Introduction to University Mathematics (5cr)

Objectives

After the course, the student understands the basic concepts of mathematics and is able to apply them to solving simple mathematical problems. He knows the basics of set theory as well as the basic properties of functions. The student is familiar with some of the proof methods used in mathematics. After completing the course, students will have sufficient prerequisites for the first basic courses in mathematics and statistics.After completing the course, the student willbe able to handle expressions and reinforce solving skills for equations, inequalities, and systems of equations.be able to investigate properties of geometric lines computationally using coordinates of points and equations of linesbe familiar with the most important real functions and their properties.understand the concept of derivatives and apply key rules of differentiationbe able to apply derivatives in determining the rate of change of function values and in finding extreme values of functionsunderstand the concept of the integral function and be able to integrate common functionsunderstand the concept of the definite integral and to be able to apply it in various applications

Content

Basic Concepts of Mathematics (common section for everyone)Numbers and EquationsFunctionsFundamentals of Set TheoryBasic Concepts of Propositional and Predicate LogicThe student chooses at least two sections from the following:Basic Concepts of Plane GeometryBasic Concepts of Discrete Mathematics (Number Theory and Algorithms)Basic Concepts of Analysis (Derivative and Integral)Basic Concepts of Statistics (Statistics and Probability)

Prerequisites

No prerequisities.

Further information

Optional sections have the following recommendations:For degree programs in engineering, it is advisable to choose Basic Concepts of Analysis.For the degree program in computer science, it is recommended to choose Basic Concepts of Discrete Mathematics.For students in the statistical data analysis study track, it is advisable to choose Basic Concepts of Statistics.In drop-in clinics, the focus is on opening up the mathematical content of the course and related thought processes. At the beginning of the drop-in clinics, the key concepts and formulas of the topic are covered, after which exercises are solved together or independently based on questions from students. Drop-in clinics are optional. In mathematics, practice makes perfect, so a significant number of exercises are solved during the course.The course uses instructional videos available on the internet, enabling independent study. Moodle is used for exercises, making it possible to complete the course through distance learning. The course is suitable for reinforcing skills in high school mathematics or supplementing skills in short mathematics. Partial completions must be done within the same academic year.This course belongs to the SEFI 0 level of engineering mathematics.