 | | |
| MATH0060-1 | Linear algebra and discrete structures
|
|
| Duration : | 50h Th, 50h Pr |
|
| Number of credits : |
|
|
| Lecturer : | Georges Hansoul |
|
Language(s) of instruction :
|
| French language |
|
Course contents :
|
| - Propositional logic (application : electric circuits) and first order logic (application : expert systems, formalisation of natural languages);
- Arithmetic (application : various position numeration systems);
- Naive set theory (including finite and infinite cardinal arithmetic);
- Introduction to finite structures such as groups or rings (application to cryptography);
- Classical combinatory, linear recurring equations, inclusion-exclusion principle.
- Linear algebra : Fundamental concepts are introduced at a medium abstraction level : vector spaces, linear mappings, rank, kernel, linear systems of equations, ... Matrix serve both as an example of vector space and as an useful tool to solve problems that arise within or around linear algebra. |
|
Learning outcomes of the course :
|
| Its objective is twofold :
- to give a first background for various mathematical topics closely linked with theoretical computer science,
- to improve correctness of inductive reasonning, and in particular to insure a good translation from natural to formal languages. |
|
Prerequisites and co-requisites/ Recommended optional programme components :
|
| None. |
|
Planned learning activities and teaching methods :
|
| The exercice lessons have a double objective : first illustrate the concepts and results of the theoretical part, and second provide applications of the theory. |
|
Mode of delivery (face-to-face ; distance-learning) :
|
| First semester, discrete mathematics and graph theory at the Institute of Mathematics, B37.
Second semester, linear algebra and linear recurring equations, also at the Institute of Mathematics, B37. |
|
Recommended or required readings :
|
| Two syllabi are available. |
|
Assessment methods and criteria :
|
| January, written examination on discrete structures, theory and exercices.
June :
a) for those who failed in January, written examination on discrete structures, theory and exercices;
b) written examination on linear algebra, exercices;
c) oral examination on linear algebra, theory.
September :
a) oral examination on discrete structures, theory and exercices,
b) oral examination on linear algebra, theory and exercices. |
|
Organizational remarks :
|
| None. |
|
Contacts :
|
| HANSOUL Georges
Institute of Mathematics - B37
Office 059
Grande Traverse, 12 - 4000 Liege
(Sart Tilman)
Phone : 04/366.94.69
Fax : 04/366.96.47
E-mail : G.Hansoul@ulg.ac.be
CAVUS Rukiye
Phone : 04/366.94.04
E-mail : R.Cavus@ulg.ac.be
ZIHINDULA Elie
Phone : 04/366.94.70
E-mail : Elie.ZihindulaMushengezi@ulg.ac.be |
|
