Library

Learn how to find a function from its derivative, using common antiderivatives, composite functions and the link to integration.

Gradually explore integral calculus, from antiderivatives to calculating areas under curves, to master a key pillar of analysis.

Master integration by parts, from its proof to cyclic integrals and recurrence relations, by correctly choosing the functions to be differentiated and integrated.

Learn how to solve first- and second-order differential equations, from separable variables to the resonance of forced systems.

Understand limited expansions using the Taylor–Young formula and use them to resolve indeterminacies and study the local behaviour of curves.

Find out how to model a list of numbers that changes step by step, and get to grips with arithmetic and geometric sequences.

Discover arithmetic sequences: definition, explicit formula, direction of variation and calculation of sums, with examples of increasing complexity.

Discover geometric sequences, which grow by multiplication and can be used to model growth, decline and compound interest.

Learn how to determine whether a sequence is increasing, decreasing or constant using rigorous methods illustrated with examples.

Move from intuition to rigour with the epsilon-N definition, convergence theorems and techniques for calculating the limits of sequences.

Congruences, modular inverses and fast exponentiation: the mathematical tools underpinning RSA and Diffie-Hellman.

How can you agree on a secret without ever having met? The idea that made online shopping possible, and the way RSA works.

Proving that a file hasn’t been altered, storing a password without knowing it, signing a document: what encryption doesn’t do.

How have people been hiding messages for 2,000 years? Caesar’s cipher, substitution ciphers, and why they all eventually fail. No prior knowledge required.

The number that remained ‘indecipherable’ for three centuries, and the method that cracked it. A lesson on repetition, the enemy of secrecy.

Why does ice float? Why does boiling water remain at 100 °C? And what really happens at the molecular level when matter changes state?

From the invisible atom to the chemical formulas H₂O and CO₂, right through to the ions that power your table salt and your batteries: the building block of all chemistry.

Why burning wood has nothing to do with melting ice, how Lavoisier changed chemistry forever, and how to balance a chemical equation step by step.

Find out how chemists organised all the known elements into a single table, and why this classification still enables us to predict the properties of matter today.

Find out why chemists count atoms and molecules in huge bundles called moles, and how to easily convert from mass to the number of particles.

Understand what pH actually measures, Brønsted’s definition of an acid and a base, and why diluting an acid tenfold increases its pH by exactly one unit.

Find out how electrons flow between chemical species: oxidising agents, reducing agents, half-reactions, and two everyday examples: the electric cell and rust.

Explore why the carbon atom is capable of forming millions of different molecules, and learn to recognise chains, functional groups and isomers.

Traditional ciphers are all cracked on a computer. Here’s how encryption really works today: in blocks, using AES, and why the method matters just as much as the algorithm.