Articles

I am slowly trying to wrap my head around the deeper parts of Exterior Algebra, which I think is still more important than people give it credit for. So far I’ve got:

• 0. Oriented Areas and the Shoelace Formula
• 1. Matrices and Determinants
• 2. The Inner product
• 3. The Hodge Star
• 4. The Interior Product
• 5. EA as Linearized Set Theory?
• 6. Oriented Projective Geometry
• 7. Simplex Volumes and Boundaries
• 8. All the Exterior Algebra Operations

I’m also playing around with the weird calculus of delta functions, pseudoinverses, and dividing by zero.

• How To Invert Anything
• Delta Function Miscellanea
• Divergences and Delta Functions
• Delta Functions via Inverse Differentials
• The Essence of Lagrange Multipliers
• Notations for Vector Division
• Triple Products and Dual Bases
• Weird Takes on Angles

I’m also down a rabbit hole trying to make sense of fractional permutations and the identity \((-\frac{1}{2})! = \sqrt{\pi}\).

• Investigations on n-Spheres
• Factorials as Multiplicative Integrals
• More on √π

I’m slowly working through my undergraduate math and physics curriculum and trying to “compress” it in a way that makes sense to me. This is because I want to learn QFT to understand how the universe works, but getting through the math hurts my brain. I think the foundations can be made a lot simpler and then it would be easier.

• Some Intuition For Entropy
• Geometric Mean and Standard Deviation
• All About Taylor Series
• The Essence of Complex Analysis
• The Essence of Quantum Mechanics

And every once in a while I write other miscellaneous math-related musings.

• Meditation on Taylor Series
• Infinite Summations and You
• Aphantasia, or how not to do math in your head
• A possible derivation of the Born Rule
• The Case Against Geometric Algebra

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References

Here are some references which, dunno, could be useful to somebody else. These are generally less polished and might just be wrong in places, watch out.

• Bayesian Inference
• A particular calculation for the Pauli Hamiltonian in QM
• A long WIP reference on Fourier transforms
• Some notes on Survival Analysis
• Quaternions
• The various forms of the Triangle Inequality
• Trigonometric Formulas
• Vector and Matrix notations