Unlock your mathematical potential with our extensive collection of online mathematics courses and exercises, designed for high school, undergraduate, and graduate students. We provide bilingual educational resources in both English and French, available in convenient PDF and engaging video formats.
I. Mathematics for Baccalauréat (French Baccalaureate)
Baccalauréat: Access our rich selection of math courses and exercises specifically tailored for students in Terminale (final year of high school), preparing for the Baccalauréat or equivalent levels.
Accédez à notre riche sélection de cours et exercices de maths, conçus sur mesure pour les élèves en Terminale toutes filières, préparant le Baccalauréat ou un niveau équivalent.
II. Mathematics for Final High School and Equivalent Levels
Final High School: Immerse yourself in our specialized math lessons, perfectly suited for students aiming for the Baccalaureate, final high school year, A-Levels, Class 10, or similar academic milestones.
III. Advanced Mathematics: Measure Theory, Lebesgue Integral, and Probability
Measure Theory, Lebesgue Integral, and Probability: Our Measure Theory, Lebesgue Integral, and Probability Theory materials provide in-depth coverage with detailed PDFs, informative video lectures, and carefully designed exercises.
- Measure Theory: Learn the fundamentals of Measure Theory with our comprehensive guide, covering key concepts such as σ-algebras, measurable functions, and the properties of measures. Explore the Dirac measure and the Lebesgue measure on ℝ^n.
- Lebesgue Integral: Delve into the Lebesgue Integral with our comprehensive guide, covering its construction, convergence properties, Fubini’s Theorem, the Radon-Nikodym Theorem, and the intricacies of Lp spaces.
- Probability Theory: Advance your understanding of Probability Theory with our detailed course, from its measure-theoretic foundations to concepts such as random variables, distribution functions, and the monotone and dominated convergence theorems.
- Discrete Random Variables and their Transform: This course covers discrete random variables, and the use of probability generating functions to analyze their distributions and moments.
- Continous Random Variables and their Transforms: The lecture explores continuous random variables, and delve into the moment generating function, characteristic function, and the Laplace transform to understand and solve related probability problems.
- Convergence of Random Variables: This lesson covers the various modes of convergence for random variables in probability theory, starting with almost-sure convergence, then moving to convergence in probability, quadratic mean, and weak convergence, while also examining their interrelations and concluding with Prohorov’s Theorem.
- Exercises with Solutions: Reinforce your knowledge with our collection of exercises covering measure theory, the Lebesgue integral, and probability theory. Each exercise has detailed solutions to support your learning.