Interactive lessons

Math
from first principles

Fundamentals of what I was taught. Not comprehensive and with high probability of error, so take it with a grain of salt. I hope it helps you gather intuition of how abstract numbers are stiched together through functions to explain our universe; from points, lines, planes to space/time.


Foundations

— 7 of 8 complete
(x, y) Point Segment Vector
Foundations — 01
Trigonometry
Trigonometric fundamentals.
2 −1 4 3 0 7 2 × 3 Transform Eigenval
Foundations — 02
Matrix Algebra
Matrix algebra fundamentals.
x y z sqrt(a2+b2) c ||v||
Foundations — 03
Vector Calculus
Vector fundamentals.

Basic Statistics

— 10 lessons
μ Foundations Inference Distributions
Statistics — 10 lessons
Basic Statistics
Foundations, distributions, and inference — from mean and variance through the normal curve, hypothesis testing, and confidence intervals.

Calculus

— 2 courses
dy/dx f(x) Limits Derivatives Applications
Calculus — 10 lessons
Calculus I — Limits & Derivatives
Intuition-first: start with a ball on a track before touching a formula. Limits, the ε-δ definition, differentiation rules, implicit differentiation, curve sketching, optimization, and L'Hôpital's rule.
Integration Techniques Series
Coming soon
Calculus II — Integration & Series
Riemann sums, the Fundamental Theorem, u-substitution, integration by parts, Taylor series, and volumes of revolution — each as a draggable interactive.