What subjects do I need to study before I am capable of understanding the mathematical problem being solved in Bitcoin mining?

What subjects do I need to study before I am capable of understanding the mathematical problem being solved in Bitcoin mining?

I am a post graduate electrical engineering student, specialising in digital electronics. I would like to foray into ASICs for bitcoin mining. But first I need to understand the mathematics of Bitcoin mining. What subjects do I need to study to get a good idea of what my ASIC has to tackle?

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