IN BRIEF Definition of scientific notation: expressing very large or very small numbers. Facilitates comparison and reading of numeric values. Allows determining the order of magnitude of a number by the power of 10. Writing a number in the form of a product of a decimal value and a power of 10. Used for estimates … Read more
IN BRIEF Interactions between mathematics and physical sciences. Use of statistical analysis in genetics. Relationship of mathematics with human sciences via statistics. Mathematical models in all scientific fields. Mathematics as the foundation of other disciplines. Expansion of the scope of sciences by mathematicians. Examples of practical applications in various industrial sectors. Mathematics plays a central … Read more
IN BRIEF Major impact of mathematics on the economy and finance. High recruitment of mathematicians in the financial sector. Mathematical models for financial risk assessment. Steady interest in mathematical finance since economic crises. Essential mathematical tools for economists. Application of applied mathematics to optimize economic decisions. Role of mathematics in the modernization of financial practices. … Read more
IN SHORT Mathematics: a blend of science and art. Philosophy influences the perception of mathematics. Mathematics as thought of structures according to Alain Badiou. Ambiguous relationships between mathematics and philosophy. Creativity and freedom in mathematical processes. Debate on the existence of an infinity in mathematics. Study of crucial theorems and their impact on the world. … Read more
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