470-2101/05 – Principles of Mathematics (ZMA)
| Gurantor department | Department of Applied Mathematics | Credits | 6 |
| Subject guarantor | RNDr. Pavel Jahoda, Ph.D. | Subject version guarantor | RNDr. Pavel Jahoda, Ph.D. |
| Study level | undergraduate or graduate | Requirement | Compulsory |
| Year | 1 | Semester | winter |
| | Study language | Czech |
| Year of introduction | 2024/2025 | Year of cancellation | |
| Intended for the faculties | FEI | Intended for study types | Bachelor |
Subject aims expressed by acquired skills and competences
Student gets the bysic knowledges and skills which are neresary for further studies at VSB-TUO during the course.
Students are able to evaluate the truth value of the logical statement, explain the difference between the basic numeric sets, edit the algebraic expression to describe the properties of functions, their domains, to quantify the functional values of elementary functions in the notable points and draw the graphs of these functions. In addition, the student is able to solve linear, quadratic, exponential, logarithmic and trigonometric equations and inequalities and to use this skills to solve elementary problems of analytic geometry.
Teaching methods
Tutorials
Summary
Precalculus is an advanced form of secondary school algebra. Precalculus are intended to prepare students for the study of calculus and includes a review of algebra and trigonometry, as well as an introduction to exponential, logarithmic and trigonometric functions, vectors, complex numbers and analytic geometry.
Compulsory literature:
R. G. Brown, D. P. Robbins: Advanced Mathematics (A Precalculus Course), Houghton Mifflin Comp., Boston 1989.
Libor Šindel: Principles of mathematics (The text is in electronic form).
Recommended literature:
Richard G. Brown, David P. Robbins, Advanced Mathematics a precalculus course
Additional study materials
Way of continuous check of knowledge in the course of semester
Students will solve practice examples during the exercises.
The condition for granting credit is active participation in the exercises, submission and defense of the assigned project and successful completion of the credit paper. For successfully defending the project, the student receives 6 points. It will be possible to get up to 24 points from the paper. To receive a credit, a student must defend his project and obtain at least 15 points.
E-learning
Basic materials are available on the educator's website: www.fei.vsb.cz/470/cs/osobni-stranky/jahoda/zam/zamKomb/index.html
and
www.fei.vsb.cz/470/cs/osobni-stranky/jahoda/zam/zamVMA/
Other requirements
The condition for granting credit is active participation in the exercises, submission and defense of the assigned project and successful completion of the credit paper. For successfully defending the project, the student receives 6 points. It will be possible to get up to 24 points from the paper. To receive a credit, a student must defend his project and obtain at least 15 points.
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
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.).
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction