Tuesday, June 2, 2020

Maths to Learn

In the previous post I discussed the five categories of knowledge. These posts will go through different subjects that I'm interested in, starting with Mathematics.

  • Theory of computation - key ideas of computation. It's interesting how a mathematical idea about computation grew into physical computers.
    • Turing and Godel's theorems and how they relate to each other. Is there a way one can exclude the halting problem and build a machine that can determine if almost everything will halt?
    • How high level code actually executes on a machine.
  • Review of basic calculus
    • Intuitive understanding of derivatives and integrals.
    • Optimization and related-rates problems
    • Applications to physics
  • Probability & statistics - Ultimately all knowledge comes down to probabilities. Statistics are useful for interpreting studies and experiments and everything else.
    • Review fundamentals of probability
    • Bayesian probability and statistics
    • Pascal's triangle, the normal distribution, the central limit theorem
    • Applying statistics to real-world examples
    • Tools for stats (e.g Google sheets, R, Python)
    • Stats for machine learning
  • Using Mathematica for real world math problems

Besides for calculus, it's interesting how little these topics are taught in schools. Many students don't know basic topics like fractions well and schools should focus on teaching them better. Other students can learn more advanced topics but it does not need to be limited to a narrow curriculum of trigonometry and geometry and specific parts of algebra. (See also my post from 2011.)

Carthago delenda est 

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