Theoretical Computer Science Cheat Sheet [pdf]
tug.org
tug.org
And I think a bit more theoretical CS stuff, maybe a few diagrams, would be more helpful than e.g. the Pythagorean theorem or the powers of 2 which shouldn't be a problem to just memorize at that level.
I used to know most of this when I was in uni, including how to derive it when I needed it. Back then this kind of cheat-sheet would not have helped me apply my knowledge. The actual knowledge was very clear in my head from solving problems, or I remembered some key idea used during derivation and from there could work out the rest.
If you need this kind of cheat-sheet you don't understand the concepts deep enough.
Unfortunately most of this knowledge is now 15 years later either very fuzzy or completely lost from my mind. I guess that happens when it is not being refreshed/applied during the career I chose.
This cheat-sheet serves a reminder of how much knowledge I have lost ;)
Def agree on Stirling's though.
Or, to phrase it differently, trigonometry is just a different language for the restriction of the complex exponential to the imaginary axis, and you are remembering the facts in translated form. (Which I agree is much better—it's certainly the only way I can ever remember the thicket of identities! But I'd argue that it's still remembering trigonometry.)
This seems like a math cheat sheet that can be improved removing simple derivations of some formulas.
However it can be handy.
https://link.springer.com/book/10.1007/978-94-010-9314-9
Not just math, but properties of matter, physical constants, thermodynamics and fluids (oblique shocks!), electricity (Semiconductors, Verilog!), solid mechanics, and random stuff like screw threads.
They had us get this in undergrad, all the Engineering students at Oxford know it as HLT.
How can you have Verilog, btw? It is from 1984.
https://www.amazon.com/Handbook-Mathematics-Computational-Sc...
[1] - https://en.wikipedia.org/wiki/Theoretical_computer_science
Do people really write f(x) = O(g(x)) ?
Because that doesn't seem to make sense. It could make sense if we read O as an operator (so f is the upper bound on g, but the definition is the other way around) but saying that a function is equal to an upper bound is just odd, even leaving aside the fact that the definition uses "f(x)", i.e., the application of f, to express the function itself.
Jokes aside, in my college we would write something like:
O( f(n) ) = O(n^2) + O(n)
In the same way that ceiling(1.2) = ceiling(1.9) is symmetric, even if their contents are not equal.
Naively, one would assume that that implies O( f(n) ) - O(n) = O(n^2), which is not correct. However, O( f(n) ) = O(n^2) + O(n) implies O( f(n) ) = O(n^2), which would have been obvious if proper notation had been used.
I prefer O to remain the set of functions usually.
An Eulerian Square of order 10.
2. If you have to deal with a lot of sums involving hypergeometric terms (such as a many series involving binomial coefficients), the book "A=B" by Marko Petkovsek, Herbert Wilf, and Doron Zeilberger might be of interest. It is downloadable from Wilf's site [1].
n ln n + n(ln ln n - 1) < p_n < n ln n + n ln ln n (for n >= 6)As the TeX Showcase master page [2] notes, the author was Steve Seiden, from LSU. He died in a bike accident in 2002.
Not sure how useful this is in practice. Probably not very. Thanks nonetheless