Discrete Mathematics and Graphs - BE5B01DMG

Czech Technical University in Prague
Faculty of Electrical Engineering
Bachelor Degree in Electrical Engineering and Computer Science
Academic Year 2020/2021

Announcements:

  • NEW!!! Exam dates available. More details are on Teams.
  • Updated information on Midterm and homeworks (see the Exam Modalities).
  • The Course will be taught via Microsoft Teams.

Information on the Exams:

  • Exam Modalities.
  • Exam period: January 11, 2021 - February 14, 2021.
  • There will be 6 written exams in the exam period (check in KOS for details):

    • Wednesday 6 January (Pretermin)
    • Monday 11 January
    • Monday 18 January
    • Monday 25 January
    • Monday 1 February
    • Monday 8 February
  • Dates for the (non mandatory) oral exam:

    • Tuesday 12 January
    • Tuesday 19 January
    • Tuesday 26 January
    • Tuesday 2 February
    • Tuesday 9 February

Contents and Materials:

Many thanks to Prof. Marie Demlova for generously sharing her notes with us.
  1. Chapter 1. Logic
    Propositional logic, predicate logic, quantifiers, interpretation.
    Materials: Lect1, Ex1, Lect2, Ex2.
  2. Chapter 2. Sets
    Functions, operations on sets, countable and uncountable sets, equivalence relations, partial orders.
    Materials: Lect3, Ex3, Lect4, Ex4.
  3. Chapter 3. Arithmetic
    Euclid algorithms, Diophantine equations, relation modulo n, operations on Zn.
    Materials: Lect5, Ex5, Lect6, Ex6.
  4. 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.
  5. Chapter 5. Combinatorics
    Combinations, variations, dispositions, Pascal triangle.
    Materials: Lect10, Ex10.
  6. 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.
Sample of exams (will be added later):

References:

  • L.N. Childs, A Concrete Introduction to Higher Algebra, Springer.
  • R. Johnsonbaugh, Discrete Mathematics, Prentice Hall.
Responsible person: doc. RNDr. Martin Bohata, Ph.D.