Duration
30h Th, 20h Pr
Number of credits
Master in mathematics (120 ECTS) (Even years, not organized in 2023-2024) | 8 crédits |
Lecturer
Language(s) of instruction
French language
Organisation and examination
Teaching in the first semester, review in January
Schedule
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