Topic Requests


#1

A collection of frequent topic requests. I research and take notes, looking for Aha! moments. Feel free to browse or join the discussion.

Topics In Progress


Math

  • Difference between exponentials (e^x) and power functions (x^2, x^3, etc.)
  • Arithmetic
  • Geometry Proofs
  • Functions
  • Algebra
  • Word problems
  • Derivatives of Trig Functions
  • More on Flux/Div/Curl - research in Feynman Lectures
  • LaGrange / Vector Calculus
  • Total derivative: http://en.wikipedia.org/wiki/Total_derivative
  • LaPlacian Operator (vector calc)
  • Statistics
  • Why we use squared error (see this post)
  • Normal probability distributions
  • More on Bayes Theorem
  • Infinite series / Taylor series
  • Congruency
  • Unit circle
  • Jacobian of Matrix
  • History of Riemann Integrals (link)
  • Asymptotic Notation
  • Kernel method: https://en.wikipedia.org/wiki/Kernel_method
  • Neural networks: http://iamtrask.github.io/2015/07/12/basic-python-network/?
  • Vectors: what do they mean [generalized numbers]
  • Time value of money [have decay happening in front of us? Put a drop down that gets bigger?]
  • Monte Carlo Simulation
  • Quadratic formula
  • Mathematical modeling / converting word problems to math
  • Fundamental Theorem of Algebra
  • Taxicab geometry (link). Learn to specify what a circle, ellipse, parabola, hyperbola are in terms of properties (vs. equations!). You can just write out the equations that give you the property you need. Usually just based on the distance formula.
  • Roll a disk along the ground and the curve a point on the rim follows is a cycloid. Invert it, and it is the curve of fastest descent under gravity (brachistochrone)
  • Trig substitutions for calculus integrals

Other Math (Need To Learn)

Physics

  • Electricity & Magnetism
  • Maxwell’s Equations
  • Quantum Mechanics
  • Wave equations
  • Fluid mechanics / Navier-Stokes
  • Langrangian and Hamiltonian mechanics
  • Tensors
  • Antennas and beamforming - an antenna “scoops” the signal (and noise) from a volume of air.
  • Beer’s Law dealing with concentration chemistry
  • General & Special Relativity
  • Heisenberg’s uncertainty principle
  • Energy (http://en.wikipedia.org/wiki/Noether's_theorem)

Finance:

Machine Learning / Signal Processing / AI

Programming

Puzzles That Teach Math

  • Pirate problem - game theory
  • Black hat / white hat - information theory
  • Making a fair coin out of a non-fair one. Or a 1/3 coin. Etc. - probability
  • Crypto puzzles and work out ways to share (securely) using it.

Concepts

  • Yin/Yang in science: Newtons 3rd law, Lenz’s law, particle/antiparticle pair existence, Pauli exclusion principle, wave/particle duality
    basic rule of storms: run until the imbalance that created them is balanced
    integration, both infinitely large and infinitely small are needed for it to make sense
  • Tau vs. Pi
  • Adjective order in English (implicit understanding of the rules vs. explicit application)
  • Gotcha: How x, x^2, x^3 are all 1-dimensional in math. Not “square units”, we’re just saying 9 = x^2, so x = 3 (1d) and x^2 = 9 (also 1d).
  • Scenarios where getting to zero is winning (factoring). Neutral means you’ve won (you’re “on target”).

#6

#7

in the trigonometry article i couldn’t find anything about the relation of sin^2θ+cos^2θ=1
i missed it? if not would be nice to be part of trig part2.


#8

Thanks, that one comes from the Pythagorean Theorem (mentioned briefly in the article). There’s a diagram here: http://betterexplained.com/wp-content/uploads/trig/trig-identities.png which might help. I’d like to do a trig part 2 with the other identities as well.


#9

#10

This proof of the Fundamental Theorem of Algebra reminded me of Better Explained, maybe you will find it useful if you decide to do an article on the subject:

(the proof starts at 1:06:34)