Discrete Mathematics II

Course code

MLM6229.DT

old course code

Course title in Estonian

Diskreetne matemaatika II

Course title in English

Discrete Mathematics II

ECTS credits

3.0

Assessment form

assessment

lecturer of 2023/2024 Autumn semester

Not opened for teaching. Click the study programme link below to see the nominal division schedule.

lecturer of 2023/2024 Spring 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.

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:

- is able to solve some simpler recurrent equations;

- knows the basic rules of combinatorics, including the formulas for the number of permutations, binomial formulas and their applications;

- is able to transform the combinatorial problems using recurrent equations and solve the problems solving recurrent equation;

- knows the main types of graphs and is able to use them in order to describe practical situations.

- is able to solve some simpler recurrent equations;

- knows the basic rules of combinatorics, including the formulas for the number of permutations, binomial formulas and their applications;

- is able to transform the combinatorial problems using recurrent equations and solve the problems solving recurrent equation;

- knows the main types of graphs and is able to use them in order to describe practical situations.

Teacher

Tatjana Tamberg

Study programmes containing that course

Mathematics, Mathematical Economics and Data Analysis (MLMB/23.DT)

Mathematics, Mathematical Economics and Data Analysis (MLMB/22.DT)

Mathematics, Mathematical Economics and Data Analysis (MLMB/21.DT)

Mathematics, Mathematical Economics and Data Analysis (MLMB/20.DT)

Mathematics, Mathematical Economics and Data Analysis (MLMB/19.DT)

Mathematics, Mathematical Economics and Data Analysis (MLMB/18.DT)

Mathematics, Mathematical Economics and Data Analysis (MLMB/22.DT)

Mathematics, Mathematical Economics and Data Analysis (MLMB/21.DT)

Mathematics, Mathematical Economics and Data Analysis (MLMB/20.DT)

Mathematics, Mathematical Economics and Data Analysis (MLMB/19.DT)

Mathematics, Mathematical Economics and Data Analysis (MLMB/18.DT)