Discrete Mathematics

Course code

MLM6202.DT

old course code

MLM6202

Course title in Estonian

Diskreetne matemaatika

Course title in English

Discrete Mathematics

ECTS credits

5.0

approximate amount of contact lessons

56

Teaching semester

autumn

Assessment form

Examination

lecturer of 2019/2020 Spring semester

õppejõud on määramata

lecturer of 2020/2021 Autumn semester

lecturer not assigned

Course aims

Focus subject in the mathematics and computer science curricula. To teach students to follow the correctness of proofs, to introduce the main results of discrete mathematics and their applications, to create the bases for the acquisition of other mathematical and computer science subjects, in particular of discrete probability theory.

Brief description of the course

Elements of logic. Predicates and quantifiers. The main rules of logic. Methods of proof. Mathematical induction. Sets, set operations. Functions, relations and their properties. Cardinality of sets and enumerable sets. The basics of counting, inclusion-exclusion. Permutations and combinations, their generalisations. Binomial theorem and multinomial theorem. Discrete probability. Solving recurrent relations. Generating functions. Graph terminology. Representing graphs and graph isomorphisms. Connectivity of graphs, Euler and Hamilton paths. Planar graphs. Graph colouring. Trees. Applications of graphs.

Independent work

Acquiring of the theory, solving problems

Learning outcomes in the course

Knows mathematical facts and is able to use methods in volume of a subject.

Assessment methods

Two in-class tests (2*20 points) and two individual home tests (2*20 points). In order to qualify to sit the examination a minimum of 10 points is needed. The examination (50 points) comprises an oral (presentation of two topics) and written (test) section.

Teacher

lekt Anna Šeletski

The course is a prerequisite

Replacement literature

Graham, R. L.; Knuth, D. E.; Patashnik, O. 1998 Concrete mathematics. A Foundation for Computer Science: 2nd ed. New-York: Addison-Wesley (Moskva: Mir vene k.);

Redi, E. 2009 Diskreetne matemaatika: Õppevahend (käsikiri, kättesaadav IVA õpikeskkonnas);

Rosen, K. H. 1995 Discrete Mathematics and its applications. New York: McGraw-Hill.

Redi, E. 2009 Diskreetne matemaatika: Õppevahend (käsikiri, kättesaadav IVA õpikeskkonnas);

Rosen, K. H. 1995 Discrete Mathematics and its applications. New York: McGraw-Hill.