Course Overview

The joint development of areas such as discrete mathematics, probability, operational research and computer theory is continuous and relevant. The solution of theoretical and applied problems in these areas can be given in terms of a probabilistic modeling that arises from physics as well as the analysis of engineering systems or areas such as economics, biology, engineering, neuroscience. The tools used in such modeling include Markov chains, martingales, stochastic optimization, coupling and combinatorics.

Learning Achievement

Introduce and apply probability topics such as Markov chains, coupling and Poisson approaches through concrete examples such as those from the stochastic models for information theory, engineering, combinatorics, biology, neuroscience and other areas of application of Probability and Stochastic Processes.

Competence

Course prerequisites

Grading Philosophy

The evaluation will consist of the score’s average of tests and lists of exercises.

Course schedule

1. Discrete Probability Models; 2. Markov chains; 3. Recurrence and ergodicity; 4. Coupling and limiting behavior; 5. Martingales; 6. Renewal processes; 7. Contemporary Topics: Variable Range, Poisson Approximations, Reliability Theory, and Queue Theory

Course type

Online Course Requirement

Instructor

Fabio Prates Machado, Luiz Renato Goncalves Fontes, Miguel Natalio Abadi

Other information

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