The curriculum
Twelve courses, three tiers,
one way of teaching.
Every course works the same way: pictures before symbols, plain language before jargon, something to touch in every lesson. The tiers below show what builds on what — or follow a guided pathway instead.
01 · Foundations — start here
The shared language of everything above: unknowns, shapes, and waves. Comfortable already? Skip ahead; each topic page lists exactly what it assumes.
Algebra foundations4 lessonsThe art of working with the unknown.Algebra is arithmetic with a placeholder: a letter standing for a number you don't know yet. That one move — naming the unknown — turns puzzles you'd solve by guessing into puzzles you solve by steps.Geometry4 lessonsSpace, shape, and the logic of seeing.Geometry is mathematics you can point at: lengths, angles, areas, and the surprising rules that connect them. It's also where you first watch a fact get proven — not asserted, proven.Trigonometry5 lessonsTriangles, circles, and everything that repeats.Trig starts as a tool for finding unknown sides of triangles — and then turns out to be the mathematics of anything that cycles: sound, light, tides, seasons, heartbeats. Two functions, sine and cosine, carry the whole subject.Counting & combinatorics4 lessonsThe bridge from foundations to probability.How many passwords, poker hands, or committees are possible? Counting answers questions too big to list — and since probability is just 'favorable outcomes ÷ total outcomes', counting is the doorway into probability and statistics. This short course is a real bridge, not a footnote.
02 · Core mathematics
The four pillars. Calculus handles change, linear algebra handles structure, statistics handles uncertainty, discrete math handles computation. Any order works — calculus first is the classic route.
Calculus12 lessonsThe mathematics of change and accumulation.How fast is it changing right now, and how much has piled up in total? Calculus answers both — for anything a curve can describe. It's the subject this platform was built around, and every lesson is live today.Linear algebra9 lessonsThe mathematics of many things at once.A vector is a list of numbers treated as one object; a matrix transforms whole collections of them in a single move. Linear algebra is how mathematics handles a thousand variables with the same ease as one.Probability & statistics13 lessonsHonest reasoning under uncertainty.You can't know whether the coin lands heads — but you can know exactly how often it will in the long run. Probability quantifies uncertainty; statistics reads evidence backwards from data to truth. Together they're the mathematics of not being fooled.Discrete mathematics4 lessonsThe mathematics of steps, networks, and code.Calculus studies smooth, continuous change. Discrete math studies things that come in whole pieces: yes/no decisions, network connections, countable arrangements. It's the native mathematics of computers — which can only ever count.
03 · Applied tracks — where it all assembles
Dynamics and signal processing: courses where the foundations and pillars combine into engineering-grade tools. Each lists its prerequisites up front.
Differential equations5 lessonsThe laws of nature, written as change.Nature rarely tells you what a quantity is — it tells you how the quantity changes. “Cooling is proportional to temperature difference.” “Growth is proportional to population.” A differential equation is that sentence in symbols; solving it reveals the future.Optimization & gradient descent5 lessonsHow machines learn — calculus turned into training.How does a model actually learn? It defines what 'wrong' means (a loss), computes which way is downhill (the gradient), and steps that way over and over (gradient descent). This course is the engine room of machine learning — where calculus, linear algebra, and statistics combine into training.Signals & systems8 lessonsThe mathematics of everything that varies.Sound, sensor readings, radio, heartbeats — the measured world arrives as signals, and the devices that handle them are systems. This course builds the working vocabulary: signals as functions, LTI systems, convolution, complex numbers and phasors, resonance, and filters — the math running inside every device you own.Fourier & the frequency domain8 lessonsEvery signal is a chord. Learn to read the notes.Fourier's idea — that any signal decomposes into pure sinusoids — may be the most useful single insight in applied mathematics. This course builds it from linear algebra (signals as vectors, spectra as coordinates), makes it computable (DFT and FFT), and confronts its real-world fine print: sampling, aliasing, leakage, and windows.