Perceptron Learning Algorithm

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I attempted a class on deep learning last spring and this problem scared me away from it. I ended up doing a mathematical foundations of machine learning instead. Now I am considering another attempt at deep learning next quarter but this still haunts me.

I have read some PLA proofs and they make sense to me, but this version still confuses me. Can anyone help me understand what's going on here?

>inb4 no help on homework
It's still winter break and I am not in any classes like the rest of you, I'm just trying to understand some maths