IN BRIEF Geometric transformations : Mechanisms for modifying shapes 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. Varied applications : Used in various fields such as physics and computer science. Pedagogical approach : … Read more
IN BRIEF Read carefully the statement to fully understand the problem. Rephrase 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 consistent and relevant. Solving simple mathematical problems is an essential skill, … Read more
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 the values. In mathematics, understanding decimal numbers and their place value is … Read more
IN BRIEF Differential equations: fundamental in applied mathematics. Homogeneous solutions: functions of the form x ↦ λe−A(x). Cauchy problem: method of variation of the constant. Linear equations: of order 1 and 2, written in canonical form. Numerical resolution: approach to solutions by series. Variation method: development of particular solutions. Applications: utility in various industrial fields. … Read more
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 improve robot intelligence. Geometry: Fundamental for understanding space and movement. Trajectories: Mathematical modeling of movements. Educational robots: Used to make mathematics more accessible to students. Interdisciplinarity: The … Read more
IN BRIEF Applied mathematics to quantum mechanics Use of complex numbers to model wave-like phenomena Emission of electrons by 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 … Read more
IN SHORT Mathematical logic as the foundation of philosophical thinking. The relationship between mathematics and philosophy through 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 to the independence of mathematics. Mathematics, as a rigorous … Read more
IN BRIEF Set ℕ: Natural integers (0, 1, 2, …) Set ℤ: Relative integers (positive and negative) Set ℚ: Rational numbers (fractions) Set ℝ: Real numbers including irrationals Set ℝ⁺: Positive real numbers Set ℝ⁻: Negative real numbers Use of the number line to represent the sets Importance of properties and relations between the sets … Read more
IN BRIEF Squares: A number raised to the power of 2. Cubes: A number raised to the power of 3. Square and cube numbers can add together. Examples of numbers: 1 and 64 are both squares and cubes. Calculating a square root or cube root is the inverse operation of raising a number. Used in … Read more
IN BRIEF Modeling 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 play an essential role in understanding and solving environmental problems. Through predictive models and equations, they allow for the … Read more