2023-2024 / MATH0075-1

Discrete mathematics

Duration

30h Th, 20h Pr

Number of credits

 Master in mathematics (120 ECTS) (Even years, not organized in 2023-2024) 8 crédits 

Lecturer

Emilie Charlier

Language(s) of instruction

French language

Organisation and examination

Teaching in the first semester, review in January

Schedule

Schedule online

Units courses prerequisite and corequisite

Prerequisite or corequisite units are presented within each program

Learning unit contents

In this lecture we are concerned with the algebraic theory of commutative and non-commutative formal series. We then will study some applications as linear recurrence sequences, regular sequences or p-adic numbers...

Learning outcomes of the learning unit

The student will master fundamental notions seen during the lectures as well as the corresponding proofs. He will be able to present them clearly and succinctly. Also, he will be able to apply those notions in order to solve related problems.

Prerequisite knowledge and skills

We assume a good knowledge of the concepts of groups, rings, fields and vector spaces.

Planned learning activities and teaching methods

Theoretical lectures using "blackboard and chalk" or beamer, interacting with students. During exercises sessions, students are facing exercises that must be solved and situations that must be modeled on a computer.

Mode of delivery (face to face, distance learning, hybrid learning)

Face-to-face course


Additional information:

Lectures are mainly dedicated to theoretical aspects. Pratical sessions are devoted to solve exercises and to enlighten the concepts presented during the lecture.

Recommended or required readings

The lecture notes are available on eCampus.

Suggested readings are:

  • J. Berstel and C. Reutenauer. Non-commutative rational series with applications. Encyclopedia in Mathematics and its Applications, vol. 137, Cambridge University Press, Cambridge, 2011.
  • É. Charlier, C. Cisternino and M. Stipulanti. Regular sequences and synchronized sequences in abstract numeration systems. European Journal of Combinatorics 101 (2022) 103475.
  • A. Salomaa et Matti Soittola. Automata-Theoretic Aspects of Formal Power Series. Texts and Monographs in Computer Science, Springer-Verlag, New York-Heidelberg, 1978.
  • M.-P. Schützenberger. On the definition of a family of automata, Inf. Control 4 (1961) 245-270.

Exam(s) in session

Any session

- In-person

oral exam


Additional information:

The final examination is an oral one. focuses on the theory and its direct applications. The student might be asked to solve some exercises. Details about the examination will be precisely stated during the year.

Work placement(s)

Organisational remarks and main changes to the course

This course is organized on academic years starting on an even year : 2020-2021, 2022-2023, ...

Contacts

Émilie Charlier

Institute of Mathematics (B37)
Allée de la découverte 12
Sart Tilman, 4000 Liège
Tél. : 04 366.93.84
E-mail : echarlier@uliege.be

Association of one or more MOOCs