Foundations of Discrete Mathematics
Course code
MLM6219.DT
old course code
Course title in Estonian
Diskreetse matemaatika elemendid
Course title in English
Foundations of Discrete Mathematics
ECTS credits
3.0
Assessment form
assessment
lecturer of 2025/2026 Spring semester
Not opened for teaching. Click the study programme link below to see the nominal division schedule.
lecturer of 2026/2027 Autumn semester
Not opened for teaching. Click the study programme link below to see the nominal division schedule.
Course aims
To provide the basics of combinatorics and graph theory. To introduce the methods used in these fields with their applications.
Brief description of the course
General term of a sequence and recurrent equations for expressing the general of a sequence using previous terms. Solving of recurrent equations. Homogeneous and non-homogeneous recurrent equations, solving recurrent equations. The basics of counting. Pigeonhole principle: inclusion-exclusion. Permutations and combinations, their generalisations. Permutations and combinations with repetitions allowed. Binomial coeffcients. Binomial theorem and multinomial theorem. Generating permutations and combinations with the help of the computer. Combinatorial problems. Generating functions. Graph terminology. Representing graphs and graph isomorphisms. Connectivity of graphs, Euler and Hamilton paths. Planar graphs. Graph colouring. Cromatic number of a graph. Trees. Applications of graphs.
Learning outcomes in the course
Upon completing the course the student:
- proves easier facts about recurrent equations and binomial coefficients;
- solves some simpler recurrent equations;
- uses the basic rules of combinatorics, including the formulas for the number of permutations, binomial formulas and their applications;
- transforms the combinatorial problems using recurrent equations and solve the problems solving recurrent equation;
- distinguishes the main types of graphs and uses them in order to describe practical situations.
- proves easier facts about recurrent equations and binomial coefficients;
- solves some simpler recurrent equations;
- uses the basic rules of combinatorics, including the formulas for the number of permutations, binomial formulas and their applications;
- transforms the combinatorial problems using recurrent equations and solve the problems solving recurrent equation;
- distinguishes the main types of graphs and uses them in order to describe practical situations.
Teacher
Tatjana Tamberg
The course is a prerequisite
Study programmes containing that course