mathematics

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

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

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

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

Comment mathematics shaped modern philosophy

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Comment les mathématiques ont façonné la philosophie moderne

IN BRIEF Mathematical logic as the basis of philosophical thought. Relationship between mathematics and philosophy throughout the centuries. Influence of modern philosophers on mathematics. The philosophy of mathematics and its foundations. Contributions of figures like Descartes and Pascal. Abstraction and generalization in reasoning. Kant’s approaches on the independence of mathematics. Mathematics, as a rigorous discipline, … Read more

Les ensembles numériques explained simply

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Les ensembles numériques expliqués simplement

IN BRIEF Set ℕ: Natural whole numbers (0, 1, 2, …) Set ℤ: Whole numbers (positive and negative) Set ℚ: Rational numbers (fractions) Set ℝ: Real numbers including irrational numbers Set ℝ⁺: Positive real numbers Set ℝ⁻: Negative real numbers Use of the number line to represent sets Importance of properties and relationships between sets … Read more

How mathematics helps to solve environmental problems

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Comment les mathématiques aident à résoudre des problèmes environnementaux

IN BRIEF Modeling of natural phenomena Prediction of environmental effects Optimization of energy resources: solar and wind Analysis of the impact of climate change Development of new models for ecosystems Use of carbon balance for sustainability Mathematics plays an essential role in understanding and solving environmental problems. Through predictive models and equations, they allow for … Read more