, 17, 19, \ldots, 113, 127, \ldots,
8675309, 8675311, \ldots, 2^{136279841} - 1, \ldots .]
$$
The CA for Math 229 is Daishi Kiyohara.
So what’s with the whorls in the background pattern? They’re a visual illustration of an exponential sum, that is, $\sum_{n=1}^N \exp (i f(n))$. Even simple functions $f$ can give rise to interesting behavior and/or important open problems as we vary N. What function $f$ produced the background for this page? See here for more information.