Numbers, proof, algebra, topology, probability, geometry, calculus, and mathematical thought. Browse curated, sandboxed HTML presentation decks in Mathematics, each with crawlable summaries, slide outlines, and topic metadata.
This collection gathers sandboxed HTML presentation decks for readers who want structured, visual introductions instead of a static document. Each indexed deck includes a summary, slide outline, topics, and a standalone viewer link when the deck passes the editorial quality gate.
Algebra is the mathematics of structure: of operations, of equations, of the symmetries that connect one quantity to another. It begins with the idea that a number you don't yet know can still be reasoned about — that x is a respectable noun.
Mathematics put to work on the world.
Calculus is the mathematics of change — of how a quantity behaves as another quantity shifts continuously. It turned the static algebra of equation-solving into a dynamic study of motion, growth, and accumulation.
Three thousand years of attempts to make a message readable to its intended recipient and unreadable to anyone else. Until 1976, all of it ran on the same fundamental architecture. Then everything changed.
The Language of Change and Motion
The mathematics of objects you can count.
The Geometry of Nature
Game theory is what happens when you take rational-choice theory and add other rational choosers. It is the formal mathematics of multi-agent decision — not a metaphor, a proof system.
Geometry is the mathematics of shape, space, and the relations between them. It is the oldest branch of the discipline that still has a recognisable name.
The Mathematics of Connection
The Mathematics of Spaces, Transformations, and Structure
A condensed history of the longest-running argument in human thought.
The mathematical study of mathematical reasoning.
"Mathematics is the queen of the sciences," Gauss wrote, "and number theory is the queen of mathematics." The compliment was not idle. Gauss devoted his greatest energies to it.
Probability is the mathematics of uncertainty. It quantifies how often things happen — or, on a different reading, how much we should believe they will.
The Science of Learning from Data
Geometry minus distance. The study of properties that survive continuous deformation.
Newton + Leibniz, ~1665–1684
A substitution cipher maps each plaintext letter to a fixed ciphertext letter. Caesar's shift is a special case: c ≡ p + k (mod 26) .
A 13-slide tour of payoffs, equilibria, and the mathematics of mutual anticipation — from von Neumann's chessboard to the FCC spectrum auction.
A Drafting Table Deck · XIII Plates Geometry / The science of shape From the surveyor’s rope to the curvature of spacetime — thirty-five centuries of measuring the world.
Vectors, matrices, transformations.
Eleven figures, twenty-five centuries. From a Greek cult leader who heard the world as ratios to a wandering Hungarian who slept on his colleagues' couches — the people who invented the language we count, calculate, and reason in.
2 3 “Mathematics is the queen of the sciences, and number theory is the queen of mathematics.” — C. F. Gauss ❦ ❦ Chapter I The Integers §1. The playing field The Integers The integers ℤ = { … , −3, −2, −1, 0, 1, 2, 3, … } form the bedrock of arithmetic — discrete, unbounded, equipped with addition and multiplication.
a grammar for uncertainty
homeomorphism Same shape, different presentation. The puzzle To a topologist, a coffee cup is a donut. Stretch, bend, twist — but never cut, never glue. Under such deformations the cup with one handle and the torus with one hole are indistinguishable. Both are surfaces of genus one.
Some questions sit on the board for centuries. They look simple. They aren't.