Subjects

How the atom was found, taken apart and finally explained: from combining weights and Rutherford scattering to orbitals, periodic trends and the chemical bond.

A complete grounding in Japanese: read both kana and your first hundred kanji, and say what you did, where you went and what you want.

Hold a real conversation to about B1: build clauses inside sentences, give reasons, report what other people said, and choose how formally to speak.

Predict motion from forces: Newton's laws, energy and momentum, rotation, and the gravitation that holds a planet in its orbit.

Work out why things stand up: equilibrium and internal forces, stress and strain, beams and buckling, and choosing a material for a load.

How variation, heredity and selection account for adaptation and the diversity of life, and the evidence that settled the argument.

A matrix is a transformation: vectors and spaces, bases and rank, determinants and eigenvectors, and what each one does to the space it acts on.

Judge an argument by its form: truth tables, natural deduction, quantifiers and proof technique, and the gap between an argument being valid and being true.

Take a position on determinism and responsibility and defend it: the Consequence Argument, compatibilism, manipulation cases, the evidence from the brain, and what desert survives.

Reason about what to do: consequences, duties and character, and what each says about the cases that actually divide people.

Rebuild school mathematics as an adult: algebra as structure, functions and graphs, logarithms and exponentials, trigonometry, and a first taste of proof.

What a limit actually is, and then how to differentiate and integrate: the mathematics of change, built solidly enough to read the physics that uses it.

Turn a law of change into an equation and solve it: first and second order, oscillation and damping, and what a solution says about the system it describes.

Model choice under scarcity: where demand comes from, what a firm can make and at what cost, how market structure sets the price, and the four ways markets fail.

Reason about uncertainty without fooling yourself: sample spaces, conditioning, Bayes, random variables, and the distributions that keep reappearing.

Strategy when the best move depends on someone else's: dominance and equilibrium, repetition and reputation, bargaining, and where the predictions fail.

Estimate, test and interpret honestly: sampling, likelihood, confidence and significance, regression, and the ways published numbers mislead.

Read a score and say what it is doing: rhythm, intervals, scales and keys, chords, and why a progression pulls the way it does.

Write correct programs from nothing: values and types, decisions and loops, functions and data structures, and how to find what you got wrong.

Choose the right structure and justify the choice: what a program costs, sorting and searching, trees and graphs, and the strategies that keep working.

How one country broke a four-century flat line in living standards: the machines, the coal, the factory, and what the change cost.

How a city's constitution built an empire and then broke under the weight of it: from the kings to Actium, and the four centuries in between.

Five centuries of the principate: how the empire was governed, why it held together for so long, and what actually ended in the west.

How Europe learned to settle arguments by measurement: from Copernicus to Newton, and why a method that now looks obvious was anything but.

What actually crossed Eurasia and how we know: the goods a camel could afford to carry, the faiths and techniques that followed them, the plague, and what the routes really changed.

The four laws that govern energy: what heat and work are, why energy is conserved but not freely reusable, and what entropy counts.

The laws taken to real hardware: control volumes and steady flow, turbines and compressors, power and refrigeration cycles, and the price of every loss.