Mathematics 2
Objectives of the course program (competences):
Students should acquire the specified knowledge at a level that they can use when adopting the course programs for which they are a prerequisite.
Mastering the specified contents among students should improve logical thinking and reasoning, as well as advance abstract thinking and in general the types and qualities of thinking
Content of the course program:
Sets, operations with sets. Relations, equivalence relations, set factors and decompositions. Ordered sets. Networks and Boolean algebras.
Mappings and types of mappings. Equivalent sets. Cardinal numbers. Operations and algebraic structures with one and two binary operations. Natural numbers. Mathematical induction.
Integers. Binomial formula. Divisibility and elements of number theory. Congruences. One example of a field: The field of complex numbers.
Matrices and matrix operations. Determinants. Minors and algebraic complements. Nonsingular matrices. Concept of vector space and subspace. Linear dependence. Basis and dimension of vector spaces. Matrix rank. Elementary matrix transformations. Relationship between two bases.
Systems of linear equations and methods for their solution. Method of elimination of unknowns.
Kronecker-Capelli theorem.
Elements of analytical geometry in the space R3 and operations with vectors (scalar, vector product, mixed product of vectors). Equation of a line in a plane. Relations between lines. Equation of a plane in space. Relations of two planes. Equations of lines in space, relations of two lines in space, relations of a line and a plane in space. Equation of a circle, ellipse and parabola.
Learning methods: Oral presentation method, problem-based teaching method, technical aids method and independent work method
