The course has three main goals:To refresh, complement, and unify the students' knowledge of high school mathematics, To provide an introduction into selected topics from university level mathematics,To develop basic skills for writing mathematical proofs and solutions.

Lecture: theory, methods, examples. Solving exercises.

Selection of topics from the areas:                                          Sets and logicReal numbers and complex numbersEquations and inequalitiesFunctions   Polynomials                                                         Differential calculus                                          Integral calculus     Vectors and matricesCombinatorics and graph theory

High school mathematics

The final grade will be based on blackboard presentations and a written final exam. The date of the final exam will be fixed in coordination with students during the first lecture. If needed, one opportunity to retake the final exam will be given.

Assignments on the content of the course.

During the course, some time will be dedicated to solving exercises, which then will be presented by students at the blackboard.At the end of the course, a final exam will take place.For the exam, any external aids (written notes, printed materials, calculators, etc.) will not be allowed.In order to be graded, a student should take the exam and give at least one blackboard presentation.The pre-final grade in the range [0..100] will be calculated as follows:90% final exam,10% blackboard presentations.Then it will be translated into the final grade as follosw:Less than 55 ⟶ grade 5 (failing the course).Between 55 and 66 ⟶ grade 4.Between 66 and 77 ⟶ grade 3.  Between 77 and 88 ⟶ grade 2.  Above 88  ⟶ grade 1.For those who want to be graded, attendance is mandatory. (Only) one absence is possible.