Mathematical modeling

This module gives an introduction to operations research and Markov chains.
The objectives are:

Review matrix calculus,
Learn the notion of model and how to use some mathematical models: linear optimization, Markov chain...

Linear algebra, vector functions of one real variable, discrete and continuous probabilities, ...

Part 1: Matrix calculation and operations research (3h CM 8h TD 6h TP)
Chapter 1: Reminders on matrix calculation

Sum, product and matrix invertibility
Determinant, rank, trace
Eigenvalues, eigenvectors, diagonalization

Chapter 2: Operations research (OR) and reminder on matrices.
Part 2: Markov chains (6h CM 12h TD)
Chapter 1: Markov definition and property
Chapter 2: Representation
Chapter 3: Asymptotic behavior
Chapter 4: Reach time study
Grading:
Part 1: Matrix computation and operations research

Several pts of measurement during the semester (written, oral..) (coef. 1)
Written test of 1h30 at the end of this part: matrix calculation (on machine, 30 min., coef. 0.7) and OR (1h, coef. 1.3)

Part 2: Markov Chains

Several pts of measurement during the semester (written, oral..) (coef. 1)
Written 1h30 in exam period (coef. 2)


"Philosophy of TDs" :
Part 1: Matrix calculation and operational research

TDs aim to teach students to model and solve various problems.

Part 2: Markov chains

The aim is to teach students to model and solve different problems, and to learn how to manipulate Markov chains from a theoretical point of view.

"Philosophy of the practical sessions:
Part 1: Matrix calculation and operations research

More theoretical focus on matrix manipulation.
The practical sessions operate in two modes: for students familiar with these concepts, the machine exercises are to be done asynchronously; for those "discovering" the subject, the practical sessions will take place face-to-face.

Part 2: Markov chains

No practical exercises associated with this part.

"Project philosophy":
Part 1: Matrix calculation and operations research

Present a problem that can be modeled within the framework of the course, to force students to see that mathematics often appears in everyday life.

Part 2: Markov Chains

Present a problem that can be modeled within the framework of the course to force students to see that mathematics often appears in everyday life.


Assessment methods for the module:

These are detailed in the "Assessment methods" section below.
However, if it is not possible to take the planned examination papers (ES or ET) in the classroom for health reasons, these papers will be replaced by distance projects.

Applied mathematics