Discrete Mathematics and Graphs - BE5B01DMG - AY 21/22
Czech Technical University in PragueFaculty of Electrical Engineering
Bachelor Degree in Electrical Engineering and Computer Science
Academic Year 2021/2022
Announcements:
- Students who received the assessments here (with points from Midterm+Homeworks)
Information on the Exams:
- Exam Modalities
- Exam period: January 10, 2022 - February 13, 2022
- Dates for the written exams:
- Wednesday 5 January, 16:00-18:00, T2:C2-82
- Monday 17 January, 9:00-11:00, T2:C3-51
- Friday 21 January, 9:00-11:00, T2:C3-51
- Thursday 27 January, 9:00-11:00, T2:C3-51
- Monday 7 February, 9:00-11:00, T2:C3-51
- Dates for the (optional) oral exams:
- Friday 7 January
- Friday 21 January
- Friday 28 January
- Friday 11 February
Contents and Materials:
Many thanks to Prof. Marie Demlova for generously sharing her notes with us.- Chapter 1. Logic
Propositional logic, predicate logic, quantifiers, interpretation.
Materials: Lect1, Ex1, Lect2, Ex2 (also see Section 2.3 here). - Chapter 2. Sets
Functions, operations on sets, countable and uncountable sets, equivalence relations, partial orders.
Materials: Lect3, Ex3, Lect4, Ex4. - Chapter 3. Arithmetic
Euclid algorithms, Diophantine equations, relation modulo n, operations on Zn.
Materials: Lect5, Ex5, Lect6, Ex6. - Chapter 4. Algebraic structures
Semigroups, groups, Lagrange theorem, order of an element, the Euler function, rings and fields.
Materials: Lect7, Ex7, Lect8, Ex8, Lect9, Ex9. - Chapter 5. Combinatorics
Combinations, variations, dispositions, Pascal triangle.
Materials: Lect10, Ex10. - Chapter 6. Graphs
Graphs and directed graphs, walks, reachable vertices, Euler and Hamiltonian graphs, strong connectivity, spanning trees.
Materials: Lect11, Ex11, Lect12, Ex12, Lect13, Ex13.
References:
- L.N. Childs, A Concrete Introduction to Higher Algebra, Springer.
- R. Johnsonbaugh, Discrete Mathematics, Prentice Hall.
- K. Rosen, Discrete Mathematics and Its Applications, McGraw-Hill.