Duration
15h Th, 10h Pr, 25h Proj.
Number of credits
| Bachelor of Science (BSc) in Engineering | 3 crédits |
Lecturer
Language(s) of instruction
French language
Organisation and examination
Teaching in the second semester
Schedule
Units courses prerequisite and corequisite
Prerequisite or corequisite units are presented within each program
Learning unit contents
- Motivations: reasoning under uncertainties, modeling of stochastic systems, data analysis.
- Basics: random experiment, events, Kolmogorov axioms, conditional probability, Bayes theorem, independence, interpretations of the notion of probability.
- Discrete and continuous random variables: probability distribution, repartition function, density, expectation, variance, moments, characteristic and generating functions, usual distributions, functions of a random variable.
- Pairs and vectors of random variables: joint, marginal, and conditional distributions, conditional expectation and variance, independence, covariance/correlation, functions of random variables, linear and nonlinear regression.
- Convergence of sequences of random variables, central limit theorem, laws of large numbers.
- Notion of random function.
Learning outcomes of the learning unit
The student shall be able to apply probabilistic methods to problems of reasoning under uncertainty, by being able to model them and identify the main resolution steps. He will also be knowledgeable about the main analytical and computational techniques useful to compute numerical solutions.
Prerequisite knowledge and skills
Calculus, algebra, geometry, and elements of computer science and applied mathematics.
Planned learning activities and teaching methods
The course is composed of about 10 hours of theoretical lectures, 10 hours of classroom exercises, and 10 hours of assistance to the realization of practical projects with the computer.
Mode of delivery (face-to-face ; distance-learning)
Face-to-face.
Recommended or required readings
The course notes, slides, and exercise notes will be available on the course's webpage at the beginning of the semester: http://www.montefiore.ulg.ac.be/~sacre/MATH0062/.
Assessment methods and criteria
The assessment is composed of two grades: a grade for the personal projects (approximately 20% of the final grade) and a grade for the written exam covering theory and exercises (approximately 80% of the final grade).
The projects and the written exam are mandatory. An absence for one of these parts will result in an absence for the course.
Work placement(s)
Organizational remarks
Contacts
Lecturer: Pierre Sacré (p.sacre@uliege.be).
Webpage: http://www.montefiore.ulg.ac.be/~sacre/MATH0062/.
Adaptation of teaching commitments following the COVID-19 pandemic for the May-June 2020 session
Teaching methods implemented : distance-learning
Lectures are pre-recorded and posted online progressively on eCampus.
Practice sessions are replaced by detailed solutions of the exercises. The teaching team is available during and after the session to answer questions on the exercises.
Homework are submitted online on the Montefiore submission platform.
All students are encouraged to ask short questions via the eCampus forum and to request on-demand videoconferences for more complex questions.
Assessment subjects
The assessment will be about all the topics covered during the lectures and the lab/homework sessions as initially planned.
Assessment methods
The assessment will be organized as an open-book online test on eCampus. The test will be made available according to the date and time provided for in the examination schedule. Students will need to complete the test within the set deadlines.
The test will mainly consist of true/false questions, multiple choice questions, numeric questions, and short answer questions.
A blank test will be organized in mid-May to identify potential logistic problems and to help student familiarize them self to this new type of examination.
Contacts
Pierre Sacré (p.sacre@uliege.be). http://www.montefiore.ulg.ac.be/~sacre/MATH0062/.
Adaptation of teaching commitments following the COVID-19 pandemic for the Aug-Sept 2020 session
Assessment subjects
See adaptation of teaching commitments following the COVID-19 pandemic for the May-June 2020 session.
Assessment methods
See adaptation of teaching commitments following the COVID-19 pandemic for the May-June 2020 session.