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 estÂ