Library

How a quantum particle can pass through a barrier that, classically, it does not have the energy to cross. Wave-based origin, exponential dependence on the width of the barrier, and major applications: alpha radioactivity, scanning tunnelling microscope, flash memory. Numerous diagrams.

The experiment that gave birth to quantum physics in 1900: black-body radiation, the "ultraviolet catastrophe" of classical physics, and Planck's stroke of genius when he postulated that energy is exchanged in grains. With spectral curves and the laws of Wien and Planck.

Master proof by induction, the method that lets you prove a property for all natural numbers from just two steps, thanks to the domino analogy.

Learn to compute a probability knowing that an event has already occurred, to build a probability tree and to use it to solve concrete problems such as medical tests.

Discover matrices, these arrays of numbers that let you manipulate whole systems at once. Learn to add them, multiply them and use them to transform points.

Learn to speed up recursive algorithms that keep recalculating the same results, by memoizing what has already been computed. Tree and table diagrams illustrate the difference.

Learn to find a value in a sorted array in as few steps as possible, by cutting the search space in two each time. An interval diagram helps you visualise each step.

Discover two fundamental data structures that organise the order in which elements are processed: the stack (LIFO) and the queue (FIFO). You will see their operations, step-by-step diagrams of how they evolve, concrete use cases and a Python implementation.

The concepts behind the modern quantum revolution: superposition of states, measurement that "makes a choice", Schrödinger's cat, the entanglement of two particles, and the qubit — the building block of the quantum computer. With diagrams and concrete examples.

One of the most profound ideas in physics: it is impossible to know both, with perfect precision, the position and the velocity of a particle. Not for lack of instruments, but by nature. Wave origin, the formulation ΔxΔp ≥ ħ/2, and consequences.

Why atoms emit only certain very specific colors: quantized energy levels, the Bohr model, transitions and photons. Line spectra as the fingerprints of atoms, with level diagrams and calculations on the hydrogen atom.

The strange heart of quantum physics: light sometimes behaves like a wave, sometimes like a stream of particles (photons), and matter itself has a wave nature. From the photoelectric effect to electron interference, with many diagrams.

How the body holds its constants steady: the hormonal message and its target cells, negative feedback, blood glucose regulation by insulin and glucagon, and what happens when the loop breaks — diabetes.

How life organises into networks: trophic levels and the role of decomposers, the 10 % rule that limits food chains, the carbon and nitrogen cycles, and the trophic cascades that reshape whole landscapes.

How information travels through the body: the anatomy of the neuron and the myelin sheath, the action potential and the all-or-none law, chemical transmission at the synapse, and from the reflex arc to brain plasticity.

How the body defends itself: barriers and innate immunity, the B and T lymphocytes of adaptive immunity, immune memory and vaccination, herd immunity, and the failures — allergies, autoimmunity, immunodeficiencies.

Predicting how traits are passed on: dominant and recessive alleles, genotype and phenotype, Punnett squares and the 3:1 then 9:3:3:1 ratios, and the cases — codominance, sex linkage, polygeny — that go beyond Mendel's laws.

How a gene becomes a working molecule: transcription into messenger RNA, the 64-codon genetic code, translation by ribosomes, and what a single changed base can do.

How a cell reproduces: the cell cycle and DNA replication, mitosis that makes clones, meiosis that halves the chromosome number, and the shuffling that makes two children never quite alike.

How plants turn light into living matter: the balance 6 CO₂ + 6 H₂O → glucose + 6 O₂, the role of chloroplasts, the limiting factors, and why the oxygen we breathe comes from water.

The species that inhabit the Earth today are just a snapshot of a history billions of years old. Discover Darwin's theory, the evidence for evolution, and how natural selection transforms populations, generation after generation.

DNA is the molecule that carries, in each of your cells, all the genetic information passed down by your parents. Discover its double helix structure, the concept of genes and chromosomes, and how this information shapes your hereditary traits.

The cell is the basic building block of every living being, from bacteria to humans. Discover its organization, its organelles, and what distinguishes an animal cell from a plant cell.

Explore the three main families of organic chemistry reactions — substitution, addition, elimination — through concrete examples involving alkenes and alcohols. Also learn to balance combustion equations for organic compounds, essential for understanding fuels.