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.
Brief description of the course
Elements of logic, the main rules of logic.. Predicates and quantifiers. Methods of proof. Mathematical induction. Sets, set operations. Maps, 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. Solving recurrent relations. Generating functions. Graph terminology. Representing graphs and graph isomorphism. Connectivity of graphs, Euler and Hamilton paths. Planar graphs. Graph colouring. Trees. Applications of graphs.
Learning outcomes in the course
Upon completing the course the student:
- knows mathematical facts and is able to use methods in volume of a subject.