Discrete Mathematics and Graphs

Czech Technical University in Prague
Faculty of Electrical Engineering
Bachelor Degree in Electrical Engineering and Computer Science
Academic Year 2018/19

Announcements:

  • NEW!!! The pretermin and the Midterm of Thursday 10 January 2019 will be in classroom T2:A4-203a.
    Students who want to attend such exam need to send me an email, specifying if they wish to attend the exam or the Midterm.

  • You can find the results of the Midterm here.
  • For those who didn't pass the Midterm, there is going to be a second possibility at the end of the semester, in Week13.
    In order to be admitted to such Midterm, you will need to bring me your solutions of ALL the exercises of Tutorials 1, 2, 4, 5, 6.

Information on the Exams:

  • Exam Modalities.
  • The second possibility to take the Midterm will be on Thursday, January 10 from 14:00 to 14:45 in classroom T2:A4-203a.
  • There will be a pretermin written exam on Thursday, January 10 from 14:00 to 16:00 in classroom T2:A4-203a.
    There will be the possibility to take the oral exam and see the results on Friday 11 January.
  • The written exams will be (with meeting to see the results and take the oral exam on the subsequent day, or in the afternoon):

    • Monday 21 January, from 9:00 to 11:00 in classroom T2:C3-51
    • Monday 28 January, from 9:00 to 11:00 in classroom T2:C3-51
    • Monday 04 February, from 9:00 to 11:00 in classroom T2:C3-51
    • Monday 11 February, from 9:00 to 11:00 in classroom T2:C3-51

Contents and Materials:

Many thanks to Prof. Marie Demlova for generously sharing her notes with us.
  1. Logic: Propositional logic, predicate logic, quantifiers, interpretation.
    Materials: Lect1, Ex1, Lect2, Ex2.
  2. Sets: Operations on sets, countable and uncountable sets, binary relations, equivalence relations and partial orders.
    Materials: Lect3, Ex3, Lect4, Ex4.
  3. Arithmetic: Euclid algorithms, Diophantine equations, relation modulo n, operations on Zn.
    Materials: Lect5, Ex5, Lect6, Ex6.
  4. Algebraic structures: semigroups, groups, Lagrange theorem, order of an element, the Euler function, rings and fields.
    Materials: Lect7, Ex7, Lect8, Ex8, Lect9, Ex9, Syllabus.
  5. Combinatorics: permutations, variations, combinations, the Binomial Theorem and Pascal triangle.
    Materials: Lect10, Ex10.
  6. Graphs: (directed) graphs, walks, reachable vertices, Euler and Hamiltonian graphs, strong connectivity, spanning trees.
    Materials: Lect11, Ex11, Lect12, Ex12, Lect13, Ex13, Syllabus.
Here, you may find a sample of exams:

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.