HN user
Very cool! There's definitely some similarity to Ramanujan Sums, though the approach here sort of packages the fizz-buzz divisibility properties into one function. https://en.wikipedia.org/wiki/Ramanujan%27s_sum
Yes you're right it's typically stated as "shaves all those, and those only, who do not..." https://en.wikipedia.org/wiki/Barber_paradox
I can recommend the book Guide to Graph Colouring: Algorithms and Applications by Lewis. It covers techniques including some state of the art methods for getting good but not provably optimal colorings. It discusses in depth local search and hybrid evolutionary algorithms, which tend to be the best performing on academic benchmarks (DIMACS graphs and large random graphs).
"Irresistible Integrals: Symbolics, Analysis and Experiments in the Evaluation of Integrals" - Boros and Moll
"Inside Interesting Integrals" - Nahin
Did you mean this site? It has some pretty great content. https://musicforprogramming.net/one
His article about bit manipulation is very nice, as well. https://catonmat.net/low-level-bit-hacks
Penn State has a bunch of their graduate stats courses online [1]. I worked through some of their time series class [2] and found it to be pretty good quality.
[1] https://online.stat.psu.edu/statprogram/ [2] https://online.stat.psu.edu/statprogram/stat510
And those who want to see trees go to r/marijuanaenthusiasts
This paper was posted earlier with Anonymous authors: https://news.ycombinator.com/item?id=21084748
There are some closely related difficult problems. Consider the fraction a/b, and let r be the length of the repeating fractional part. Then r <= b - 1. Moreover, if r == b - 1, then b is prime. In general, r divides phi(b), where phi is the Euler phi function.
Check out the (official?) site to buy Wheel of Fortune/Jeopardy! tickets for some nostalgia: http://www.wheeljeopardytickets.com/
I've solved 249 of them. I don't remember when I joined, but it must have been about 10 years ago. Solving PE problems was a great way to unwind in grad school (studying math) and learn some cool math in the process. There was a period where I was knocking them out pretty frequently, but I've only had the time to solve 4 problems in the past year.
Reminds me of bash roulette. http://www.bash.org/?96164
I was always fond of "presbyterians" "britneyspears".
Yeah, this proof seems to work. I was thinking of the case where you attack $e^2$ directly, instead of going after both $e$ and $e^{-1}$.
It's simply a habit from LaTeX :-)
This a very terse proof. It is stated "The same method can also be used to prove that e cannot be a root of a second degree equation with rational coefficients", but if I recall correctly, the generalization for the irrationality of $e^2$ isn't entirely straightforward, mainly due to the presence of powers of 2 in the terms of the expansion.
It's a contradiction because there are no integers strictly between 0 and 1.
That's not exactly true. Density arguments similar to this are fairly common in number theory (even if the arguments aren't rigorous). Granted, one has to be careful with arguments like this, but they can often be useful.
Ono is the most self-promoting mathematician I've ever seen. He's done some outstanding work, but he certainly enjoys the spotlight.
Most people currently studying for a Masters or PhD aren't "laymen".
Multi-section most likely means that there are several different sections of the same course running simultaneously. In addition, there are probably different professors teaching these sections.
I can understand part of the argument here - it would be important to maintain consistency among the different sections, so that students who take the class from Professor A learn basically the same material as students who take Professor B. That being said, the material presented in a low-level class like this hasn't changed in a long time, so any book should suffice.