IN BRIEF Groups: A non-empty set equipped with an internal composition law, satisfying associativity and having an identity element. Rings: A set with two internal operations, addition and multiplication, adhering to specific algebraic properties. Fields: A commutative ring where every non-zero element has a multiplicative inverse. Algebraic structures: Fundamental in mathematics, they form the basis … Read more
IN BRIEF Zeno’s Paradox: Achilles and the tortoise illustrate the infinite. Russell’s Paradox: Highlights logical contradictions. The Liar Paradox: A statement that contradicts itself. The Barber Paradox: A classic example of paradoxical logic. The Missing Dollar Riddle: Raises questions about addition. Ellsberg’s Paradox: Reveals irregularities in probability choices. Hilbert’s Hotel: Exposes the properties of the … Read more
IN BRIEF Complex analysis: study area of complex numbers. Definition of a complex number: z = a + bi with a and b real, i imaginary unit. Visualization of complex numbers in the plane with coordinates. Operations on complex numbers: addition, subtraction, multiplication, etc. Basic concepts related to imaginary numbers and their importance in applied … Read more
IN BRIEF Differential calculus: study of derivatives to measure the change in a function. Integral calculus: understanding the concept of integral to determine areas under curves. For each function, it is possible to calculate derivatives and integrals using basic techniques. Geometric concepts such as areas, perimeters, and volumes are essential. The history of differential and … Read more
IN BRIEF Numerical simulations: computation processes on computers to model physical realities. Mathematical modeling: construction of models to represent complex systems. Mathematical analysis: evaluation and interpretation of simulation results. Practical applications: use in various fields, including pandemics and engineering. Technological evolution: computing transforms and improves the approach to applied mathematics. Numerical models: implementation of discretization … Read more
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 SHORT Definition: Study of queue management systems. Application areas: Use in various industrial sectors. Analytical models: Based on probability techniques. Objective: Optimize management and flow of customers. Queue systems: Analysis of behaviors and performances. Operations research: Integration of concepts into complex systems. Terminology: Kendall-Lee notation and other methods. The queueing theory is a field … Read more
IN BRIEF Optimization of physical and informational flows in the industry. Significant contribution to logistics and competitiveness. Application of applied mathematics for predictive models. Key role in addressing industrial problems. Use of artificial intelligence to enhance processes. Conceptual models to assist in decision-making. Issues and challenges in sectors such as automotive. Emergence of operations research … Read more
IN BRIEF Trigonometry: an essential tool for navigation and astronomy. Used to calculate distances between celestial bodies. Foundation of triangulation techniques in maritime and aerial navigation. Helps to predict movements of planets and satellites. Role in the design of astronomical instruments. Importance for studying trajectories in space. Useful for mapping and modern navigation. Practical applications … 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