Lessons

Second derivatives buy something gradients cannot: a step shaped by curvature, immune to conditioning, converging quadratically. This lesson builds Newton's method, then layers it on a log barrier to get interior point methods, the machinery that made large constrained problems solvable with a certificate rather than a hope.

Gradient descent is three lines of code and a hundred years of theory. This lesson derives why a safe step size is one over the smoothness constant, why the condition number governs everything, and why acceleration reaching order one over k squared is provably the best any first-order method can do.

Convexity is what separates optimization problems you can solve with a guarantee from ones you can only hope about. This lesson defines convex sets and functions, proves why every local minimum is global, and gives you the operations that let you recognise convexity without touching a Hessian.

Most microbes on Earth have never been grown in a laboratory, so for a century microbiology studied the small fraction that cooperated. This lesson covers the great plate count anomaly, how 16S sequencing and metagenomics read organisms directly, and what those methods still cannot tell you.

An antibiotic has to break something a bacterium has and you do not. This lesson covers the four target families, how MIC is measured, the four ways bacteria defeat a drug, and how a resistance gene moves between cells that are not even related.

Bacterial growth is exponential, which makes the arithmetic simple and the intuition terrible. This lesson covers doubling time, the four phases of a culture, and the gap between the cells you can see down a microscope and the ones that will actually grow on a plate.

A bacterium and one of your cells are both alive and share almost no structure beyond that. This lesson walks the bacterial cell part by part, the wall, the loop of DNA, the smaller ribosome, and shows why each difference is exactly what an antibiotic aims at.

If your cost per round trip equals the move you are trying to capture, you need 100 percent directional accuracy to break even. This lesson computes that hurdle, replaces accuracy with metrics tied to a tradeable decision, and covers the capacity and latency limits that decide whether a real edge is worth anything.

At a one-event horizon, 92 percent of mid-price labels are exactly no-change, so a model that always predicts flat scores 92 percent accuracy. This lesson computes that baseline across horizons and works through the four mechanisms that turn a genuine measurement into a number nobody can reproduce.

Convolutional and recurrent networks have been applied to order book data with published success, and the architectures encode real assumptions about the book's structure. This lesson explains what each one assumes, why the gains over simple baselines are smaller than headline numbers suggest, and where the modelling effort is better spent.

Before choosing an architecture you have to decide what the input is, and an order book offers several incompatible representations that are not equally informative. This lesson covers what each data level contains, why raw prices are the wrong features, and the representation choices that decide more than the model does.

A market maker quotes both sides and profits from the spread, but every fill leaves an unwanted position and the counterparties who trade most eagerly are the ones who know something. This lesson simulates the inventory-skew trade-off, showing a 63 percent cut in exposure for 2.5 percent of profit, and locates where a learned policy genuinely helps.

Reinforcement learning needs an environment that responds to the agent, and historical market data is a fixed recording that does not. This lesson shows that replaying the same day gives a fill rate anywhere from 38 to 73 percent depending on an assumption the data cannot settle, and covers what to do about it.

An agent optimises the reward you wrote, not the objective you meant, and in execution the gap between those is unusually easy to open. This lesson computes how a mis-sized penalty makes leaving part of the order unexecuted rationally optimal, and covers the shaping that provably does not change the policy.

A static execution schedule is an open-loop policy: it commits to a plan before seeing anything. This lesson formulates execution as an MDP so the plan can react, and computes the ceiling on what any adaptive policy could win, which turns out to collapse as market impact grows.

Shuffled cross-validation reports 54 percent accuracy on data containing no signal, because neighbouring samples share their futures. This lesson builds purging, embargo and sample uniqueness weights, shows the illusion scaling with label overlap and vanishing when the fix is applied, and covers why a single walk-forward path is weak evidence.

Prices are non-stationary and returns are stationary but forget everything, so the standard fix throws away the level information a model needed. This lesson builds fractional differentiation, which makes the choice a dial rather than a switch, and shows by computation that most of the memory can be kept while still passing a stationarity test.

The default label, the sign of the return over a fixed horizon, describes a trade nobody would take: no stop, no target, and a holding period chosen by the modeller rather than by the market. This lesson builds the triple-barrier method and meta-labelling, and shows with computed numbers how much of a fixed-horizon dataset is fiction.

Machine learning practice assumes independent samples, a stable data-generating process, and an environment that does not react to you. Financial data violates all three, and the result is models that validate beautifully and lose money. This lesson establishes what is actually broken before the rest of the course fixes it.

Revised estimates put British growth during the classic Industrial Revolution far lower than the name implies, and real wages barely moved for half a century while output per worker rose sharply. This lesson works through the numbers, explains why a transformative technology can take decades to show up in the statistics, and separates what is measured from what is inferred.

Before the factory, textile work was done in houses by people who set their own hours. This lesson follows the bottleneck that moved between spinning and weaving as each was mechanised, explains the two reasons work was gathered into buildings, and looks at what the Luddites were actually objecting to.

The steam engine began as a fix for one problem, flooded coal mines, and was so inefficient that it made sense only where fuel was nearly free. This lesson traces how a device that wasted 99.5 percent of its fuel became the first source of power that could be put anywhere, and why each improvement targeted the constraint that limited the last one.

Mechanised industry appeared in one place before anywhere else, and explaining that is one of the most contested questions in economic history. This lesson sets out what actually needs explaining, works through the wage-and-coal argument, the useful-knowledge argument and the institutional one, and is explicit about which parts are established and which remain in dispute.

There are tens of thousands of engineering materials and no way to compare them by intuition. This lesson builds the material index, the single combined number that ranks candidates for a stated job, shows why steel, aluminium and titanium have almost identical stiffness per kilogram, and covers the environment and processing constraints that overrule the ranking.