The main aim of the course is to train students abstract thinking and acquire basic knowledge in the field of classical combinatorial objects, non-classical combinatorial objects and graph theory. Students will learn to classify combinatorial problems and solve them using well-known combinatorial methods, through the acquisition of theoretical knowledge and solving practical examples. Through the learning of well-known concepts and theorems from graph theory, students will be able to set graphic formal models from other fields (e.g. computer science and transport engineering). Properties of graphs will be precisely mathematically proved, with the aim of further development of students skills for deriving proofs.

As outcome of the course, students will acquire basic knowledge in the field of classical combinatorial objects, non-classical combinatorial objects and graph theory, with their abstract thinking and the skills of proofing being greatly improved. Students will be able to recognize combinatorial objects and solve them by known methods, as well as to develop and analyse graph models in some other fields.

Lectures (Theoretical lectures). Logic relations, classical combinatorial objects (permutations, variations and combinations with and without repetition), partition sets, Stirling numbers, combinatorics on words, recurrent formulas, generative functions, basic concepts of graph theory, connection graphs, special classes of graphs, isomorphism of graphs, matrices neighborhoods, operations on graphs, trees, planar graphs (the fundamental theorem), Euler and Hamiltonian paths, Hamiltonian contours. Practice lectures (lab): In laboratory exercises adequate examples and tests from the theoretical lectures are done in order to exercise lectured theory where exercises contribute to understanding of the theory.

Lectures; Computing practice. Consultations. Lectures are dynamic and interactive. In lectures theoretical part of the course is presented accompanied by characteristic and representative examples in order to better understand the matter. In practice, which follows lectures, typical problems are solved and lectured theory is deepened. Besides lectures and practice, regular consultations and group consultations are also held. Part of the course, which is a logical unit, can be passed within the teaching process in the following 2 modules. The first module: Combinatorics. The second module: Graph theory.