IN BRIEF Philosophy and mathematics: a complex connection. Conceptions of infinity throughout history. The Euclidean axioms and their limitations. The debate on the nature of infinity in the real world. Aristotle and the concept of potential infinity. Impact of Descartes‘ reflections on infinity. The early attempts to understand infinity by Zeno. Applications of infinity in … Read more
IN BRIEF Prime number: a natural number divisible only by 1 and itself. Examples of prime numbers: 2, 3, 5, 7, 11, 13. Importance in arithmetic: every number can be uniquely decomposed into products of prime numbers. Cryptography: prime numbers ensure the security of online data. Historical developments, notably by Eratosthenes and his sieve. Essential … Read more
IN BRIEF Interdisciplinarity : Facilitates links between disciplines. Statistical tools : Used in sociology and psychology. Education : Learning mathematics related to other subjects. Mathematical models : Essential element for scientific understanding. Geometry, numbers, and other sub-disciplines : Fundamental links. Scientific popularization : Making mathematical concepts accessible. Innovation : Encouraged by the integration of mathematics … Read more
IN BRIEF Multiples: product of a number and an integer. Example: 6 multiplied by 8 gives 48. Divisors: numbers that can divide another without a remainder. Relation: if a is a multiple of b, then b is a divisor of a. Prime numbers: only two divisors, 1 and itself. Examples of prime numbers: 2, 3, … Read more
IN BRIEF Probabilities and games of chance: Introduction to the basic concepts. Calculation of probabilities: Strategies to increase winning chances. The role of combinatorial calculation in evaluating options. Examples of modeling related to well-known games. Importance of laws of chance: Failures and successes in games. Specific strategies for games like poker and lottery. History of … Read more
IN BRIEF Mathematical optimization: finding the best solution among several alternatives. Proven techniques such as the walking line to reduce the number of vertex evaluations. Importance of modeling to transform complex problems into linear analyses. Metaheuristic algorithms simplify solving optimization problems. Practical application in various fields, including supply chain and optimization under constraints. Identification of … Read more
IN BRIEF Definition of multiple integrals: integration of functions of multiple real variables. Types of integrals: double integrals and triple integrals. Applications: calculation of areas and volumes of irregular shapes, evaluation of the mass of objects with variable density. Use in mechanics: calculation of moments of inertia by analogy with double integrals. Techniques: importance of … Read more
IN BRIEF Use interactive games to make learning fun. Integrate hands-on activities, such as cooking, to teach quantities. Incorporate educational books that address mathematics in an accessible way. Utilize everyday objects for counting and measuring exercises. Create a stimulating environment with appropriate tools, like dice and cards. Creating a mathematics learning workshop at home can … Read more
IN BRIEF Geometric transformations: Mechanisms for modifying figures in the plane. Main types: Translation, Rotation, Reflection, Homothety. 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: Presentation and exercises in student textbooks. … 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. Verify that the solution found is coherent and relevant. The resolution of simple mathematical problems is an … Read more