Literature recommended by individual subjects during the whole bachelor study.
State examination for the completion of a bachelor's degree in teacher education in combination with informaticsInformatics
1. Data types in the Scratch environment.
2. New (custom) blocks in the Scratch environment.
3. Using text files in the Scratch environment.
4. Multiple characters in a Scratch environment.
5. Keyboard and mouse events in the Scratch environment.
6. Advanced Scratch environment options, custom variables.
7. Working with the field. Associative fields. (Python)
8. Characteristics of object-oriented programming. Classes. Inheritance. (Python)
9. Characteristics and use of files. Text files and ways to work with them. (Python)
10. Working with graphic information. Working with the tkinter module. (Python)
11. Turtle graphics. Recursion. Working with the turtle module. (Python)
12. Dynamic data structures.
13. Representation of sets.
14. Finding information in tables
15. Sorting algorithms.
Didactics of informatics
1. Teaching informatics at primary and secondary schools. Basic school documents. General and partial educational goals. Facts, concepts, generalizations.
2. Taxonomy of educational goals. Significance of taxonomies, levels of cognitive taxonomy (Bloom).
3. Preparation of a lesson for work with a spreadsheet editor at elementary school.
4. Preparation of a lesson on security in high school.
5. Children's programming languages. Features of a programming language that is suitable for teaching programming to students at the 2nd level of elementary school. Comparison Karel, Scratch.
6. Digital technologies in teaching.
7. E-learning. Advantages and disadvantages of various forms of e-learning. Risks and pitfalls of e-learning.
8. Use of software in education.
9. Organizational forms.
10. Evaluation. Forms and functions of evaluation.
11. Didactic principles.
Slovak
Programming in a higher level programming language. PPE and its principles. Basic mathematical concepts and principles needed to solve problems in the practice of computer science teachers. Mathematical structures (graphs, formal languages and automata, fractals). Creation of an educational program for the subject of informatics at primary and secondary school. Data structures (list, stack, row, trees, lexicographic trees, graphs). Parallel processes. Solving tasks in school informatics at primary and secondary school in a programming language that is suitable for a given level of education.
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State examination for the completion of a bachelor's degree in teacher education in combination with computer science.
Geometry
1. Study of affine space by analytical method
(subspaces - linear varieties, their parametric and general equations, intersections and mutual positions)
2. Study of Euclidean space by analytical method
(scalar product of vectors and metrics, perpendicularity of subspaces, distances of subspaces, angles)
3. Affine representations of spaces
(analytical expression of affine mapping, invariants of affine transformations, group of similarities of Euclidean space)
4. Axiomatic construction of geometry: incidental and ordered plane
(axioms of incidence and arrangement and their consequences, models of incident and ordered plane.)
5. Axiomatic construction of geometry: Hilbert's and Euclidean planes
(axioms of similarity and their consequences: triangles of similarity of triangles, properties of a triangle, construction of perpendiculars and parallels; axioms of parallelism and axioms of continuity)
Combinatorics, probability and statistics
1. Mathematical induction (principle of mathematical induction; connection with good arrangement of natural numbers; examples of use).
2. Pigeon/Dirichlet principle (formulation and some applications).
3. Combinatorial principles (addition principle, multiplication principle, bijection principle, counting in two ways).
4. Binomial coefficients and binomial theorem (definition and formula for binomial coefficients and some of their properties; binomial theorem formulation).
5. Principle of inclusion and exclusion (formulation and examples of use).
6. Probability, its basic properties. Conditional probability and independence of events. Complete Probability Theorem, Bayes Theorem.
7. Probability distributions, their properties and characteristics (distribution function, density, mean value, dispersion). Special types of distributions (alternative, binomial, geometric, exponential, normal). Central limit theorem.
8. Descriptive statistics (location and variability characteristics). Point estimates (random selection; estimates of mean and dispersion and their properties).
9. Confidence intervals for the mean value. Hypothesis testing, one-choice tests on the mean value.
Algebra and theoretical arithmetic
1. Linear representations and their matrices, product of matrices, inverse matrices.
2. Vector spaces and subspaces, linear combinations of vectors, linear representations.
3. Finite-dimensional vector spaces, base and dimension of finite-dimensional vector space.
4. Systems of linear equations, the existence of a solution of an inhomogeneous system of linear equations, the structure of the set of solutions of a homogeneous system of linear equations.
5. Divisibility in the field of integers. Theorem on division with the rest. The largest common divisor and the smallest common multiple of two integers. Euclidean algorithm for calculating the greatest common divisor.
6. Prime numbers, their properties, theorem about the decomposition of a natural number into the product of prime numbers. Number systems.
7. Congruences, divisibility criteria of natural numbers expressed in the decimal system, Euler's theorem, small Fermat's theorem.
Mathematical analysis
1. Limits of sequence and function, basic theorems about limits.
2. Continuity, properties of continuous functions on intervals, optimization - search for global extrema of continuous functions on closed intervals, relationship between continuity and differentiability of a function.
3. Derivation of a function, Lagrange's theorem on mean value and its use in investigating the monotonicity of functions, necessary and sufficient conditions for the existence of local extrema of differentiable functions.
4. Approximation of differentiable function by polynomials, equation of tangent, equation of Taylor polynomial of n-th degree.
5. Indefinite integral and primitive function, basic integration formulas, per partes method and substitutions.
6. Riemann integral, definition and calculation, heuristic derivation of formulas for calculation of area content, length of curve, volume of rotating body and surface of rotating body.
The course 1-UMA-951/15 Fundamentals of Mathematics has two parts:
A) School mathematics test
The test uses the types of tasks from mathematics tests for the external part of the Matura exam and from mathematics tests at the entrance exams at FMFI UK, a total of 20 short-answer tasks or with a choice of several options.
B) Oral exam
The student draws an assignment, which has 3 parts - three different circuits
1. geometry, 2. combinatorics, probability and statistics, 3. algebra and theoretical arithmetic, 4. mathematical analysis.
Each part contains
- the task from the relevant area, the solution of which (including the justification of individual steps) the student will demonstrate during the oral answer,
- definition of the area of the relevant heading, which is related to the solved task; in the oral answer the student will state the basic concepts and statements of this area, or their relationship to the problem.
Maximum points:
• 20 points from the school mathematics test (1 point for each correct answer),
• 25 points for each of the three parts of the assignment (10 for solving the problem, 15 for the theoretical part),
thus a maximum of 20 + 3.25 = 95 points in total.
A student completes the course if he/she obtains at least 5 points for each of the three parts of the assignment and a total of at least 46 points.
slovak, enghlish
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State exam from selected areas of the core subjects of the program.
according to the topic of the bachelor thesis
Examination: state examination
Slovak, English
Course contents:
1. Contribution of the final thesis for the given field of study applied in the collection, interpretation and processing of basic professional literature, or the extent to which the student has mastered the application of theoretical principles in practice and whether the hypotheses presented in the work are verifiable;
2. Originality of the thesis (the final thesis must not have the character of a plagiarism, must not infringe the copyrights of other authors), part of the documentation for the defense of the final thesis as a subject of state examination is the protocol of originality from the central register.
3. Correctness and correctness of citation of used information sources, research results of other authors and author groups, correctness of description of methods and working procedures of other authors or author groups;
4. Compliance of the structure of the final work with the prescribed composition defined by Internal Regulation no. 12/2013;
5. Respecting the recommended scope of the final thesis (the recommended scope of the bachelor's thesis is usually 30 - 40 standard pages - 54,000 to 72,000 characters, including spaces), the adequacy of the scope of the thesis is assessed by its supervisor;
6. Linguistic and stylistic level of work and formal arrangement;
7. The method and form of the defense of the final thesis and the student's ability to adequately respond to comments and questions in the opinions of the supervisor and the opponent.
8. In the teaching of art-educational subjects, the final work and its defense may also include the presentation of artistic outputs and performances.
0/100
When designing the bachelor's thesis, the student is able to demonstrate the ability to work creatively in the field of study in which he completed the study program. The student is able to demonstrate adequate knowledge of the issue and apply their skills in the collection, interpretation and processing of basic literature, or its application in practice or is able to solve a partial task related to the student's focus.