 # Topic Requests

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

## 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
• 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
• 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

## 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)

## 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”).
4 Likes

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.

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.

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)