Request for “Tests” for the MIRI Research Guide

Lately I’ve been looking into learning the material in the MIRI research guide. After some time, I noticed that my biggest trepidation about diving in was the nagging question of, “But how will I know if I actually learned the stuff?”

Once I realized that was the thing holding me back, it became easier to think about solutions. Some of the topics correspond with courses that are common in universities, so I can pilfer final exams from their sites (woot to MIT open courseware). But for other topics I wanted to see what people here thought.

In whatever domain you specialize in, what are some examples of problems or questions that one can only answer by having a solid understanding of a huge swath of said domain? Below I’ve listed everything from the MIRI research guide that I could perceive as a distinct category.

(ex. If you were learning about Digital Systems and Computer Architecture, my test would be “In systemVerilog, simulate a basic 16-bit processor that can be programmed using a RISC assembly language of your design.”)

(edit: I know that “huge swaths” is pretty vague, and suggestions don’t have to be things that you think certify/​prove that you get a topic. While a “comprehensive test” would be nice, problems/​prompts like what Qiaochu commented are exactly what I’m looking for)

  1. Set theory

  2. Probability

  3. Probabilistic Inference

  4. Statistics

  5. Machine Learning

  6. Solomonoff Induction

  7. Naturalized Induction

  8. VNM Decision Theory

  9. Functional Decision Theory

  10. Logical Uncertainty

  11. First Order Logic

  12. Vingean Reflection

  13. Corrigibility

  14. Linear Algebra

  15. Topology

  16. Category Theory

  17. Type Theory