Learn
anything
one lesson at a time.

Math

advanced

Convex Optimization: From Gradient Descent to Interior Point Methods

The real divide in optimization is convex against nonconvex, and it decides whether you can prove your answer is best or merely hope so. Start by learning to recognise convexity without touching a Hessian. Derive why the safe step size is one over the smoothness constant, and why the condition number governs everything. Pick up duality and the KKT conditions as your certificate. Then add curvature, and see how a log barrier turned constrained problems into something solvable in polynomial time.

Science

intermediate

Microbiology: the cell that plays by different rules

Bacteria share almost no structure with your cells, and every difference matters. Work through the bacterial envelope and genome, then the arithmetic of exponential growth and why a plate count lies to you, then how antibiotics exploit those differences and how resistance defeats them, and finally how sequencing reads the vast majority of microbes nobody can grow. You will finish able to read a growth curve, work a viable count, and explain why a resistant infection is a population event rather than a patient one.

AI

advanced

Deep Learning on Limit Order Book Data

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. That single number explains most of the gap between published order book results and what happens on a trading desk. This path covers what the book actually contains, what the architectures assume, why results fail to replicate, and the cost hurdle that decides whether a real edge is worth anything.

AI

advanced

Reinforcement Learning for Trade Execution and Market Making

A classical execution schedule is an open-loop policy: it commits to a plan before seeing anything, and reinforcement learning's entire value here is closing that loop. This path measures what closing it is actually worth, shows how a mis-sized penalty makes leaving part of the order unexecuted rationally optimal, and demonstrates that one unverifiable queue assumption moves the simulated fill rate by a factor of two. Every figure is computed.

AI

advanced

Financial Machine Learning: Building a Dataset That Does Not Lie

Shuffled cross-validation reports 54 percent accuracy on market data containing no signal whatsoever, and that number is why competent machine learning so often fails on markets. This path fixes the dataset rather than the model: labels that describe trades someone would actually place, features that are stationary without being amnesiac, and a validation scheme that returns chance when there is nothing there. Every figure in it is computed and reproducible.

History

intermediate

How the Industrial Revolution Actually Happened

Machines that were technically feasible in several places were adopted in one of them, and explaining that is still argued about. This path sets out the competing answers and what each rests on, follows the steam engine from a mine pump to a portable prime mover, explains why work moved out of houses and into buildings, and works through the revised numbers showing that output per worker outran wages for roughly fifty years.