You can check the courses taught on coursera:

  - Algorithms part I
  - Algorithms, design and analysis. Part I
  - Computer Architecture
  - Calculus : single variable
  - pre-calculus
  - introduction to logic
  - introduction to computer networks

How does one teach himself to write such a thing?

How To Write a Computer Emulator: http://fms.komkon.org/EMUL8/HOWTO.html

Study of the techniques for emulation programming: http://www.scribd.com/doc/94546/Study-of-the-techniques-for-...

This makes for a good start: http://imrannazar.com/GameBoy-Emulation-in-JavaScript:-The-C...