IN BRIEF Definition: A vector space is a set of objects called vectors. Properties: It must have an internal law of addition and multiplication. Applications: Crucial in linear algebra for solving various scientific and industrial problems. Linear combinations: Allows for the creation of new expressions from existing vectors. Dimensions: Measures the number of independent vectors … Read more
IN BRIEF Origins of probability theory in games of chance. 1654: Correspondence between Pierre de Fermat and Blaise Pascal marking the beginning of probability calculation. Development of probability during the 19th century. Kolmogorov introduced the axiomatic approach in 1933. Abraham de Moivre and his contribution with “The Doctrine of Chances” in 1718. Probability theory was … Read more
IN BRIEF Historical link between music and mathematics since Antiquity. Pythagoras established mathematical principles in music, revealing the harmony of numbers. Rhythms and harmonies follow precise mathematical laws. Luthiers use mathematics for instrument design. Applications of algorithms in modern musical creation. Exploration of musical numbers and their impact on musical writing. Fractals and chaos theory … Read more
IN BRIEF Analytical Geometry: study of geometric figures using equations. Reduced equation of a line: y = mx + p, where m is the slope. Analysis of the line and the circle in an orthonormal coordinate system. Use of vectors to determine line equations. Study of the intersections between lines and circles. Properties of circles: … Read more
IN SHORT Adopt an effective learning method Participate actively in classes Repeat the fundamentals of mental arithmetic Break down mathematical problems Use graded exercises to progress Take the time to review lessons and exercises Work in collaboration with others Stay motivated and persevere Attend seminars to enrich your knowledge Be attentive and participate in class … Read more
IN BRIEF Origins : Ancient Greece, works of Euclid. Elements : Major publication by Euclid, serving as a geometric reference for over 2000 years. Axiom : Five fundamental principles form the basis of Euclidean geometry. Pythagorean theorem : Known to Babylonians and Egyptians long before Euclid. Evolution : New geometry developed in the 19th century … Read more
IN BRIEF Even numbers : integers that are multiples of 2. Odd numbers : integers that are not multiples of 2. An integer is even if it ends with 0, 2, 4, 6, or 8. An integer is odd if it cannot be divided by 2 without a remainder. The sum of several odd integers … Read more
IN BRIEF Use of mathematics to model complex systems. Neural networks and their mathematical foundation. Statistics to analyze and interpret data. Supervised learning and parameter tuning. Modern theories to predict chaotic phenomena. Applied mathematics in operations research. Influence on education and the teaching of mathematics. Optimization of learning methods through mathematics. Data security through mathematical … Read more
IN BRIEF Definition of topology: study of properties invariant under continuous deformation. Introduction to topological spaces and the notion of neighborhood. Importance of limits and separation between sets. Basic concepts: normality, open and closed. Practical applications in various disciplines. Resources: recommended books and exercises for learning. Topology is a fascinating branch of mathematics that looks … Read more
IN BRIEF Definition of a function: Relation between two sets with a unique correspondence. Differential calculus: Allows finding the derivative of a function to analyze its slope. Mathematical analysis: Deepens the understanding of continuity and the behavior of functions. Types of graphs: Learning expression through different visual representations. Practical applications: Used in various fields like … Read more