Logic anad Graphs

Garant předmětu:

Marie Demlová

Lecturer:

Alena Gollová

Tutor:

Matěj Dostál, Alena Gollová

Supervisor:

Department of Mathematics

Synopsis:

This course covers basics of mathematical logic and graph theory. Syntax and semantics of propositional and predicate logic are introduced. The importance of the notion of consequence and of the relationship between a formula and its model is stressed. Further, basic notions from graph theory are introduced.

Requirements:

None.

Syllabus of lectures:

Topics in propositional logic (approx. 4 weeks):

1. Formal language. The language of propositional logic.

2. Semantics and semantic entailment.

3. The resolution method in propositional logic.

4. Deriving conclusions (natural deduction).

Topics in predicate logic (approx. 4 weeks):

1. The language of predicate logic.

2. Semantics and semantic entailment in predicate logic.

3. The resolution method in predicate logic.

4. Reserve lecture.

Topics in graph theory (approx. 6 weeks):

1. Basic concepts of graph theory.

2. Trees and minimum spanning trees.

3. Acyclic graphs. Strong connectivity.

4. Euler graphs.

5. Colouring. Planar graphs.

6. Reserve lecture.

Syllabus of tutorials:

In the exercise classes students solve theoretical and algorithmic problems from logic and graph theory.

Students strenghten and extend their knowledge and skills obtained from the lectures.

Study Objective:

The aim of the course is to introduce students to the basics of mathematical logic and graph theory.

Study materials:

[1] M. Huth, M. Ryan: Logic in Computer Science: Modelling and Reasoning about Systems, Cambridge University Press, 2004.

[2] J. A. Bondy, U. S. R. Murty: Graph theory with applications. Elsevier Science Ltd/North-Holland, 1976.

Note:

Further information:

https://math.fel.cvut.cz/en/people/gollova/lgr.html

Time-table for winter semester 2024/2025:

	06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
Mon
Tue	roomT2:C4-365 Gollová A. 09:15–10:45 (lecture parallel1 parallel nr.101) Dejvice CvičebnaroomT2:C4-365 Gollová A. 11:00–12:30 (lecture parallel1 parallel nr.102) Dejvice CvičebnaroomT2:C4-363 Gollová A. 12:45–14:15 (lecture parallel1 parallel nr.107) Dejvice Cvicebna
Wed	roomT2:C4-365 Gollová A. 09:15–10:45 (lecture parallel1 parallel nr.106) Dejvice CvičebnaroomT2:C4-365 Gollová A. 11:00–12:30 (lecture parallel1 parallel nr.104) Dejvice Cvičebna
Thu	roomT2:C4-78 Dostál M. 09:15–10:45 (lecture parallel1 parallel nr.103) Dejvice T2:C4-78roomT2:C4-364 Dostál M. 11:00–12:30 (lecture parallel1 parallel nr.105) Dejvice CvicebnaroomT2:C4-365 Dostál M. 16:15–17:45 (lecture parallel1 parallel nr.108) Dejvice Cvičebna roomT4:D2-256 Gollová A. 14:30–16:00 (lecture parallel1) Dejvice Posluchárna 256
Fri	roomT2:C4-363 09:15–10:45 (lecture parallel1 parallel nr.109) Dejvice CvicebnaroomT2:D3-309 Gollová A. 11:00–12:30 (lecture parallel1) Dejvice T2:D3-309

Time-table for summer semester 2024/2025:

Time-table is not available yet

The course is a part of the following study plans:

• Cybernetics and Robotics 2016 (compulsory course in the program)
• Open Informatics - Computer Science 2016 (compulsory course in the program)
• Open Informatics - Internet of Things 2016 (compulsory course in the program)
• Open Informatics - Software 2016 (compulsory course in the program)
• Open Informatics - Computer Games and Graphics 2016 (compulsory course in the program)
• Open Informatics (compulsory course in the program)
• Medical electronics and bioinformatics (compulsory elective course)
• Open Informatics (compulsory course in the program)
• Open Informatics - Artificial Intelligence and Computer Science 2018 (compulsory course in the program)
• Open Informatics - Internet of Things 2018 (compulsory course in the program)
• Open Informatics - Software 2018 (compulsory course in the program)
• Open Informatics - Computer Games and Graphics 2018 (compulsory course in the program)
• Cybernetics and Robotics 2016 (compulsory course in the program)