Current Year 13 Mark I

Discrete maths puts me off maths to be honest.

Let me guess, because of the D modules? The person who invented those modules should be taken out and shot. The moment those modules were introduced, the image of computer science has been forever tarnished.

Define for any set $S$ the set $S_{\bot} = S \cup \{ \bot \}$ for some weird and wacky object $\bot \notin S$

We introduce the concept of higher-order functions, which are functions that could take other functions as arguments. For example the higher-order function $f : \left( \mathbb{N} \rightarrow \mathbb{N} \right) \rightarrow \mathbb{N}$ takes in an N->N function as its argument and gives an N as the result. A concrete example:

Now define a function $f : \mathbb{N} \rightarrow \mathbb{N}_{\bot}$ as almost total if $f\left(x\right)=\bot$ for exactly one value of x. An ancient question asked whether there exists an oracle higher-order function $r: \left( \mathbb{N} \rightarrow \mathbb{N}_{\bot} \right) \rightarrow \mathbb{N}$ such that for all possible almost total f, $g\left(f\right) = x \iff f\left(x\right) = \bot$. In other words, the oracle spots for which value the almost total function given to it returns the weird and wacky $\bot$.

Prove that the oracle does not exist.

I really like discrete maths. I also think it's much ability on combinatorics is much more closely connected to raw mathematical intuition than the other subjects in maths. Anyway, here's a nice problem.

Each square of a 1998 by 2002 chess board contains the numbers 1 or 0 such that the total number of squares containing 1 is odd in each row and each column. Prove that the number of white unit squares containing 1 is even.

So how do you do it?

I feel pretty dumb too

Worrying thing I'm not sure if I'm meant to know this stuff. :/

Ask this guy:

You don't need to know anything in the last few pages


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What if I told you I'll be applying for a joint maths course as LSE?

What is an almost total function?

What is an almost total function?

Sounds like something the symbolic maths guy came up with.

I am insulted!

I really like discrete maths. I also think it's ability in combinatorics is much more closely connected to raw mathematical intuition than the other subjects in maths. Anyway, here's a nice problem.

Each square of a 1998 by 2002 chess board contains the numbers 1 or 0 such that the total number of squares containing 1 is odd in each row and each column. Prove that the number of white unit squares containing 1 is even.

It's become the new maths insult

...

I think I should just reveal the answer to my question. I think I started with one that's too abstract for people to understand.



As a CompSci, please tell me you get what the question is about (and you should really get the in-joke too )

I think I should just reveal the answer to my question. I think I started with one that's too abstract for people to understand.



As a CompSci, please tell me you get what the question is about (and you should really get the in-joke too )

I know what the question is about. I don't get the joke however