Course: Mathematics

ECTS credits: 6

Language: Croatian

Duration: 1 semester

Status: type D1 – mandatory course for the students of the main study

Method of teaching:

Prerequisite:

Assessment:

Course description: 1. Set, element of set, describing sets. Finite set, infinite set, countable set. Cardinal number. set equality, empty set, universal set. Subset, power set. Set operations, union of sets, intersection of sets, complement of a set, difference of sets. Ordered pair, Cartesian product.

2. Relation. Binary relation, proprties of binary relations. Equivalence relation, equivalence class. Ordering relation. Partial order, infimum, supremum, minimum, maximum. Function, domain, codomain, image of a function. Properties of functions, injection, surjection, bijection. Permutation, composition of functions, inverse function. Power, polynom, exponential function, lagarithmic function.

3. Natural numbers. Mathematical induction. Recurrences. Linear recurrences with constant coefficients.

4. Linear algebra. Vector space. Vectors, Metric, distance vector. Matrix. null matrix, unit matrix, diagonal matrix, triangular matrix. Addition, subtraction, scalar multiplication, transposed matrix, matrix product. Matrix reduced form. Inverse matrix. System of linear equations. Gauss-Jordan method for solving systems of linear equations.

5. Graph. Graph definition, graph drawing, vertex of graph, edge. Incidence matrix. Degree of a vertex of a graph. Path on a graph, graph cycle. Connected graph, acyclic graph. Planar graph, Euler characteristic. Eulerian path, Eulerian cycle, Eulerian graph. Hamiltonian path, Hamiltonian cycle, Hamiltonian graph. Tree, subtree.

Course objectives: After attendance lectures and after passing the exam students will understand parts of the mathematical analysis and vector spaces, the term of the real number, and functions. They will also understand procedures for solving systems of linear equations.

Quality check and success of the course: written and oral exam

Reading list:

D. Veljan, Kombinatorna i diskretna matematika, Algoritm, Zagreb 2001.

N. Elezović, Linearna algebra, Element, Zagreb 2003.

P. Javor, Matematičke analize, Element, Zagreb 2001.

B. Tepeš, Predavanja i vježbe iz kombinatorika i grafova, Faculty of Humanities and Social Sciences, Zagreb 2007.