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This idea is a complete rip off an article that appeared in Wired a little while ago and it got me thinking what would my list for Computer Science look like? Plus I thought it might be a fun post and unlike the Wired list this one goes to eleven. So here they are in no particular order:
The Binomial Coefficient equation generates Pascal’s Triangle and gives you the coefficients for the Binomial Theorem these ideas are often attributed to Pascal but in fact they have been known in part for over a millennia.
As I mentioned that this list is no particular order and I don’t wish to play favorites but if there is one equation here that you should really consider learning and committing to memory this is it. It is central to Combinitorics which has connections to many areas of math, I guess I should qualify that if you are serious about computer science and math related programming topics then you should be able to recite and apply it from memory, even when you are drunk, sleep deprived or being held at gun point. Ok that might be a bit much but you get the idea. If you are programmer and you haven’t learned it, or need a refresher, I have a post that relates it to theJava Collections API.
Ok so that’s like four "equations" for DeMorgan’s Laws, one can’t help but to struck by the similarity between the two sets and this is not a coincidence these two sets of formulas are essentially the same thing, they are special cases of complemented distributive lattices† which means technically it’s really just two formulas:
In this case the ∨ symbol means lattice join operation and the ∧ symbol is the lattice meetoperation and the dash with the right downward mark means lattice complementation, I used this to differentiate from the tilde for Boolean complementation. Also...