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Biologie – Génétique (3)

  • From DNA to protein
  • DNA and Genes
  • Mendelian genetics

Biologie – Immunologie (1)

  • The immune system

Biologie – Le vivant (2)

  • The cell
  • Cell division: mitosis and meiosis

Biologie – Métabolisme (1)

  • Photosynthesis

Biologie – Physiologie (2)

  • Hormonal regulation and homeostasis
  • The neuron and the nerve message

Biologie – Écologie (1)

  • Ecosystems

Biologie – Évolution (1)

  • The evolution of species

Chimie – Chimie supramoléculaire (1)

  • Supramolecular Self-Assembly: Metal-Organic Cages and Bowls

Chimie – La matière (4)

  • Atoms, molecules and ions
  • The periodic table of elements
  • Chemical bonds
  • The states of matter and changes of state

Chimie – Organique (2)

  • Organic chemistry: the main reactions
  • Organic chemistry: carbon molecules

Chimie – Quantités (3)

  • The mole and the amount of substance
  • Gases and the Ideal Gas Law
  • Solutions and concentration

Chimie – Transformations (7)

  • Acids, bases and pH
  • Chemical kinetics and equilibria
  • Redox reactions
  • Electrochemistry and Galvanic Cells
  • Thermochemistry
  • Chemical reactions and their equations
  • Acid-base titrations

Cryptographie – Applications (4)

  • Strong authentication: TOTP and FIDO2
  • The blockchain: hashing, Merkle trees and proof of work
  • Steganography: hiding the very existence of the message
  • Passwords: salting, hashing, and key derivation

Cryptographie – Attaques (2)

  • Side-channel attacks
  • Attacks on RSA

Cryptographie – Avancée (1)

  • Homomorphic encryption

Cryptographie – Clé publique (3)

  • The Diffie-Hellman key exchange
  • Elliptic curve cryptography
  • Public-key cryptography and RSA

Cryptographie – Fondamentaux (6)

  • Randomness in cryptography
  • The one-time pad and perfect secrecy
  • Kerckhoffs's principle and secure design
  • Secret codes: encryption and decryption
  • One-way functions: the foundations
  • Vigenère and the early days of cryptanalysis

Cryptographie – Intégrité (3)

  • Hash functions and digital signatures
  • Hash functions: construction and attacks
  • MAC and HMAC: authenticating messages

Cryptographie – Mathématiques (2)

  • Modular arithmetic, the foundation of cryptography
  • Post-quantum cryptography

Cryptographie – Messagerie (2)

  • End-to-end encryption
  • Signal: forward secrecy and the double ratchet

Cryptographie – Protocoles (4)

  • Schnorr identification and the Fiat-Shamir transform
  • Secure multiparty computation
  • Shamir's Secret Sharing
  • Zero-Knowledge Proofs

Cryptographie – Quantique (1)

  • Quantum key distribution (BB84)

Cryptographie – Réseau (2)

  • Certificates and the chain of trust
  • TLS and HTTPS: web security

Cryptographie – Symétrique (3)

  • AES, the Encryption Standard
  • Block ciphers and their modes
  • Modern symmetric encryption: AES and operating modes

Informatique – Algorithmique (6)

  • Introduction to dynamic programming
  • Algorithmic Complexity
  • Binary search
  • Recursion
  • Sorting Algorithms
  • The Basics of Algorithms

Informatique – Architecture (1)

  • Logic Circuits and Computer Architecture

Informatique – Codage (1)

  • Error-Correcting Codes

Informatique – Données (1)

  • Databases and SQL

Informatique – Information (1)

  • Information Theory and Compression

Informatique – Programmation (4)

  • Functions
  • Lists and dictionaries in Python
  • First steps in Python
  • Variables, loops and conditions

Informatique – Réseaux (1)

  • How the Internet works

Informatique – Structures de données (3)

  • Binary Trees
  • Graphs and their traversals
  • Stacks and queues

Informatique – Théorie (1)

  • Finite automata

Mathématiques (2)

  • Discovering Algebra
  • The basics of the calculation

Mathématiques – Algèbre (13)

  • Expand an expression
  • Factoring an expression
  • First-degree inequalities
  • Literal calculation
  • The second degree: canonical form
  • Notable figures
  • Matrices
  • Formulating problems as equations
  • Polynomials and factorisation
  • Sign of a trinomial
  • Systems of two equations
  • First-degree equations
  • Quadratic equations

Mathématiques – Algèbre linéaire (6)

  • Linear maps
  • Determinants
  • Vector spaces
  • Linear systems and Gaussian elimination
  • Invertible matrices and solving systems
  • Eigenvalues and diagonalisation

Mathématiques – Analyse (31)

  • Fourier Analysis and Signal Processing
  • Applications of differentiation
  • Bolzano-Weierstrass by Bisection
  • Continuity and the Intermediate Value Theorem
  • A comparison of growth rates
  • Calculus assignment: the function ln(1 + x)/x and its associated sequence
  • Derivatives and variations
  • Limited developments
  • Integration by parts
  • The Area Between Two Curves
  • Integration by Substitution
  • The square function
  • The derivative
  • The exponential function
  • The inverse function
  • The natural logarithm function
  • The concept of a function
  • The Average Value of a Function
  • Integral calculus
  • The derivative
  • Proof by induction
  • Heine's Theorem
  • Rolle's Theorem and the Mean Value Theorem
  • The Banach Fixed-Point Theorem
  • Affine functions
  • Reference functions
  • Function limits
  • Riemann Sums
  • Primitives of a function
  • Direction of variation of a function
  • Differential equations

Mathématiques – Analyse numérique (1)

  • Numerical Integration

Mathématiques – Arithmétique (14)

  • Bézout, Gauss and Diophantine equations
  • Assignment: the Josephus problem
  • Divisibility, multiples and divisors
  • The Irrationality of e
  • Fractions: meaning and representation
  • Decimal numbers
  • Whole numbers and the number system
  • Prime numbers
  • Relative numbers
  • The four operations set out
  • Operations on fractions
  • GCD and irreducible fractions
  • Proportionality and percentages
  • Powers and scientific notation

Mathématiques – Géométrie (12)

  • Areas and perimeters
  • Angles and parallelism
  • Circle, disc and inscribed angles
  • Solid Geometry
  • Geometry with reference points in the plane
  • Pythagoras’s theorem
  • Thales’ theorem
  • Rotations and homothecies
  • Symmetries and translations
  • Triangles and their properties
  • Trigonometry of a right-angled triangle
  • Volumes of common solids

Mathématiques – Logique (2)

  • Cantor's Diagonal Argument
  • Logic and Methods of Proof

Mathématiques – Nombres complexes (3)

  • The d'Alembert–Gauss Theorem
  • Complex numbers: algebraic form
  • Modulus, argument and exponential form

Mathématiques – Probabilités (6)

  • Counting and combinatorics
  • The binomial distribution
  • The normal distribution
  • Conditional probability
  • Probability on a finite sample space
  • Random variables, expectation and variance

Mathématiques – Statistiques (2)

  • Descriptive statistics
  • Inferential Statistics

Mathématiques – Suites (5)

  • Digital suites
  • Limit of a sequence
  • Direction of variation of a sequence
  • Arithmetic sequences
  • Geometric sequences

Mathématiques – Suites et récurrence (1)

  • The Fibonacci sequence

Mathématiques – Trigonométrie (5)

  • Cosine and sine of a real number
  • Sine and cosine functions
  • The unit circle
  • Trigonometric formulas
  • Trigonometric equations

Mathématiques – Vecteurs (6)

  • Applications of the scalar product
  • Collinearity and alignment
  • The scalar product
  • The vector product
  • Vectors in the plane
  • Vectors in space

Physique (2)

  • Quantities, units and measurement
  • Motion and forces

Physique – Fluides (4)

  • Fluid flow
  • Archimedes’ principle
  • Bernoulli’s equation
  • Fluid Pressure and Statics

Physique – Mesure et méthode (6)

  • Significant figures and uncertainties
  • Creating and interpreting a graph
  • Quantities, values and units
  • The experimental approach
  • Prefixes and conversions
  • Scientific notation and orders of magnitude

Physique – Mécanique (22)

  • Collisions and the conservation of momentum
  • Conservation of mechanical energy
  • Describing a movement: the frame of reference
  • Acceleration
  • Kinetic energy
  • Potential gravitational energy
  • Freefall
  • Newton’s second law
  • Universal gravitation
  • Mechanical power
  • Momentum
  • Newton’s third law
  • Uniform circular motion
  • Uniform linear motion
  • The principle of inertia
  • The work done by a force
  • Forces: mechanical actions
  • The motion of projectiles
  • Oscillators and pendulums
  • Weight and mass
  • Satellites and Kepler’s laws
  • Average and instantaneous speed

Physique – Ondes (2)

  • The Doppler Effect
  • Mechanical Waves and Acoustics

Physique – Optique (9)

  • Dispersion and spectra
  • Interference and diffraction
  • The eye and optical instruments
  • The construction of images
  • Light: a wave
  • The propagation of light
  • The reflection of light
  • Refraction and Snell–Descartes’ laws
  • Thin lenses

Physique – Physique nucléaire (1)

  • Radioactivity and Nuclear Decay

Physique – Physique quantique (10)

  • The Photoelectric Effect
  • Quantum tunnelling
  • Wave-Particle Duality
  • Energy Quantization and Spectra
  • The black body and the birth of the quanta
  • The laser: stimulated emission and population inversion
  • Heisenberg's uncertainty principle
  • Spin and the Pauli Principle
  • Atomic orbitals and quantum numbers
  • Superposition, entanglement and qubits

Physique – Relativité (1)

  • Special Relativity

Physique – Thermodynamique (3)

  • The ideal gas law
  • Thermodynamics and Heat Engines
  • Heat Transfer

Physique – Thermodynamique quantique (1)

  • Autonomizing Quantum Systems and the Work Operator

Physique – Électricité (14)

  • Charging and discharging a capacitor (RC)
  • The current intensity
  • The coil and inductance
  • Ohm's Law
  • Electrical voltage
  • The RL circuit
  • The electrical circuit
  • The capacitor
  • Alternating current
  • The transistor and amplification
  • Resistance organisations
  • Laws of Loops and Knots
  • Oscillations in an RLC circuit
  • Electrical power and energy

Physique – Électromagnétisme (7)

  • Electromagnetic induction
  • Laplace's force
  • The Lorentz force
  • The magnetic field
  • The electric field
  • Maxwell’s equations
  • Electrostatic potential and energy

Physique – Électrostatique (1)

  • Coulomb's law
272 / 272 courses
LibraryRotations and homothecies

Rotations and homothecies

Discover two transformations of the plane that rotate or enlarge shapes: rotation and similarity, along with their properties and common pitfalls.

Intermediate 50 min 19 viewsmathsgeometrielycee
Start the course— Definition and construction of a rotation

Table of contents

  1. 01

    Rotation in a plane

    • Definition and construction of a rotation(not finished)
    • Properties of rotation(not finished)
    • Recognising the properties of a rotationMCQ
    • Angle of a compound rotationShort answer
  2. 02

    Homothety

    • Definition and ratio of a homothety(not finished)
    • Properties of homothety(not finished)
    • Effect of the k-ratio on a figureMCQ
    • Constructing a homothety with a negative ratioOpen answer

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