IN BRIEF Introduction of Arabic numeration in the West during the Middle Ages. Significant inventions such as Indian arithmetic, algebra, and concepts of trigonometry. Stagnation of mathematical knowledge during the High Middle Ages. Works of mathematicians like Abu Al-Wafa, bringing innovative concepts. Dissemination of mathematical texts including The Elements of Euclid and other classical works. … Read more
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 calculus. Development of probabilities during the 19th century. Kolmogorov introduced axiomatic in 1933. Abraham de Moivre and his contribution with “The Doctrine of Chances” in 1718. Probability theory was systematized from … 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 in the design of instruments. Applications of algorithms in modern musical creation. Exploration of musical numbers and their impact on musical writing. Fractals and … Read more
IN BRIEF Analytic geometry: study of geometric figures using equations. Slope-intercept form 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 intersections between lines and circles. Properties of circles: equations … Read more
IN BRIEF Adopt an effective learning method Participate actively in classes Reiterate the basics of mental arithmetic Dissect mathematical problems Use graded exercises to progress Take 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 Advancing quickly … Read more
IN BRIEF Origins : Ancient Greece, works of Euclid. Elements : Major publication of Euclid, serving as a geometric reference for over 2000 years. Axiom : Five fundamental principles form the basis of Euclidean geometry. Pythagorean Theorem : Known to the Babylonians and Egyptians long before Euclid. Evolution : New geometry developed in the 19th … Read more
IN BRIEF Even numbers: integers that are multiples of 2. Odd numbers: integers that are not multiples of 2. A number is even if it ends in 0, 2, 4, 6, or 8. A number is odd if it cannot be divided by 2 without a remainder. The sum of several odd integers: even if … Read more
IN BRIEF Use of mathematics to model complex systems. Neural networks and their mathematical foundations. Statistics to analyze and interpret data. Supervised learning and parameter tuning. Modern theories to predict chaotic phenomena. Applied mathematics in operational research. Influence on education and mathematics teaching. Optimization of learning methods through mathematics. Data security via mathematical approaches. Mathematics … 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, opens, and closes. Practical applications in various disciplines. Resources: recommended books and exercises for learning. Topology is a fascinating branch of mathematics that examines … Read more