Duration
30h Th, 20h Pr
Number of credits
| Master in mathematics, research focus (Even years, organized in 2024-2025) | 8 crédits | |||
| Master in mathematics, teaching focus (Even years, organized in 2024-2025) | 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 course we focus on the algebraic theory of commutative and non-commutative formal series. We then will study some applications such 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. They will be able to present them clearly and succinctly. Also, they 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 with the traditional "blackboard and chalk" or beamer, interacting with students. During exercises sessions, students face exercises that must be solved and situations that must be modeled on computers.
Mode of delivery (face to face, distance learning, hybrid learning)
Blended learning
Further information:
Lectures are mainly dedicated to theoretical aspects. Pratical sessions are devoted to solve exercises and to enlighten the concepts presented during the lecture.
Course materials and recommended or required readings
Platform(s) used for course materials:
- eCampus
- MyULiège
Other site(s) used for course materials
- Personal website (https://www.manon-stipulanti.be/)
Further information:
Lecture notes are currently not available.
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
written exam ( open-ended questions ) AND oral exam
Written work / report
Further information:
The final examination is an oral one. It 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, etc.
Contacts
Manon Stipulanti
Institute of Mathematics (B37)
Allée de la Découverte 12
Sart Tilman, 4000 Liège
Email: m.stipulanti@uliege.be