Marion Lefevre

Mathematical models for predicting climate and weather

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Les modèles mathématiques pour prévoir le climat et la météo

IN BRIEF Climate models: Digital representations of the climate system. Nonlinear dynamic systems: Underlying mathematics of the models. Differential equations: Used to model climate phenomena. Climate change: Data analysis to understand climate evolution. Temperature, wind, and precipitation: Observed phenomena to refine predictions. Data engineering: Combining information for accurate forecasts. Forecasting history: Evolution of methods since … Read more

Introduction to Mathematical Logic and Its Principles

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Introduction à la logique mathématique et ses principes

IN BRIEF Presentation of mathematical logic. Introduction to logical connectors: ¬, ∧, ∨, ⇒, and ⇔. Description of propositions and their value: true or false. Classic statement: example of logical reasoning with Socrates. Distinction between formal logic, material logic, and inductive logic. Importance of symbols and principles in formal demonstrations. Exploration of the fundamental principles … Read more

The best podcasts to learn mathematics

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Les meilleurs podcasts pour apprendre les mathématiques

IN SHORT Listen to podcasts to discover mathematics in a different way. The best podcasts include: Maths en tête, L’oreille mathématique. Popularization of mathematics by renowned experts. Diverse themes: from combinatorics to theoretical physics. Educational shows in line with school curricula. Learning opportunities while having fun through games and interactions. Podcasts can be an excellent … Read more

Mathematics in religions and beliefs

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Les mathématiques dans les religions et les croyances

IN BRIEF Mathematics and religion: A fascinating link Do beliefs influence the perception of mathematics? The question of the existence of God through mathematics Applied mathematics to spirituality and religious practices Debates around ontological proofs by Gödel The impact of mathematics in religious cultures, especially in Islam Mathematical theorems and their influence on religious thought … Read more

The futuristic visions of mathematics in the service of humanity

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Les visions futuristes des mathématiques au service de l’humanité

IN SHORT Mathematics as a forecasting tool for various sectors. Challenges posed by machines and artificial intelligence. The importance of collaborative work between scientific disciplines. Essential role of mathematical models in societal understanding. The debate around mathematics: human invention or universal discovery. Celebration of the International Day of Mathematics. Exploration of fractals and chaos theory. … Read more

Algebraic structures: groups, rings, and fields

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Les structures algébriques : groupes, anneaux et corps

IN BRIEF Groups: A non-empty set equipped with an internal composition law, verifying associativity and possessing a neutral element. Rings: A set with two internal operations, addition and multiplication, complying with certain algebraic properties. Fields: A commutative ring where every non-zero element has a multiplicative inverse. Algebraic structures: Fundamental in mathematics, they form the basis … Read more

Understanding famous paradoxes in mathematics

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Comprendre les paradoxes célèbres en mathématiques

IN BRIEF Zenon’s Paradox: Achilles and the tortoise illustrates infinity. Russell’s Paradox: Highlights logical contradictions. The Liar Paradox: A statement that contradicts itself. The Barber Paradox: A classic example of paradoxical logic. The Missing Dollar Puzzle: Raises questions about addition. Ellsberg’s Paradox: Reveals irregularities in probability choices. Hilbert’s Hotel: Exposes the properties of infinity. Goodstein’s … Read more

Complex analysis: introduction to imaginary numbers

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Analyse complexe : introduction aux nombres imaginaires

IN BRIEF Complex analysis: field of study of complex numbers. Definition of a complex number: z = a + bi with a and b real, i imaginary unit. Visualization of complex numbers in the plane with coordinates. Operations on complex numbers: addition, subtraction, multiplication, etc. Basic concepts related to imaginary numbers and their importance in … Read more

Introduction to Differential and Integral Calculus: Key Concepts

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Introduction au calcul différentiel et intégral : concepts clés

IN BRIEF Differential calculus: study of derivatives to measure the change of a function. Integral calculus: understanding the concept of integral to determine areas under curves. For each function, it is possible to calculate derivatives and integrals using basic techniques. Geometric concepts such as areas, perimeters, and volumes are essential. The history of differential and … Read more

The mathematics behind numerical simulations

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Les mathématiques derrière les simulations numériques

IN BRIEF Numerical simulations: computational processes on a computer to model physical realities. Mathematical modeling: building models to represent complex systems. Mathematical analysis: evaluation and interpretation of simulation results. Practical applications: use in various fields, including pandemics and engineering. Technological evolution: computing transforms and improves the approach to applied mathematics. Numerical models: implementation of discretization … Read more