Topics covered in the course:
- Repetition of selected topics of high school mathematics. Functions, their definition, basic properties, basic elementary functions and their properties. Solving selected types of equations and inequalities.
- Basics of mathematical logic, statements, logical conjunctions, quantifiers, quantified statements and their negations.
- Mathematical proofs. Proof - direct, indirect, by contradiction, strong and weak induction. Application of these proof techniques to the presented problems by students.
- Basics of theoretical arithmetic, set of natural, integral, rational, real and complex numbers. Operations on these sets.
- Basic skills necessary for studying mathematical analysis and linear algebra (for example, calculating the determinant, recognizing subspaces in different vector spaces, operations with polynomials and their decomposition into partial fractions).
- Sets, relations, set operations, set cardinality, countable and uncountable sets, continuum hypothesis.
- Geometry. Analytical geometry in affine space, lines, planes, quadrics and their relative position.
- Space will be left for the study of mathematical topics currently needed to successfully master the studies (compensation of differences in knowledge from high school, if necessary additional explanations of difficult topics discussed in other mathematical subjects, etc.).
- Repetition of selected topics of high school mathematics. Functions, their definition, basic properties, basic elementary functions and their properties. Solving selected types of equations and inequalities.
- Basics of mathematical logic, statements, logical conjunctions, quantifiers, quantified statements and their negations.
- Mathematical proofs. Proof - direct, indirect, by contradiction, strong and weak induction. Application of these proof techniques to the presented problems by students.
- Basics of theoretical arithmetic, set of natural, integral, rational, real and complex numbers. Operations on these sets.
- Basic skills necessary for studying mathematical analysis and linear algebra (for example, calculating the determinant, recognizing subspaces in different vector spaces, operations with polynomials and their decomposition into partial fractions).
- Sets, relations, set operations, set cardinality, countable and uncountable sets, continuum hypothesis.
- Geometry. Analytical geometry in affine space, lines, planes, quadrics and their relative position.
- Space will be left for the study of mathematical topics currently needed to successfully master the studies (compensation of differences in knowledge from high school, if necessary additional explanations of difficult topics discussed in other mathematical subjects, etc.).