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
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Quaternions - notes in progress
- Gimbal lock - Euler (gimbal lock) Explained - YouTube
- Quaternions - linear algebra - The gimbal lock shows up in my quaternions - MathOverflow
- Gimbal lock intuition: At the North Pole, all directions are South. No East/West anymore.
Math
- Difference between exponentials (e^x) and power functions (x^2, x^3, etc.)
- Arithmetic
- Geometry Proofs
- Functions
- Algebra
- Word problems
- More on Flux/Div/Curl - research in Feynman Lectures
- LaGrange / Vector Calculus
- Total derivative: Total derivative - Wikipedia
- LaPlacian Operator (vector calc)
- Statistics
- Why we use squared error (see this post)
- Normal probability distributions
- More on Bayes Theorem
- Infinite series / Taylor series
- Calculus continuity
- Congruency
- Unit circle
- Jacobian of Matrix
- History of Riemann Integrals (link)
- Asymptotic Notation
- Kernel method: Kernel method - Wikipedia
- Neural networks: A Neural Network in 11 lines of Python (Part 1) - i am trask?
- 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
- Wiener-Khinchin
- Stochastic Calculus
- Bayesian vs. Frequentist interpretations of stats
- P-Value
- Bezier curves (video: http://vimeo.com/106757336)
- CORDIC algorithm
- Group Theory
- Category Theory - my notes
- Information theory
- Godel’s incompleteness theorem
- Euclid’s Division Lemma and the Fundamental Theorem of Arithmetic
- Mathematical Logic & Analysis
- Simplex method. Also, top 10 algorithms of the 20th century (CSDL | IEEE Computer Society)
- Duplation and mediation
- Residue analysis
- Measurement
- Total derivative
- Emmy Noether’s link between symmetries and conservation laws
- Kronecker Product
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 (Noether's theorem - Wikipedia)
Finance:
- The Fed Open Market Operations
- Taxes
- Economics in general, Econometrics
- Bitcoin
- Random walk and why it’s $ \sqrt{n} $ - Also Random Walks
Machine Learning / Signal Processing / AI
- Kalman filter, popular request - my notes
- Principal Component Analysis
- Constrained optimisation, Lagrange Multipliers, Least Squares
- Machine learning (self study: Sanukcode - Machine Learning Self-study Resources)
- Aliasing (signal processing)
- Singular Value Decomposition (SVD)
- AI - https://www.youtube.com/playlist?list=PLUl4u3cNGP63gFHB6xb-kVBiQHYe_4hSi
- Time series
Programming
- Intro to programming. (Excel is a nice env — immediate feedback. Applicable. Undo-able.)
- Math for Game Developers (stack overflow)
- Boolean logic
- Haskell Tutorial: Haskell · How I Start.
- Cryptography
- Robotics - MooC
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”).
