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Discrete Mathematics 2 - course description

General information
Course name Discrete Mathematics 2
Course ID 11.1-WK-MATEP-DM2-S22
Faculty Faculty of Exact and Natural Sciences
Field of study Mathematics
Education profile academic
Level of studies First-cycle studies leading to Bachelor's degree
Beginning semester winter term 2022/2023
Course information
Semester 4
ECTS credits to win 5
Available in specialities Mathematical computer science
Course type optional
Teaching language english
Author of syllabus
  • dr hab. Ewa Drgas-Burchardt, prof. UZ
  • dr hab. Elżbieta Sidorowicz, prof. UZ
Classes forms
The class form Hours per semester (full-time) Hours per week (full-time) Hours per semester (part-time) Hours per week (part-time) Form of assignment
Lecture 30 2 - - Exam
Class 30 2 - - Credit with grade

Aim of the course

Understanding advanced concepts of discrete mathematics from both theoretical and algorithmic perspectives.

Prerequisites

Discrete Mathematics 1

Scope

Lecture/classes:

  1. Selected graph classes: interval graphs, k-trees, chordal graphs, edge graphs, and their properties.
  2. Various types of domination in graphs.
  3. Directed graphs, definitions, and notations.
  4. Strongly connected, transitive, and acyclic directed graphs, their properties.
  5. Selected algorithms for directed graphs.
  6. Definition of a matroid. Examples and basic properties.

 

Teaching methods

Lecture: conventional, conversational.

Classes: classical problem-solving method.

Learning outcomes and methods of theirs verification

Outcome description Outcome symbols Methods of verification The class form

Assignment conditions

Conditions for passing classes and lectures:

  1. Checking students' level of preparedness and their activity during exercises.
  2. A test with tasks of varying difficulty levels, allowing assessment of whether and to what extent a student has achieved the mentioned learning outcomes, mainly in terms of skills and competencies.
  3. Conversation during the lecture to verify higher levels of learning outcomes in terms of knowledge and skills.
  4. Exam. 

The final grade for the course consists of the exercise grade (50%) and the lecture grade (50%). The condition for passing the course is obtaining positive passing grades for both exercises and the lecture.

Recommended reading

  1. J. Bang-Jensen, G.Gutin, Digraphs, Theory and Algorithms, 2001.
  2. A. Brandstadt, V.B. Le, J.P.Spinrad, Graph Classes: a survey, SIAM 2004
  3. R. Distel, Graph Theory, Springer-Verlag, New York 1997
  4. D. J. A. Welsh, Matroid theory, Academic Press, Inc., New York, 2010.

Further reading

H. L. Bodlaender, A partial k-arboretum of graphs with bounded treewidth,Theoretical Computer Science 209 (1998) 1-45.

Notes


Modified by dr hab. Elżbieta Sidorowicz, prof. UZ (last modification: 12-01-2024 18:36)