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.

Why a reaction goes, how fast, and how far: kinetics and equilibrium, acids and bases, and the electron transfers behind every battery.

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.

Follow the field from Coulomb to Maxwell: charge and current, induction, and the four equations that turn out to describe light itself.

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.

The machinery every living thing shares: membranes and transport, metabolism, the flow from DNA to protein, and how a cell divides.

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.

From the principate to the fall: 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.

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