Exercises: Moles, Combinatorics, and Large Numbers Now is the time to apply what you have learned with practical exercises that will help you master essential thermodynamic concepts, such as moles, combinatorics, and calculations with large numbers. If you haven’t done so already, I recommend reviewing the previous lessons, as they...
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...
The Intuitive Idea of Heat and Temperature The heat of coffee, the cold of an ice cube, and the functioning of a refrigerator share a key concept: heat and its relationship with temperature. In this class, let's explore how thermodynamics connects the intuitive with the scientific, through practical experiments and...
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...
