Marion Lefevre

Geometric transformations in advanced mathematics

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Les transformations géométriques en mathématiques avancées

IN BRIEF Geometric transformations: Mechanisms for modifying figures in the plane. Main types: Translation, Rotation, Reflection, Dilation. Bijectivity: Unique association between original points and image points. Conservations: Lengths, angles, areas, and alignments preserved during transformations. Various applications: Used in various fields such as physics and computer science. Pedagogical approach: Presentation and exercises in student textbooks. … Read more

The contributions of ancient civilizations to modern mathematics

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Les contributions des civilisations anciennes aux mathématiques modernes

IN BRIEF Ancient Mathematics: From Antiquity to the Present Day. Babylonian Contributions: Advanced methods for commerce. Egyptians: Use of mathematics for measuring monuments. Mesopotamia: Innovative calculation approaches. Arab-Muslim Civilizations: Hubs of mathematical knowledge in the Middle Ages. Thales of Miletus: Invention of geometry and the beginning of Greek mathematics. African Origins: Major contributions to modern … Read more

Probability and Statistics for Beginners

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Notions de probabilité et statistiques pour les débutants

IN BRIEF Probability: measure of the chance that an event occurs (value between 0 and 1). Statistics: analysis of qualitative and quantitative data. Essential concepts: mean, median, mode. Probability calculation: favorable events divided by the total number of events. Random variables and probability distributions: fundamental concepts. Difference between probabilities and statistics: use of data. The … Read more

How to solve simple math problems step by step

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Comment résoudre les problèmes mathématiques simples étape par étape

IN SHORT Read carefully the statement to fully understand the problem. Reformulate the problem to grasp its essence. Develop a strategy to determine the appropriate method. Put into practice the chosen strategy and carry out the necessary calculations. Check that the solution found is coherent and relevant. The resolution of simple mathematical problems constitutes an … Read more

The fundamentals of mathematics: addition, subtraction, multiplication, and division

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Les bases des mathématiques : addition, soustraction, multiplication et division

IN BRIEF Four basic operations: addition, subtraction, multiplication, division Order of operations: PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) Multiplication and Division are inverses of addition and subtraction Importance of parentheses in the order of calculations Practice exercises available to master the operations Math tables to learn for quick mastery The fundamentals of … Read more

Understanding the place value and decimal numbers

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Comprendre la place de valeur et les nombres décimaux

IN BRIEF Definition of place value in decimal numbers. Difference between whole numbers and decimal numbers. Importance of digits after the decimal point (tenths, hundredths, etc.). Concept of truncation and approximate value. Writing decimal numbers in expanded form. Place value tables to organize values. In the field of mathematics, understanding decimal numbers and their place … Read more

Resolution of differential equations: simplified methodologies

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Résolution d'équations différentielles : méthodologies simplifiées

IN BRIEF Differential equations: fundamental in applied mathematics. Homogeneous solutions: functions of the form x ↦ λe−A(x). Cauchy problem: method of varying the constant. Linear equations: of order 1 and 2, canonical form. Numerical resolution: approach to solutions via series. Variation method: development of particular solutions. Applications: usefulness in various industrial fields. The resolution of … Read more

Use of mathematics in robotics and automation

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Utilisation des mathématiques dans la robotique et l’automatisation

IN BRIEF Applied Mathematics: An essential foundation for robotics. Predictive Models: Used in designing robot movements. Algorithms: Designed using mathematics to guide robotic actions. Machine Learning: Integrated to enhance robot intelligence. Geometry: Fundamental to understanding space and movement. Trajectories: Mathematical modeling of movements. Educational Robots: Used to make mathematics more accessible to students. Interdisciplinarity: The … Read more

Difference between equations and expressions in algebra

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Différence entre les équations et les expressions en algèbre

IN BRIEF Algebraic expression: combination of numbers and letters without equality. Equation: an algebraic expression set equal to a constant term or another expression. An equation includes an unknown to solve, whereas an expression does not. Example of an equation: a x + b = c. Algebra: study of relationships between numbers, as opposed to … Read more

How mathematics is used in quantum physics

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Comment les mathématiques sont utilisées en physique quantique

IN BRIEF Applied mathematics to quantum mechanics Use of complex numbers to model wave-like phenomena Electron emissions from metallic materials under light radiation Applications of group theory to describe the symmetries of physical systems Solutions described by periodic vibration modes Impact of mathematics on advances in quantum physics Mathematics plays a fundamental role in understanding … Read more