Useful Theorems for Probability Calculation SummaryThis class presents solved exercises demonstrating some useful theorems for probability calculation, including proofs and deductions. The exercises cover topics such as complementary probability, set inclusion, and event convergence. Completing these exercises will provide you with a solid foundation for further studying probability theory. LEARNING...
Factorization of Quadratic and 2n-Quadratic Polynomials Summary: In this class, we will review in detail the process of factoring quadratic polynomials and -quadratic polynomials , breaking them down into simple factors. The procedures will be mathematically developed, and practical examples will be shown. Learning Objectives Learn how to factor quadratic...
Practical Problems with Fundamental Probability Concepts Abstract In this class, we will review practical exercises such as the reliability of a control system, card game strategies, and probability calculations in everyday situations. The solutions to the problems are presented in video format, allowing you to strengthen your understanding and skills...
Completeness and Soundness in Propositional Logic SUMMARYThis class addresses the relationship between completeness and soundness in propositional logic. Although deduction techniques and semantics in propositional logic have been widely discussed, little attention has been paid to the relationship between these two facets. Soundness refers to the property of a logical...
Induction Proofs: Generalized Rules of De Morgan and Distribution SUMMARYThis class addresses the topic of induction proofs in mathematics and propositional logic. The two types of existing proofs are explained: internal or deductive proofs, which are based on the rules of logic, and external or metamathematical proofs, which are necessary...
Induction on the Complexity of Formulas SUMMARYIn this class, you will learn about a variant of mathematical induction, known as "induction on the complexity of expressions," which is very useful for proving properties in propositional logic. Through a simple example, the substitution theorem, you will see how this technique is...
Normal Forms and Their Properties SUMMARYPropositional logic is a fundamental tool in mathematics and computer science. In this class, an interesting and useful result related to normal forms will be presented. To achieve this, the concepts of literal, conjunctive normal form (CNF), and disjunctive normal form (DNF) will be defined....
Conditional Probability and Independence Between Events SummaryIn this session, we will explore the concept of conditional probability and the interaction between events. We will acquire the skills to calculate conditional probabilities and determine the dependence or independence between events. We will apply practical examples, such as the study of the...
Equation of the Line and Cartesian Systems Summary: In this class, we will cover the fundamentals of analytic geometry, showing how to represent points on a plane using coordinates and how to formulate the equation of the line from the slope and a given point. Key concepts such as the...
Bayes' Theorem and Compound Probability AbstractIn this class, two fundamental concepts in probability were discussed: conditional probability and compound probability. The difference between and was emphasized. The Compound Probability Theorem states that the probability of an event can be expressed as the sum of the conditional probabilities multiplied by the...
