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
 Cross Product (Done) 4/15

Quaternions  notes in progress
 Gimbal lock  https://www.youtube.com/watch?v=zc8b2Jo7mno
 Quaternions  http://mathoverflow.net/questions/95902/thegimballockshowsupinmyquaternions
 Gimbal lock intuition: At the North Pole, all directions are South. No East/West anymore.
 How to learn trigonometry intuitively (part 2)
 Trig identities  done 11/4
 Hyperbolic trig  quick notes
 LaPlace Transform  notes
 Convolution  draft article
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/basicpythonnetwork/?
 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)
 Topology
 Wavelet transforms
 WienerKhinchin
 Stochastic Calculus
 Bayesian vs. Frequentist interpretations of stats
 PValue
 Bezier curves (video: http://vimeo.com/106757336)
 CORDIC algorithm
 Group Theory
 Category Theory  my notes
 Information theory
 Godelâ€™s incompleteness theorem
 Euclidâ€™s Division Lemma and the Fundamental Theorem of Arithmetic
 Mathematical Logic & Analysis
 Simplex method. Also, top 10 algorithms of the 20th century (http://www.computer.org/csdl/mags/cs/2000/01/c1022.html)
 Duplation and mediation
 Residue analysis
 Measurement
 Total derivative
 Emmy Noetherâ€™s link between symmetries and conservation laws
 Kronecker Product
Physics
 Electricity & Magnetism
 Maxwellâ€™s Equations
 Quantum Mechanics
 Wave equations
 Fluid mechanics / NavierStokes
 Langrangian and Hamiltonian mechanics
 Tensors
 Antennas and beamforming  an antenna â€śscoopsâ€ť the signal (and noise) from a volume of air.
 Beerâ€™s Law dealing with concentration chemistry
 General & Special Relativity
 Heisenbergâ€™s uncertainty principle
 Energy (http://en.wikipedia.org/wiki/Noether's_theorem)
Finance:
 The Fed Open Market Operations
 Taxes
 Economics in general, Econometrics
 Bitcoin
 Random walk and why itâ€™s $ \sqrt{n} $  Also http://www.mit.edu/~kardar/teaching/projects/chemotaxis(AndreaSchmidt)/random.htm
Machine Learning / Signal Processing / AI
 Kalman filter, popular request  my notes
 Principal Component Analysis
 Constrained optimisation, Lagrange Multipliers, Least Squares
 Machine learning (self study: http://ragle.sanukcode.net/articles/machinelearningselfstudyresources/)
 Aliasing (signal processing)
 Singular Value Decomposition (SVD)
 AI  https://www.youtube.com/playlist?list=PLUl4u3cNGP63gFHB6xbkVBiQHYe_4hSi
 Time series
Programming
 Intro to programming. (Excel is a nice env â€” immediate feedback. Applicable. Undoable.)
 Math for Game Developers (stack overflow)
 Boolean logic
 Haskell Tutorial: http://howistart.org/posts/haskell/1
 Cryptography
 Robotics  MooC
Puzzles That Teach Math
 Pirate problem  game theory
 Black hat / white hat  information theory
 Making a fair coin out of a nonfair 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, Lenzâ€™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 1dimensional in math. Not â€śsquare unitsâ€ť, weâ€™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 youâ€™ve won (youâ€™re â€śon targetâ€ť).