Mathematics
From 'what a proof is' to deriving a gradient and a learning algorithm. Every idea implemented in code, so none of it stays abstract.
Logic & the Nature of Proof
0/5What truth and implication mean, and the three proof techniques everything else rests on.
Truth, implication, and why 'convincing' isn't enough
AND, OR, NOT, implies — the skeleton of all reasoning
'for all' and 'there exists', the reach of a claim
The two workhorse proof techniques
Assume the opposite and break it — √2 is irrational
Sets, Functions & Induction
0/5The containers and mappings under all of math, and proving infinitely many things at once.
The container under everything — union, intersection, complement
Mappings: injective, surjective, bijective
Counting the uncountable — Cantor's diagonal
Proving infinitely many statements at once
Why a recursive function is a proof
Number Theory & Combinatorics
0/5gcd, modular arithmetic, primes, and how to count without listing.
gcd — the oldest algorithm still in use
Clock math — the heart of crypto and hashing
The atoms of the integers
How many ways — counting without listing
Two counting ideas with enormous reach
Linear Algebra I — Vectors & Space
0/5A vector is a list of numbers that is also an arrow. Span, independence, basis.
A list of numbers that is also an arrow in space
Addition, scaling, and the number that measures alignment
All the geometry hiding in the dot product
What a set of vectors can and cannot reach
The coordinate system of a space
Linear Algebra II — Matrices as Transformations
0/5A matrix is a function that moves space. Multiplication, inverse, determinant.
Linear maps that move all of space at once
Composing transformations — and why order matters
Undoing a transformation, when you can
The volume-scaling factor — and when space collapses
Solving systems, by hand and in code
Linear Algebra III — Eigen & Decomposition
0/5The directions a transform doesn't rotate, and the SVD behind all of data.
The directions a transform only stretches
Seeing a matrix in its own natural coordinates
The geometry of right angles
The master factorization behind all of data
Build a tiny vector/matrix library from nothing
Calculus I — Change & the Derivative
0/5Limits, the derivative from first principles, and the chain rule backprop is built on.
What 'approaching' means, rigorously
Instantaneous rate of change, from first principles
Power, product, quotient — the mechanics
The single rule backpropagation is built on
Numerical vs analytic — checking one against the other
Calculus II — Gradients & Optimization
0/5Partial derivatives, the gradient, and gradient descent — the engine of learning.
Slope in many directions at once
The direction of steepest ascent
Following the slope downhill to a minimum
Derivatives of vectors, and curvature
Accumulation, area, and expectation
Probability — Reasoning Under Uncertainty
0/5Events, Bayes, random variables, and why the bell curve is everywhere.
The grammar of chance
Updating belief in the face of evidence
Discrete and continuous, and what a PDF is
The center and the spread of randomness
Why the bell curve shows up everywhere
Statistics & the Bridge to AI
0/5Estimation, maximum likelihood, and deriving your first learning algorithm.
Inferring the whole from a part
The principle underneath fitting any model
What 'significant' actually claims
The first learning algorithm, derived
Least squares as maximum likelihood — derive it, then code it