SYLLABUS
COURSE TITLE
Faculty/Institute
COURSE CODE
DEGREE PROGRAMME
FIELD OF STUDY
Computer Science
COURSE FORMAT
YEAR AND SEMESTER
Name of the teacher
Discrete Mathematics
Mathematics and Natural Sciences/ Institute of
Computer Science
Degree LEVEL
1
Forma studiów/
STUDY MODE
Full time
year I, semester I
Maria Kwaśnik, DSc, PhD
COURSE OBJECTIVES
The purpose of the course is to provide the students with several concepts and methods of the
number theory, graph theory and their applications in engineering and computer science.
PREREQUISITES
High school course in mathematics.
LEARNING OUTCOMES
KNOWLEDGE:
Students are supposed to know how to construct mathematical
models for several technical problems.
COURSE ORGANISATION –LEARNING FORMAT AND NUMBER OF HOURS
Lecture - 30 hours
Classes – 30 hours
COURSE DESCRIPTION
Theme of the lectures and classes:
Relations: types, algebraic and geometric interpretations, ordered relations, Hasse diagrams.
Recurrence relations: creating functions, the Fibonacci numbers, the Lucas numbers and their
several interpretations. The ”floor” and “ceiling” operations. Methods of theorem proving.
Boolean algebra. Selected topics in a graph theory: basic definitions and notions,
characterization of trees, vector vacuum of a graph, planarity of graphs, Hamiltonian and
Eulerian cycles. Edge – and vertex colourings of graphs: chromatic number, chromatic index,
map colour theorem, four – colour problem. Independence theory in combinatorics. Kernels
and Grundy function in directed digraphs. Flow networks. Applications.
METHODS OF INSTRUCTION
REQUIREMENTS AND ASSESSMENTS
GRADING SYSTEM
Lectures, classes and consultation hours
CLASSES: Two mid-term written tests.
Lecture: Written exam.
TOTAL STUDENT WORKLOAD
NEEDED TO ACHIEVE EXPECTED
LEARNING OUTCOMES EXPRESSED
IN TIME AND ECTS CREDIT POINTS
LANGUAGE OF INSTRUCTION
INTERNSHIP
MATERIALS
Lecture – 30 hours
Classes – 30 hours
ETCS – 5
Polish, English
PRIMARY OR REQUIRED BOOKS/READINGS:
1. V. Bryant, Aspects of combinatorics, Cambridge
University Press 1993 (or WNT Warszawa 1997).
2. R. Diestel, Graph Theory, Springer Verlag, New
York 1997.
3. K. A. Ross, Ch. R. B. Wright, Discrete
Mathematics, Prentice Hall Inc., 1992 (or PWN
Warszawa 1996).