The objective of this course is introducing students to basic combinatorics and discrete mathematical structures which they will later need to use in informatics. This includes foundations of set theory, basic methods in combinatorics and counting, concepts of probability theory, elementary number theory and graph theory.

Upon completing this course, students are expected to be able to work with finite and infinite sets and relations, use basic methods in combinatorics and notions of probability theory, learn elementary number theory with applications, and to understand and utilize concepts of graph theory. Finally, students should be enabled to apply the topics from this course in further studies, especially in informatics.

- Sets (basic operations, relations, cardinality of finite and infinite sets) - Counting (counting methods, binomial coefficients, permutations and combinations) - Introduction to probability (finite probability, union of events, independent events, conditional probability, random variables, expected value) - Elementary number theory (divisibility, prime numbers, congruences, applications in cryptography) - Graphs (terminology, special types of graphs, isomorphism, trees) - Game theory (introduction and examples)

in accordance with the lectures

defined by the curriculum

"Discrete Mathematics and Its Applications", 7th edition - K.H. Rosen, Monmouth University (2012), ISBN 0–07–338309–0 "Discrete mathematics: Introduction to combinatorics and graph theory - problem book" (in Serbian) - Д. Стевановић, М. Милошевић, В. Балтић (Друштво математичара Србије, Београд, 2004), ISBN 86–81453–52–1 Materials for lectures and tutorials (in Serbian): https://nastava.mas.bg.ac.rs/nastava/viewtopic.php?f=1288&t=9812

Total assigned hours: 60

New material: 10
Elaboration and examples (recapitulation): 10

Auditory exercises: 20
Laboratory exercises: 0
Calculation tasks: 10
Seminar paper: 0
Project: 0
Consultations: 0
Discussion/workshop: 0
Research study work: 0

Review and grading of calculation tasks: 0
Review and grading of lab reports: 0
Review and grading of seminar papers: 0
Review and grading of the project: 0
Test: 6
Test: 0
Final exam: 4

Activity during lectures: 0
Test/test: 50
Laboratory practice: 0
Calculation tasks: 0
Seminar paper: 0
Project: 0
Final exam: 50
Requirement for taking the exam (required number of points): 50

"Discrete Mathematics and Its Applications", 7th edition - K.H. Rosen, Monmouth University (2012), ISBN 0–07–338309–0; "Discrete mathematics: Introduction to combinatorics and graph theory - problem book" (in Serbian) - Д. Стевановић, М. Милошевић, В. Балтић (ДМС, Београд, 2004), ISBN 86–81453–52–1; Materials for lectures and tutorials (in Serbian): https://nastava.mas.bg.ac.rs/nastava/viewtopic.php?f=1288&t=9812