Pioneering Proofs
In this channel, I derive math formulas that are used in science and engineering. Enjoy!!
About Me:
Hi, my name is J.T. and I like math. I have a bachelor’s degree from UD and Master’s degree from UPenn, both in bioengineering. I'm also working toward a PhD. I’m the type of person who needs to understand everything on a deep level, especially math. That’s why I created this channel; It’s a documentation of my progress in learning how the universe operates. But I also want to share my discoveries with others to inspire the innovative pioneering spirit, thus contributing to a more rapid accumulation of knowledge and expedited progression of technology and understanding.
Why is this channel called "Pioneering Proofs?"
Because through these videos, I want to train our thought processes so that they are optimized for discovery (the ideal mental state of a pioneer); I want to inspire this way of thinking in others.
Derivation of Fritz John Conditions
Proof of Farka's Lemma
Proof of Separating Hyperplane Theorem
Proof of First Order Condition of Convexity
Proof of Monotonicity of Secant Slopes
Proof of Definition of Convexity
Road to Fritz John Conditions: Introduction
Derivation of the Multivariable Euler-Lagrange Equation of Higher-Order Terms
General Euler-Lagrange Equation for Optimization of Functionals
Introduction to Calculus of Variations
Machine Learning Regression, But with Error Bars
Deriving a Formula for Reflection of Light off a Surface in 2D Space
Can you Solve this Lever Engineering Puzzle?
Why I CAN'T Derive Curvature
I made Taylor and Fourier Ebooks! (Link in comments)
Neural Network Series Part 2: NN Mathematical Structure
Neural Network Series Part 1: The Jacobian Chain Rule
Linear Regression
Information, Entropy, Cross-Entropy, and KL Divergence
Derivation of Principle Components (PCA)
Derivation of the Lagrangian for Constrained Optimization Problems
The Intuition Behind Hypothesis Testing
Phasors: How and Why They Work
Directional Derivative Derivation (DDD)
I Made a 2D Circle in 3D Space
Writing a Python Program that Computes the Multinomial Theorem
An Algebraic Derivation of Lagrange Multipliers
The Bernoulli Distribution
Part 1: My MATLAB Particle-Spring Simulation
The Hypergeometric Distribution