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 2020/2021  Autumn semester
õppejõud on määramata
lecturer of 2020/2021  Spring 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.