To master the fundamentals of the common language and basic technical terms of particular fields of study; with pre-intermediate students emphasis on reading technical texts and presentations of technical articles, application of French Internet websites.
Capelle Guy, Menand Robert: Le Nouveau taxi 1, Hachette FLE Paris, France 2009, ISBN 978-2-01-155548 - 9
test
French language is taught at two levels: beginner and intermediate. Students opt for one of them depending on whether they wish to obtain the fundamentals of the language or wish to maintain and/or improve previous knowledge of French.
100/0
To master the fundamentals of the common language and basic technical terms of particular fields of study; with pre-intermediate students emphasis on reading technical texts and presentations of technical articles, application of French Internet websites.
Capelle Guy, Menand Robert: Le Nouveau taxi 1, Hachette FLE Paris, France 2009, ISBN 978-2-01-155548 - 9
test
The subject continues the program of French language (1) and provides courses of essential and intermediate French language.
100/0
To master the fundamentals of the common language and basic technical terms of particular fields of study (depending on the student's level of German proficiency )
Appropriate study material is supplied by teacher based on the participants’level of German proficiency.
test
German language is taught at three levels: beginner, intermediate and advanced. Students opt for one of them depending on whether they need to learn the fundamentals or maintain and/or improve their previous knowledge.
This course’s focus is to master the fundamentals of the common language and basic technical terms of particular fields of study (depending on the student's level of German proficiency )
100/0
To master the fundamentals of the common language and basic technical terms of particular fields of study (depending on the student's level of German proficiency )
To master the fundamentals of the common language and basic technical terms of particular fields of study (depending on the student's level of German proficiency )
Appropriate study material is supplied by teacher based on the participants’level of German proficiency
test
German language is taught at two levels: beginner and intermediate. Students opt for one of them depending on whether they wish to obtain the fundamentals of the language or wish to maintain and/or improve previous knowledge of German.
This course’s focus is to to master the fundamentals of the common language and basic technical terms of particular fields of study (depending on the student's level of German proficiency )
100/0
To master the fundamentals of the common language and basic technical terms of particular fields of study (depending on the student's level of German proficiency )
To master the fundamentals of general Russian. The language level is A1.
Learning the Cyrillic (Russian) alphabet, gaining basic language competence, building up skills and confidence in dealing with unfamiliar authentic and semi-authentic texts.
The textbook: : Точка Ру A1 (Ольга Долматова, Екатерина Новачац), рracovné karty Падежи 1 (Л.С. Безкоровайная, В.Е. Штыленко).
test
To master the fundamentals of general Russian. The language level is A1.
Learning the Cyrillic (Russian) alphabet, gaining basic language competence, building up skills and confidence in dealing with unfamiliar authentic and semi-authentic texts.
The subject provides a course in Russian language for beginners.
100/0
Basic communication in Russian, developing other Russian language skills - listening comprehension, reading and writing.
To master the fundamentals of general Russian.
Learning the Cyrillic (Russian) alphabet, gaining basic language competence, building up skills and confidence in dealing with unfamiliar authentic and semi-authentic texts.
Textbook: Точка Ру A1 (Ольга Долматова, Екатерина Новачац), рracovné karty Падежи 1 (Л.С. Безкоровайная, В.Е. Штыленко).
test
To master the fundamentals of general Russian.
Learning the Cyrillic (Russian) alphabet, gaining basic language competence, building up skills and confidence in dealing with unfamiliar authentic and semi-authentic texts.
The subject continues the program of Russian language (1) and provides a course of Russian for beginners.
100/0
Basic communication in Russian, developing other Russian language skills - listening comprehension, reading and writing.
Krížom- Krážom Slovenčina 1, additional material to further support the covered topics.
tests
Course prerequisites:
https://fmph.uniba.sk/microsites/kjp/katedra-jazykovej-pripravy/poziadavky-na-udelenie-priebezneho-hodnotenia-aj1aj2aj3-ostatne-kurzy/
The sylabus is targeted at the comprehension of the basics of the Slovak language for the absolute beginners (A1).
100/0
This course is aimed for foreign students to learn the fundamentals of the Slovak language with the focus on basic communication as well as all other language skills- listening comprehension,reading and writing.
Krížom- Krážom Slovenčina 1, additional material to further support the covered topics
tests
Course prerequisites:
https://fmph.uniba.sk/microsites/kjp/katedra-jazykovej-pripravy/poziadavky-na-udelenie-priebezneho-hodnotenia-aj1aj2aj3-ostatne-kurzy/
The sylabus is targeted at the comprehension of the basics of the Slovak language for the absolute beginners (A1) and this course is a follow up course to the Slovak language course 1.
100/0
This course is aimed for foreign students to learn the fundamentals of the Slovak language with the focus on basic communication as well as all other language skills- listening comprehension,reading and writing.
Continual improvement of all language skills focused on communication/speaking, listening comprehension and writing. The emphasis is on discourse, lexicology and morphology, word-bank broadening of communicational English as well as English for specific purposes appropriate for university students. This course is a follow up of the previously taught ESP course.
Appropriate study material is supplied based on the participants’level of English by the lecturer.(Sources- The Guardian, The Herald Morning Sun. The Nine News, The West Australian, BBC News and podcasts, CNN podcasts).
tests, oral presentations, essays
tests, presentations, essays
Course prerequisites:
https://fmph.uniba.sk/microsites/kjp/katedra-jazykovej-pripravy/poziadavky-na-udelenie-priebezneho-hodnotenia-aj1aj2aj3-ostatne-kurzy/
This course’s focus is to broaden spoken/communicational English for students with B2/C1 level of English knowledge.
100/0
Continual improvement of all language skills focused on communication/speaking, listening comprehension and writing. The emphasis is on discourse, lexicology and morphology, word-bank broadening of communicational English as well as English for specific purposes appropriate for university students. This course is a follow up of the previously taught ESP course.
tests
Continual improvement of all language skills focused on communication/speaking, listening comprehension and writing. The emphasis is on discourse, lexicology and morphology, word-bank broadening of communicational/spoken English as well as English for specific purpose appropriate for university students. This course is a follow up of the Conversational English course 1.
Appropriate study material is supplied based on the participants’level of English by the lecturer.(Sources- The Guardian, The Herald Morning Sun. The Nine News, The West Australian, BBC News and podcasts, CNN podcasts).
tests, oral presentations, essays
tests, oral presentations, essays
Course prerequisites:
https://fmph.uniba.sk/microsites/kjp/katedra-jazykovej-pripravy/poziadavky-na-udelenie-priebezneho-hodnotenia-aj1aj2aj3-ostatne-kurzy/
This course’s focus is to broaden spoken/communicational English for students with B2/C1 level of English knowledge( Upper-Intermediate/Lower Advanced).
100/0
Continual improvement of all language skills focused on communication/speaking, listening comprehension and writing. The emphasis is on discourse, lexicology and morphology, word-bank broadening of communicational/spoken English as well as English for specific purpose appropriate for university students. This course is a follow up of the Conversational English course 1.
tests
Improvement of common language, deepening the knowledge of technical terms, reading technical texts, presentations of popular scientific articles.
Capelle Guy, Menand Robert: Le Nouveau taxi 1, Hachette FLE Paris, France 2009, ISBN 978-2-01-155548 - 9
test
The subject provides a course of intermediate French language, covering not only general, but also technical language.
100/0
Improvement of common language, deepening the knowledge of technical terms, reading technical texts, presentations of popular scientific articles.
Menand Robert: Le Nouveau taxi 2, Hachette FLE, Paris, France 2009, ISBN 978-2-01-155551 - 9
test
The subject provides a course of intermediate French covering not only general, but also technical French language.
100/0
Deepening the knowledge of the common language and basic technical terms of particular fields of study (depending on the student's level of German proficiency).
Appropriate study material is supplied by teacher based on the participants’level of German proficiency.
test
The course is a follow-up to the German language (1,2). The subject provides a course of intermediate or advanced German language.
This course’s focus is to deepen the knowledge of the common language and basic technical terms of particular fields of study (depending on the student's level of German proficiency).
100/0
Master the basics of general language and basic professional terminology of individual fields of study (depending on the advanced level of students)
Deepening the knowledge of the common language and basic technical terms of particular fields of study (depending on the student's level of German proficiency).
Appropriate study material is supplied by teacher based on the participants’level of German proficiency.
test
The course is a follow-up to the German language (1-3). It provides a course of intermediate and advanced German language.
This course’s focus is to deepen the knowledge of the common language and basic technical terms of particular fields of study (depending on the student's level of German proficiency).
100/0
Master the basics of general language and basic professional terminology of individual fields of study (depending on the advanced level of students)
Learning the handwritten Russian (Russian Cursive Cyrillic), developing further language skills, gaining knowledge of Russian culture, history and way of life, pre-intermediate to intermediate grammar and vocabulary.
Точка Ру A2 (Ольга Долматова, Екатерина Новачац) a Short Stories in Russian (Olly Richards, Alex Rowlings)
test
Learning the handwritten Russian (Russian Cursive Cyrillic), developing further language skills, gaining knowledge of Russian culture, history and way of life, pre-intermediate to intermediate grammar and vocabulary.
The course "Russian for Intermediate Students" is a follow-up to "Russian for Beginners". The subject of the course is general Russian in the range appropriate to the given level.
100/0
Basic communication in Russian, developing other Russian language skills - listening comprehension, reading and writing.
Learning the handwritten Russian (Russian Cursive Cyrillic), developing further language skills, gaining knowledge of Russian culture, history and way of life, pre-intermediate to intermediate grammar and vocabulary.
Точка Ру A2 (Ольга Долматова, Екатерина Новачац) a Short Stories in Russian (Olly Richards, Alex Rowlings)
test
Learning the handwritten Russian (Russian Cursive Cyrillic), developing further language skills, gaining knowledge of Russian culture, history and way of life, pre-intermediate to intermediate grammar and vocabulary.
The course "Russian for Intermediate Students" is a follow-up to "Russian for Beginners". The subject of the course is general Russian in the range appropriate to the given level.
100/0
Learning the handwritten Russian (Russian Cursive Cyrillic), developing further language skills, gaining knowledge of Russian culture, history and way of life, pre-intermediate to intermediate grammar and vocabulary.
Krížom-Krážom Slovenčina 2, additional material to further support the covered topics.
tests
Course prerequisites:
https://fmph.uniba.sk/microsites/kjp/katedra-jazykovej-pripravy/poziadavky-na-udelenie-priebezneho-hodnotenia-aj1aj2aj3-ostatne-kurzy/
The sylabus is targeted at the comprehension of all the language skills of the Slovak language , and it is a follow up course to the Slovak language course 2.
100/0
This course is aimed for foreign students to better comprehend all the language skills important to enable correct usage of the Slovak language – listening comprehension, reading, writing and speaking.
Krížom-Krážom Slovenčina 2, additional material to further support the covered topics.
tests
Course prerequisites:
https://fmph.uniba.sk/microsites/kjp/katedra-jazykovej-pripravy/poziadavky-na-udelenie-priebezneho-hodnotenia-aj1aj2aj3-ostatne-kurzy/
The sylabus is targeted at the comprehension of all the language skills of the Slovak language , and it is a follow up course to the Slovak language course 3.
100/0
This course is aimed for foreign students to better comprehend all the language skills important to enable correct usage of the Slovak language – listening comprehension, reading, writing and speaking.
Basic practicing and improvement of locomotion skills in various selected sports: aerobics, basketball, volleyball, football, floorball, hockey, badminton, tennis, table tennis, swimming, body building, trampoline jumping, paddling. Development of a harmonic personality in the sense of “kalokagatia” – to cultivate the students´ mental and physical values.
Slovak, English
Practicing of the students´ game skills in collective sports: basketball, volleyball, football, floorball and hockey. Mastering of the basic technique of a particular sport discipline in other sports. In paddling, basic training on still and slightly flowing water. Development of coordination skills, improvement of articular mobility and cardiovascular system.
100/0
Grades: A 90%, B 80%, C 70%, D 60%, E 50%
The condition for the award of 1 or 2 credits is the completion of a multi-day course in its full scope, or the completion of one-day courses in the scope of 4 days. Candidates can apply to the leaders of individual courses. From the presented offer of courses, you can choose the one that suits your interests, abilities and deadlines.
Slovak
KTVŠ does not rent ski equipment.
The student can sign up for the outdoor sports courses offered by the department: skiing, snowboarding. The lessons in the courses are focused on the development of basic and special movement skills and mastering the techniques needed for the sports.
Acquisition and development of basic motor skills and abilities in selected sports: skiing and snowboarding. Mastering the correct technique of performing individual movements, which are necessary for skiing and snowboarding.
Grades: A 90%, B 80%, C 70%, D 60%, E 50%.
The condition for the award of 1 or 2 credits is the completion of a multi-day course in its full scope, or the completion of one-day courses in the scope of 4 days. Candidates can apply to the leaders of individual courses. From the presented offer of courses, you can choose the one that suits your interests, abilities and deadlines.
Slovak
KTVŠ will provide sports equipment.
The student can sign up for the outdoor sports courses offered by the department: water tourism - river rafting, windsurfing, beach volleyball, hiking and other hobby sports. The lessons in the courses are focused on the development of basic and special movement skills and, mastering the techniques needed for the sports.
Creating a positive and lasting relationship with physical activity. Acquisition and mastery of basic motor skills and abilities in outdoor sports: windsurfing, beach volleyball, water tourism - river rafting, hiking and other sports according to interest. Training and improving the technique needed for the sports.
Improvement training in a selected sport aimed at enhancing locomotion skills in the selected sport. To improve the students´ resistance against various vices, stresses and risk factors.
Slovak, English
Practicing of offensive and defensive game combinations and playing with modified rules in collective sports such as basketball, volleyball, football, floorball, hockey. Command of elements of higher difficulty in locomotion skills (swimming - crawl stroke, breast stroke, butterfly stroke, trampoline jumping and aerobics – practicing of areobics compositions, bodybuilding – development of the main muscle groups, paddling on running water. Testing of the level of physical fitness and coordination skills.
100/0
Russell S., Norwig P. (2010). Artificial Intelligence: A Modern Approach, (3rd ed.), Prentice Hall. Available in faculty library.
Marsland S. (2015). Machine Learning: An Algorithmic Perspective, (2nd ed.), CRC Press.
Passing the online course https://course.elementsofai.com/ (in Enlish or Slovak version).
Slovak or English
The course consists of 20 numerical and 5 text-based tasks. Numerical tasks are checked automatically, text-based tasks are evaluated anonymously by students.
1. What is artificial intelligence: related areas, AI philosophy.
2. Troubleshooting and UI: Browsing and troubleshooting, browsing and games
3. Probability and chance, Bayes' theorem, naive Bayesian classification.
4. Machine learning: nearest neighbor classifier, regression.
5. Neural networks: basics, creation, modern techniques.
6. Consequences: on predicting the future, the effects of AI on society, summary.
The student will get acquainted with selected basic concepts of artificial intelligence and their use in solving various practical tasks.
Russell S., Norwig P. (2010). Artificial Intelligence: A Modern Approach, (3rd ed.), Prentice Hall. Available in faculty library.
Marsland S. (2015). Machine Learning: An Algorithmic Perspective, (2nd ed.), CRC Press.
Passing the online course https://course.elementsofai.com/ (in Enlish or Slovak version).
Slovak or English
The course consists of 20 numerical and 5 text-based tasks. Numerical tasks are checked automatically, text-based tasks are evaluated anonymously by students.
1. What is artificial intelligence: related areas, AI philosophy.
2. Troubleshooting and UI: Browsing and troubleshooting, browsing and games
3. Probability and chance, Bayes' theorem, naive Bayesian classification.
4. Machine learning: nearest neighbor classifier, regression.
5. Neural networks: basics, creation, modern techniques.
6. Consequences: on predicting the future, the effects of AI on society, summary.
The student will get acquainted with selected basic concepts of artificial intelligence and their use in solving various practical tasks.
- Teachers' own electronic study materials published on the course website or in the Moodle system
- Gavora, Peter a kol. 2010. Elektronická učebnica pedagogického výskumu. [online]. Bratislava : Univerzita Komenského, 2010. Dostupné na: http://www.e-metodologia.fedu.uniba.sk/ ISBN 978–80–223–2951–4.
- Tharenou, P., Donohue, R. and Cooper, B., 2007. Management research methods. Cambridge University Press.
- Topping, A., 2015: The Quantitative-Qualitative Continium. In: Gerrish, K. and Lathlean, J., The Research Process in Nursing, p. 159-172
- Williamson, K. and Johanson, G. eds., 2017. Research methods: Information, systems, and contexts. Chandos Publishing.
Continuous assessment: active participation in research in an international student team (25%), presentation of work in a workshop (25%), scientific article (50%)
Indicative evaluation scale: A 90 %, B 80 %, C 70 %, D 60 %, E 50 %
English
- Research methodology
- Design and implementation of a research project in an international group (preferably interdisciplinary)
- Methods and tools for collaboration in virtual space, collaboration in science and practice
- Academic writing, presentation of research results through scientific articles; objectives, content and structure of scientific articles; forms of academic publication, publication forums and evaluation of their quality
- Quality assurance and feedback - peer review
- Communication of results through posters or conference presentations
100/0
Students will learn in the team to agree on a common research topic, formulate research questions, determine research methods for the problem, collect and evaluate data, discuss their findings, present research results to the professional public, analyze and evaluate the scientific work of their colleagues, prepare a scientific article suitable for publication
2/1 (lecture / individual work)
Clark, Timothy R., et al. Business Model Generation. Wiley, 2010
The condition for admission to the exam is active participation in at least 80% of the lessons.
The final assessment consists of a presentation of the semester project. To successfully complete the course, it is necessary to achieve at least 50% of the overall score.
Slovak
1. Commercialization of scientific research.
2. Fundamentals of entrepreneurship and startup terminology.
3. Identification of problems and customer needs analysis (design thinking).
4. Technology transfer. Technology Readiness Levels (TRL).
5. Intellectual property and its protection.
6. Market, customer, and market potential of a technological solution.
7. Business Model Canvas. Revenue models.
8. Sources of financing for technological projects.
9. Pitching and communication of the solution.
10. Fundamentals of management and leadership.
11. Innovation support and incubation structures at national and international levels.
0/100
After completing the course, students can describe the possibilities for commercialization of scientific and technological research. They can identify market needs, assess the market potential of a technological solution, and are familiar with the terminology of entrepreneurship, technology transfer, and intellectual property protection. They understand the overall structure of a business plan and the main forms of financing for technological projects. They are familiar with the principles of communication, teamwork, and team leadership and can apply them appropriately in project work and its presentation.
To improve the students´ physical fitness, health and sport performance through sport.
Slovak, English
To improve offensive and defensive game combinations in collective sports. Practicing of tactical and technical elements in individual sports. Compensatory exercises to correct wrong body posture. Stretching. Competition rules in sport disciplines.
100/0
To strengthen the procedural aspect of university sport, stressing its health and psychological importance. To improve the students´ physical fitness.
Slovak, English
Sport training for Faculty Championships in a selected sport with modified rules. Selection of sport-talented students into teams of the Faculty Sport League, University League of Bratislava Faculties, and participation in sport events of the Faculty and University.
100/0
- Reid: Undergraduate algebraic geometry, Cambridge University Press, 1998
- Igor. R. Šafarevič: Basic algebraic geometry 1, Springer-Verlag, 2013
- A. Gathmann: Class Notes „Algebraic Geometry”, online skriptá, 2014
- Brendan Hassett: Algebraic geometry, Cambridge University Press, 2007
- David Cox, John Little, Donal O'Shea: Ideals, Varieties and Algorithms, Springer Verlag, 1996
- Justin R. Smith: Introduction to Algebraic Geometry, Five Dimensions Press, 2014
none
Written solution of problems and their consulting 60%/oral exam with written preparation 40%
Grading: A 90%; B 80%; C 70%; D 60%; E 50%
english
none
- ideals and varieties in affine space, Hilbert's basis theorem
- Nullstellensatz
- elements of algebraic geometry:
- Zariski topology,
- coordinate rings, morphisms and rational maps
- computational methods of algebraic geometry: Gröbner bases
none
Weight of the course work / exam: 60/40
The student gains an overview of the basic concepts of algebraic geometry as well as the most common computational methods there.
Deskriptivní geometrie : část 2 / Rudolf Piska, Václav Medek. Praha : Státní nakladatelství technické literatury, 1966
Deskriptivní geometrie : díl 2 / Alois Urban. Praha : Státní nakladatelství technické literatury, 1979
Využitie IKT pri vyučovaní témy ROTAČNÉ PLOCHY na všetkých úrovniach vzdelávania / Miroslav Tisoň, Dizertačná práca FMFI UK. Dostupné na http://www.rotacneplochy.sk/
Rotační plochy / Jindřich Červinka. PF MU Brno, Diplomová práce, 2006. Dostupné na http://is.muni.cz/th/52027/prif_m/Rotacni_plochy.pdf
Technické osvětlení / Jan Šafařík, Učebné texty, SF VUT Brno, 2006. Dostupné na http://math.fce.vutbr.cz/vyuka/podpora/jan.safarik-technicke.osvetleni.pdf
The student can obtain 100% of the grade for the work during the semester. The student prepares technical drawing assignments. To successfully obtain the grade, he / she needs at least half of the available points.
Grading: A (100-91), B (90-81), C (80-71), D (70-61), E (60-51), Fx (50-0).
Slovak, English
Surfaces of revolution, planar sections and intersections of surfaces of revolution. Parallel and technical lighting of surfaces of revolution. Quadratic surfaces of revolution, planar sections and intersections of these surfaces and their parallel illumination.
Preliminary assessment 100% (homework assignments) / 0% final exam
The graduate masters the solution of problems regarding curves on surfaces of revolution used in technical practice. They can construct their intersections and can use parallel lighting to increase the clarity of surface images.
Deskriptivní geometrie : díl 2 / Karel Drábek, František Harant, Ota Setzer. Praha : Státní nakladatelství technické literatury, 1979
Konštruktívna geometria pre technikov / Václav Medek, Jozef Zámožík. Bratislava : Alfa, 1978
Plochy technické praxe / Šárka Blaženková. Diplomová práce PF MU Brno, 2006. Dostupné na http://is.muni.cz/th/64132/prif_m/diplomka.pdf
Zborcené přímkové plochy - řešené příklady / Kristýna Rožánková. FA ČVUT, Praha 2011. Dostupné na http://15122.fa.cvut.cz/?download=_/elektronicka_skripta/zborcene_primkove_plochy.pdf.
Plochy stavební praxe / Petra Surynková. Bakalářská práce. MFF UK Praha, 2006. Dostupné na http://www.karlin.mff.cuni.cz/katedry/kdm/diplomky/surynkovabp/Bakalarska_prace.pdf
The student can obtain 100% of the grade for the work during the semester. The student prepares technical drawing assignments. To successfully obtain the grade, he / she needs at least half of the available points.
Grading: A (100-91), B (90-81), C (80-71), D (70-61), E (60-51), Fx (50-0).
Slovak, English
Helix. Developable line surfaces (developable helical surfaces, transition surfaces). Non-developable linear surfaces (quadrics, conoids, higher degree surfaces). Helical surfaces (linear, cyclic, general). Other surfaces of technical practice (translational, wedge, sum).
Preliminary assessment 100% (homework assignments) / 0% final exam
The course graduate masters the representation of basic types of surfaces used in technical practice, especially in civil engineering. They master the solution of basic problems regarding these surfaces.
Matematika pre gymnázia 5 / Václav Medek, Alica Sivošová. Bratislava : Slovenské pedagogické nakladateľstvo, 1979
Metodika vyučovania deskriptívnej geometrie a rysovania / František Hradecký ...[et al.]. Bratislava : Univerzita Komenského, 1969
Teória vyučovania matematiky 2 / Milan Hejný ... [et al.]. Bratislava : Slovenské pedagogické nakladateľstvo, 1990
The student can get 40% for exercises and 60% for the final exam. The student must obtain at least half of the points for the exercises in order to pass to the final exam.
During the exercises, the student has the opportunity to obtain points evaluation for written and technical drawing assignments. To successfully obtain continuous assessment, he / she needs at least half of the available points.
The final exam consists of an oral part, where the student draws several questions. Unsolicited supplementary questions may also be asked to clarify the assessment.
Grading: A (100-91), B (90-81), C (80-71), D (70-61), E (60-51), Fx (50-0).
Slovak, English
Historical development stages of descriptive geometry. The importance of didactics of descriptive geometry. Curriculum, syllabi, thematic plans. Concepts of teaching descriptive geometry. Analysis, synthesis, deduction, induction in teaching descriptive geometry. Conceptual process - axioms, sentences, definitions in terms of teaching descriptive geometry. Teaching proofs in descriptive geometry.
Preliminary assessment 40% (written homework and technical drawing assignments) / 60% final exam (oral).
The graduate will acquire specialized didactic training for teaching descriptive geometry at secondary schools, thanks to theoretical lectures and modeled exercises.
Metodika vyučovania deskriptívnej geometrie a rysovania / František Hradecký ...[et al.]. Bratislava : Univerzita Komenského, 1969
Matematika pre gymnázia 5 / Václav Medek, Alica Sivošová. Bratislava : Slovenské pedagogické nakladateľstvo, 1979
Teória vyučovania matematiky 2 / Milan Hejný ... [et al.]. Bratislava : Slovenské pedagogické nakladateľstvo, 1990
The student can get 40% for exercises and 60% for the final exam. The student must obtain at least half of the points for the exercises in order to pass to the final exam.
During the exercises, the student has the opportunity to obtain points evaluation for a project. To successfully obtain continuous assessment, he / she needs at least half of the available points.
The final exam consists of an oral part, where the student draws several questions. Unsolicited supplementary questions may also be asked to clarify the assessment.
Grading: A (100-91), B (90-81), C (80-71), D (70-61), E (60-51), Fx (50-0).
Slovak, English
Principles of teaching descriptive geometry. Preparation for a lesson in descriptive geometry, types of lessons, organization of teaching descriptive geometry. Use of computer in teaching descriptive geometry. Basic concepts of the theory of didactic situations with respect to didactics of descriptive geometry. Problem teaching, open problems, problem solving. Teaching of Monge's projection in high school. Teaching conic sections and technical curves in high school. Selected applications of descriptive geometry in high school (cartography, topography, theoretical solution of roofs, penetration of basic bodies, etc.). Empirical semestral research project in the didactics of descriptive geometry.
Preliminary assessment 40% exercises (project) / 60% final exam (oral).
The course graduate expands their theoretical preparation for teaching descriptive geometry at secondary schools. Masters the theory of didactic situations with respect to teaching of descriptive geometry.
Wolfgang Kühnel: Differential Geometry, Curves-Surfaces-Manifolds, AMS, 2015
Analytická a diferenciální geometrie / Bruno Budinský. Praha : Státní nakladatelství technické literatury, 1983
Lectures on classical differential geometry / Dirk J. Struik. Cambridge : Addison-Wesley Press, 1950
Elektronické učebné texty predmetu
Homeworks (written solutions of problems and their consulting 60%), final exam (oral exam with written preparation 40%). Rough evaluation scale: A 90%, B 80%, C 70%, D 60%, E 50%
Curves, curvature, torsion, Frenet frame, fundamental theorem of curves. Surfaces, first fundamental form, Second fundamental form, Dupins indicatrix, principal curvatures, Gauss curvature, geodesics.
60/40
Student understands knowledge on curves in Euclidean space, especially in dimensions 2 and 3, the basic facts on surfaces in 3-dimensional Euclidean space necessary for studying advanced topics in descriptive geometry and its applications.
Satyan L. Devadoss, Joseph O'Rourke. Discrete and computational geometry. Princeton University Press, 2011.
Pavel Chalmovianský, Andrej Ferko, Roman Galbavý. Zložitosť geometrických algoritmov.. Univerzita Komenského, 2001.
Jörg-Rüdiger Sack, Jorge Urrutia. Handbook of computational geometry. Elsevier, 1999.
Homeworks during the term.
Oral exam
Evaluation: A 90%, B 80%, C 70%, D 60%, E 50%
English
Polygons, polygon triangulation, the art gallery problem. Fundamentals of computational complexity analysis of algorithms. Convex hulls, algorithms for their creation (incremental, gift wrapping, Graham's scan, divide and conquer). Triangulation of sets of points, their properties and algorithms for their construction (triangle splitting, incremental). Flip graphs and their properties. Voronoi diagrams, their properties and algorithms (incremental, Fortune's). Delaunay triangulations and their connection to Voronoi diagrams.
50/50
Students who complete this course will learn an algorithmic approach to solving computational geometry problems in the plane. They will be able to construct methods and their modifications for various areas of discrete geometry and analyze them in terms of computational complexity.
Duncan Marsh. Applied geometry for computer graphics and CAD. . Springer Science & Business Media, 2005.
Gerald Farin. Curves and surfaces for computer-aided geometric design: a practical guide.. Elsevier, 2014.
Przemysław Kiciak. Geometric continuity of curves and surfaces. . Morgan & Claypool, 2017.
Homeworks during the term.
Oral exam.
Evaluation: A 90%, B 80%, C 70%, D 60%, E 50%
English
Hermite curves, Bézier curves, properties of blending functions, curve modeling, and evaluation algorithms. Geometric and parametric continuity. Generation of interpolation splines (Hermite spline, cardinal spline) and approximation splines (Bézier spline, Beta spline, B-spline). Geometric creation and analytical description of surfaces determined by boundary curves (Coons and Hermite patches) and control nets (Bezier surfaces, B-spline surfaces). Partial derivatives, twist vectors in modeling and joining surfaces. Rational extension of the mathematical description of curves (rational Bézier curves, NURBS curves) and surfaces (rational Bézier surfaces, NURBS surfaces). Shaping parameters - weights - in curve and surface modeling. Conic sections as rational curves. Evaluating algorithms for rational curves and surfaces.
50/50
The students know the mathematical descriptions of curves and surfaces used in geometric modeling. They master the tools and methods for evaluation of curves, surfaces, and spline constructions. They know the mathematical descriptions of surfaces and curves used in geometric modeling.
John Ratcliffe: Foundations of Hyperbolic Manifolds, Springer, 2006
Marcel Berger: Geometry 1,2, Springer, 2009
Stavba planimetrie / Ján Gatial, Milan Hejný. Bratislava : Slovenské pedagogické nakladateľstvo, 1973
Konštrukčná geometria pre matematicko-fyzikálne a pedagogické fakulty : (Pre učiteľstvo všeobecnovzdelávacích predmetov v kombinácii s matematikou) / Vladimír Piják, Ondrej Šedivý, Michal Grajcar, Valent Zaťko. Bratislava : Slovenské pedagogické nakladateľstvo, 1985
Introduction to Geometry / H. S.M. Coxeter. New York : John Wiley, 1989
Projektívna geometria / Štefan Solčan. Bratislava : MFF UK, 1995
Neeuklidovská geometrie / Kristýna Křížová, Diplomová práce, PF MU Brno, 2010. Dostupné na http://is.muni.cz/th/175713/prif_m/Diplomova_prace.pdf
Homeworks (written solutions of problems and their consulting 100%). Rough evaluation scale: A 90%, B 80%, C 70%, D 60%, E 50%
English
History of non-Euclidean geometries (projective, elliptic, hyperbolic). Euclidean axiom on parallels and its equivalents. Spherical geometry. Minkowski space and its geometry. Beltrami-Klein model of hyperbolic plane. Parallels, length and angles in the model. Poincare model of hyperbolic plane. Higher-dimensional analogues of the hyperbolic plane.
Student masters basic knowledge on non-Euclidean geometries in analytic way. Basic spherical geometry is studied. Lobatchevskhian geometry is studied via several models in Minkowski space such as Beltrami-Klein and Poincaré.
Marcel Berger: Geometry 1, 2, Springer, 2009
Computational line geometry / Helmut Pottmann, Johannes Wallner. Berlin : Springer, 2001
Methods of algebraic geometry : Volume 1 : Book 1: Algebraic preliminaries, Book 2: Projective space / W. V. D. Hodge, D. Pedoe. Cambridge : At the University Press, 1947
Methods of algebraic geometry : Volume 2 : Book 3: General theory of algebraic varieties in projective space, Book 4: Quadrics and grassmann varieties / W. V. Hodge, D. Pedoe. Cambridge : At the University Press, 1952
Projektivní geometrie : 2. díl : Útvary dvojparametrické / Václav Hlavatý. Praha : Melantrich, 1945
Continuous assessment: a written test
Indicative evaluation scale: A 90%, B 80%, C 70%, D 60%, E 50%
English
Axiomatic construction of n-dimensional projective space above the field, especially real three-dimensional projective space. Synthetic construction of the theory of second degree surfaces in real projective space, projective formation of ruled surfaces. Polarity. Some properties of second degree surfaces and their consequences for solving problems on these surfaces.
Projective classification of second degree surfaces. Affine specializations of second degree surfaces. Affine metric classification. Bundles of straight lines, conic sections and quadrics.
100/0
The graduate knows how to compute basic analytical problems in projective space. The construction of projective space is known. Analytical and synthetic theory of bundles of lines, conic sections, quadrics is interconnected and can be used in selected problems from applications of geometry. He knows some applications of the theory of quadratic surfaces.
Written solution of problems and their consulting 100%
Grading: A 90%, B 80%, C 70%, D 60%, E 50%
- conic sections in the real/complex affine/projective plane
- the group of an elliptic curve
- unsolvability of classical problems of ancient Greek mathematics
- Grassmannian as a generalization of projective space
- enumerative geometry
- lines on a cubic surface
The student gets familiar with some topics in classical algebraic geometry.
Helmut Pottmann, Andreas Asperl, Michael Hofer, Axel Kilian, Daril Bentley: Architectural Geometry, Bentley Institute Press, 2007
Lectures on classical differential geometry / Dirk J. Struik. Cambridge : Addison-Wesley Press, 1950
Elektronické učebné texty predmetu
Homeworks (written solutions of problems and their consulting 100%). Rough evaluation scale: A 90%, B 80%, C 70%, D 60%, E 50%
English
Gears, sculpting, 3D printing, exceptional buildings, maps, font design, arts from the geometry point of view of methods and maps in differential geometry.
100/0
Student gains deeper knowledge of properties of curves and surfaces. Basic applications in practically oriented areas such as design, constructions, cartography and art are presented.
Josef Vybíral: GIMP – Praktická uživatelská příručka. Computer Press, 2008
Lubomír Čevela: Digitální fotografie v programu GIMP. Computer Press, 2012
Petr Šimčík: Inkscape – Praktický průvodce tvorbou vektorové grafiky. Computer Press, 2013
Dmitry Kirsanov: The Book of Inkscape (2nd Edition), No Starch Press, 2021
Tavmjong Bah: Inkscape – Guide to a Vector Drawing Program (4th Edition). Prentice Hall, 2011
Pavel Pokorný: Blender – Naučte se 3D grafiku. BEN - technická literatura, 2009
Jason van Gumster: Blender For Dummies (4th Edition). Wiley, 2020
For the semester, the student can get 100% for continuous assessment in the form of independent work on individual projects.
Evaluation: A (100-91), B (90-81), C (80-71), D (70-61), E (60-51), Fx (50-0).
1. Creating simple graphics, logos and animations using a graphics tablet in GIMP.
2. Advanced editing of photos (working with layers, masks, etc.) and scanned documents, overview of interesting extensions in Gimp.
3. Creating vector graphics using various tools in Inkscape.
4. Advanced tools (tile clones, filters, transformations) and the use of Inkscape extensions to create more complex vector artwork.
5. Creating simple 3D objects using standard tools. Setting up materials, lights, scenes, surroundings and cameras in Blender.
6. Use of spline surfaces and lattice deformation in the creation of 3D animal models.
7. Creating simple animations of a realistic-looking scene.
8. Creating an animated character using a skeleton and modifying the animation curves in Blender.
https://flurry.dg.fmph.uniba.sk/webog/sk/bohdal-vyucba/52-bohdal/84-prof-graf-soft
After completing the course, students will be able to create and edit complex bitmap or vector drawings and 3D models and their animations in multiplatform Open Source programs Gimp, Inkscape and Blender. Such images, drawings and possibly 3D models are often part of the final documents such as thesis.
A01 Surfaces of revolution. Basic constructions on surfaces of revolution (intersection with a plane, intersection of two surfaces of revolution, illumination).
A02 Technical illumination of surfaces of revolution.
A03 Quadratic surfaces of revolution. Basic problems on quadratic surfaces of revolution.
A04 Helix and its properties. Construction of the tangent, osculation plane and center of curvature in methods of projections.
A05 Quadratic surfaces - definition, constructions, basic properties. Ruled surfaces, non-ruled surfaces, their affine classification (ellipsoids, paraboloids, hyperboloids). Basic problems on a hyperbolic paraboloid and one-sheeted hyperboloid. Properties of one-sheeted hyperboloid of revolution.
A06 Developable surfaces, constructions and use in technical practice. Helicoid surface as a developable surface. Construction, properties and developing into a plane. Plane intersection of helicoid.
A07 Undevelopable ruled surfaces. Chasles theorem and its use (conoids, helicoid). Tangent plane of undevelopable ruled surfaces. Tangent plane construction methods at a point of a surface.
A08 Helicoid surfaces. Linear and cyclic helicoid surfaces. A helicoid as a conoid.
A09 Non-ruled surfaces of technical practice (wedge, sum, cyclical). Basic properties and examples of their use.
A10 Mathematical representations of curves and surfaces, surface patches, isoparametric curves, surface edges, corner points.
A11 Hermit and Bézier arc, their properties and evaluation algorithms.
A12 Continuity conditions in spline curves.
A13 Hermit cubic splines - construction, properties, examples of endpoint conditions.
A14 Cardinal splines, representation of a segment, shaping parameter and examples of enpoint conditions.
A15 B-spline curves, knot sequence, construction, modeling of B-spline curves.
A16 Beta-spline curves, continuity conditions, properties of a segment, modeling of a curve.
A17 Construction of rational curves, rational Bézier curves and their modeling.
A18 Surfaces determined by the edge conditions - Coons patches. Construction and mathematical description of ruled, bilinear and bicubic patches.
A19 Bézier and B-spline bicubic patches, surface properties, isoparametric curves, border curves, corner points.
A20 Torsion of a curve. Frenet's formulas.
A21 Singular points of planar curves.
A22 The first fundamental form of a surface and computation of the lengths, angles and area on a surface.
A23 Dupin's indikatrix and conjugate directions in the tangent plane of a surface.
A24 Principal directions and curvatures of a surface, Weingarten mapping.
A25 Gaussian curvature of surfaces.
A26 Ideals in commutative rings (particularly in rings of polynomials).
A27 Affine and projective algebraic varieties. Associated ideal of an algebraic variety.
A28 Radical ideal. Hilbert's nullstellensatz.
A29 Zariski's topology. Decomposition of algebraic variety into irreducible components.
A30 Coordinate ring variety. Morphisms and rational varieties.
A31 Ordering of monomes in polynomial rings. Algorithm of division, Gröbner's base ideal.
A32 Calculations in algebraic geometry, applications of Gröbner base and resultants (comparison of varieties, elimination ideal).
B01 Applying didactic principles in teaching of descriptive geometry.
B02 Organization and creation of curriculum plans in descriptive geometry.
B03 Applications of educational methods in descriptive geometry.
B04 Specifics of problem solutions in descriptive geometry (complete solution, construction problems).
B05 Steps and tools of developing of spatial imagination.
B06 Development of logical reasoning. Complete sorting with demos in descriptive geometry.
B07 Conceptual process in descriptive geometry (axioms, definitions, theorems).
B08 Functions and techniques of proving in descriptive geometry.
B09 Organizational forms of education in descriptive geometry at schools.
B10 Descriptive geometry and modern means of education.
Oral exam.
English
The questions on the state exam summarize the knowledge from subjects Didactics of Deskriptive Geometry, Surfaces of Technical Practice, Algebraic Geometry, Differential Geometry and Computer Geometry.
0/100
The student shows overview over the knowledge gained in the block Theoretical base of descriptive geometry and applications.
Dítě, škola a matematika: Konstruktivistické přístupy k vyučování / Milan Hejný, František Kuřina. Praha : Portál, 2001
Moderní vyučování / George Petty Praha : Portál, 1993
Dvacet pět kapitol z didaktiky matematiky / Milan Hejný, Jarmila Novotná, Naďa Stehlíková (Eds.) Praha, 2004
Komunikácia v inkluzívnej škole / Marta Horňáková. Bratislava: Univerzita Komenského v Bratislave. 2017
Elementary and Middle School Mathematics: Teaching Developmentally. / John A. Van de Walle, Karen Karp, Jennifer M. Bay-Williams. Pearson.
Theory of didactical situations in mathematics /Guy Brousseau. Springer, 1997
Textbook explanations: Modes of reasoning in 7th grade Israeli mathematics textbooks. / Silverman B, and Even R., CERME 9. Charles University in Prague. Faculty of Education. 2015, pp.205-212
Od obsahu vzdělávání k žákově znalosti: Kritická místa na cestě do školy a ze školy / T. Janik, Arnica 8, 2018, 1–8. Západočeská univerzita v Plzni, Plzeň.
Refining teacher design capacity: Mathematics teachers’ interactions with digital curriculum resources / Birgit Pepin, Ghislaine Gueudet, Luc Trouche. In. ZDM Mathematics Education, 2017, 49, 799–812 https://doi.org/10.1007/s11858-017-0870-8
Own electronic materials published via the subject's website (eg course in LMS Moodle)
Continuous assessment: group homework, reading of scientific articles, discussion of articles and the specified topic, group work on a lesson plan described for each group in the assignment.
The student must obtain at least 50% of the continuous assessment and each assignment must be evaluated with a non-zero number of points.
Final evaluation: oral exam, individual preparation of a lesson plan and its presentation
Indicative assessment scale: A 94%, B 86%, C 79%, D 70%, E 60%, Fx <60%
slovak, englihs
The language of mathematics, its historical development and didactic significance. A parallel between phylogeny and ontogeny of mathematical thinking. Conceptual and cognitive process in mathematics. Principles, means and forms of teaching in mathematics. Objectives of the teaching process in mathematics. Learning theories. Lesson preparation and its starting points. Resources and their use in preparation, during teaching in evaluation. Hypothetical learning trajectories.
60/40
The student will gain an overview of didactic theories, will be able to critically evaluate them and use the appropriate methods and forms. Through activities at the seminar, they will acquire modern teaching techniques that are a prevention of formal knowledge and misconceptions in mathematics. The study of scientific and research articles and the subsequent discussion or authentic experience will give graduates a better insight into the issues of inclusive school, creating preparations for the lesson (or sequence) and asking "good questions".
Dítě, škola a matematika: Konstruktivistické přístupy k vyučování / Milan Hejný, František Kuřina. Praha : Portál, 2001
Moderní vyučování / Geoffrey Petty. Praha : Portál, 1993
Is this a coincidence? The role of examples in fostering a need for proof / Buchbinder, O., Zaslavsky, O., ZDM Mathematics Education 43, 269 (2011). https://doi.org/10.1007/s11858-011-0324-7
Elementary and Middle School Mathematics: Teaching Developmentally. / John A. Van de Walle, Karen Karp, Jennifer M. Bay-Williams. Pearson. 2012
Strategies for Teaching Fractions: Using Error Analysis for Intervention and Assessment / David B. Spangler.
Dvacet pět kapitol z didaktiky matematiky / Milan Hejný, Jarmila Novotná, Naďa Stehlíková (Eds.) Praha, 2004
Dostupné učebnice Matematiky pre 5. – 9. ročník ZŠ a nižšie ročníky osemročných gymnázií / Ján Žabka, Pavol Černek / Ondrej Šedivý a kol. / Soňa Čeretková a kol. / Milan Hejný a kol.
Nový Pomocník z matematiky (5. – 9. ročník) / Iveta Kohanová a kol.
Own electronic materials published via the subject's website (eg course in LMS Moodle)
Continuous assessment: individual preparation of a lesson plan and its placement in the thematic plan, microteaching, preparation of written tests (2 equal groups), peer assessment, didactic analysis of teaching texts, reading and discussion of scientific articles.
The student must obtain at least 50% of the continuous assessment and each assignment must be evaluated with a non-zero number of points.
Exam: written with oral consultation
Indicative assessment scale: A 94%, B 86%, C 79%, D 70%, E 60%, Fx <60%
slovak, enghlish
Specifics of teaching mathematics for individual topics and concepts of mathematics at lower secondary school: educational goals, activities, the assumption of the development of student understanding in the context of educational activities and the creation of a hypothetical trajectory. Selection of adequate methods, forms and age-appropriate activities for teaching mathematics at the second stage of primary school. Integration of digital technologies into the teaching of mathematics also in order to support argumentation, reasoning, and building a mathematical culture (correctness of concepts, procedures, arguments, etc.).
60/40
The graduate of the course is acquainted with the goals of mathematics education at lower secondary school, with adequate teaching methods, forms and means, with ways of introducing selected mathematical concepts, is ready for his work in school and out of school, can transfer to pedagogical practice knowledge and skills acquired in individual professional disciplines. The study of scientific and research articles with a subsequent discussion or an authentic experience will give graduates a better insight into the cognitive and affective components of mathematics teaching at lower secondary school.
Dítě, škola a matematika: Konstruktivistické přístupy k vyučování / Milan Hejný, František Kuřina. Praha : Portál, 2001
Moderní vyučování / Geoffrey Petty Praha : Portál, 1993
Dvacet pět kapitol z didaktiky matematiky / Milan Hejný, Jarmila Novotná, Naďa Stehnlíková (Eds.) Praha, 2004
Thinking mathematically / John Mason, Leone Burton, Kaye Stacey. Pearson, 2010
Explanation and Proof in Mathematics. Philosophical and Educational Perspectives / G. Hanna, H. N. Jahnke, H. Pulte (Eds.), Springer 2010
Matematika a svet okolo nás : Zbierka úloh / Zbyněk Kubáček ... [et al.]. Bratislava : Pavol Cibulka, 2008
Učebnice matematiky pre gymnáziá / Zbyněk Kubáček
Matematika : 1 : zbierka úloh pre stredné školy / Iveta Kohanová ... [et al.]. Bratislava : Orbis Pictus Istropolitana, 2011
Own electronic materials published via the subject's website (eg course in LMS Moodle)
Continuous assessment: individual preparation of a lesson plan and its placement in the thematic plan, microteaching, preparation of written tests (2 equal groups), peer assessment, didactic analysis of teaching texts, reading and discussion of scientific articles.
The student must obtain at least 50% of the continuous assessment and each assignment must be evaluated with a non-zero number of points.
Exam: written with oral consultation
Indicative assessment scale: A 94%, B 86%, C 79%, D 70%, E 60%, Fx <60%
Specifics of the last year of lower secondary school, transition to the 1st year of upper secondary school. Appropriate activities of teaching mathematics for individual topics of the first and second year of upper secondary school: educational goals, activities, the assumption of the development of student understanding in the context of educational activities and the creation of their hypothetical scenario. Selection of adequate methods, forms and cognitively appropriate activities. Integration of digital technologies into the teaching of mathematics also in order to support argumentation, reasoning, and building a mathematical culture (correctness of concepts, procedures, arguments, etc.).
60/40
The graduate of the course is acquainted with the goals of mathematics education at upper secondary schools, with adequate teaching methods, forms and means, with ways of introducing selected mathematical concepts, is ready for his work at school and outside school, can transfer to pedagogical practice knowledge and skills acquired in individual professional disciplines. Specially, the graduate of the course will gain an overview of didactic procedures for teaching mathematics suitable for the transition from lower to upper secondary school and in the first years of upper secondary school.
Učebnice matematiky pre gymnáziá / Zbyněk Kubáček
Matematika : 1 : zbierka úloh pre stredné školy / Iveta Kohanová ... [et al.]. Bratislava : Orbis Pictus Istropolitana, 2011
Seminár z matematiky, časti 1 – 3 / Zbyněk Kubáček, Ján Žabka
Explanation and Proof in Mathematics. Philosophical and Educational Perspectives / G. Hanna, H. N. Jahnke, H. Pulte (Eds.), Springer 2010
Thinking mathematically / John Mason, Leone Burton, Kaye Stacey. Pearson, 2010
Maturitné testy z matematiky /nucem.sk
Own electronic materials published via the subject's website (eg course in LMS Moodle)
Continuous assessment: individual preparation of a lesson plan and its placement in the thematic plan, microteaching, preparation of written tests (2 equal groups), peer assessment, didactic analysis of teaching texts, reading and discussion of scientific articles.
The student must obtain at least 50% of the continuous assessment and each assignment must be evaluated with a non-zero number of points.
Exam: written with oral consultation
Indicative assessment scale: A 94%, B 86%, C 79%, D 70%, E 60%, Fx <60%
slovak, english
Selected activities for teaching mathematics on the topics of the third and fourth year of high school (for graduates and non-graduates): educational goals, activities, the assumption of the development of student understanding in the context of educational activities and the creation of hypothetical trajectories.
60/40
The graduate of the course will gain an overview of didactic procedures in the teaching of mathematics at upper secondary school and in the preparation of students for the school-leaving examination in mathematics, in extracurricular activities. The described activities of the educational process are focused on the creative use of knowledge from mathematics acquired during the study.
Diferenciální počet / Vojtech Jarník. Praha : Academia, 1984
Zbierka úloh z vyššej matematiky : 3.časť / Jozef Eliaš, Ján Horváth, Juraj Kajan. Bratislava : Slovenské vydavateľstvo technickej literatúry, 1967
Continuous assessment: homework
Final assessment: paper
Indicative assessment scale: A 90%, B 80%, C 70%, D 60%, E 50%
Examples of quantities whose change depends on several variables. Graphs of some typical functions of two variables. Space R ^ 2 and R ^ 3. Sequence convergence in R ^ 2. Limit and continuity of a function of two variables. Partial derivation. Extremes of a function of two variables.
40/60
Students will master the basic analytical methods of investigation and modeling, when the action is affected by two variables. They will be able to estimate the shape of the graph of the functions of two variables.
Integrální počet / Vojtech Jarník. Praha : Československá akademie věd, 1976
Zbierka úloh z vyššej matematiky : 4.časť / Jozef Eliaš, Ján Horváth, Juraj Kajan, Robert Šulka. Bratislava : Alfa, 1979
Matematika III, Zbierka riešených úloh z integrálneho počtu funkcie viac premenných a krivkových integrálov / Dillingerová M., Feťková J., Híc P., Tóthová M. Alfa : Bratislava 1990
Continuous assessment: homework
Final evaluation: test
Indicative assessment scale: A 90%, B 80%, C 70%, D 60%, E 50%
slovak, english
For successful completion, it is desirable to first complete the course Selected Parts of Mathematical Analysis.
Areas of type [x, y] and [y, x] and a formula for integrating the function of two variables in these areas. Calculation of areas, volumes and lengths of curves.
40/60
Students will expand their knowledge of the function of two variables. Using the double integral, they will be able to calculate different areas, volumes, lengths of curves.
seminar work / project
slovak, english
Flipped Classroom, Cooperative teaching, Brain-compatible teaching, method "Break", Realistic teaching (RME), Guided active learning, Jigsaw method, problem solving, rpg, simulation.
100/0
Students will be able to distinguish between different methods of education. They will have an overview of the principles and principles of each method and will be able to apply these principles in practice.
Homework assignments
Grading: A 90%, B 80%, C 70%, D 60%, E 50%, Fx < 50 %
Selected topics from the following areas:
Introduction to set theory. Operation with sets, functions. Cardinality, inequality between cardinal numbers, operations with cardinal numbers and their properties. Cantor's theorem. Countable and uncountable sets, applications.
Basics of group theory. Symmetry groups, permutation groups, abstract notion of a group. Subgroups, cyclic groups. Cosets and Langrange's theorem. Homomorphisms, normal subgroups, quotient groups.
Rings and fields. Modular arithmetic, polynomial rings. Construction of Q from Z, C from R, Q(sqrt(p)) from z Q. Field extensions, finite fields, impossibility of some geometric constructions.
Semester 100% (homework assignments)
Students will gain familiarity with axiomatic definitions and applications of some algebraic structures, such as groups and fields. They will be able to prove basic results about sets operations and to verify whether some commonly used sets are countable or uncountable.
Homework assignments, final exam
Grading: A 90%, B 80%, C 70%, D 60%, E 50%, Fx < 50 %
Selected topics from the following areas:
Examples of permutation groups, braid groups, groups of symmetries and matrix groups. Description by generators, relations, consequences of non-commutativity. Abstract notion of a group. Subgroups, orders, cyclic groups. Cosets and Langrange's theorem. Homomorphisms, normal subgroups, quotient groups. Group actions, stabilizers, orbits. Symmetries of Platonic solids.
Rings, fields and integral domains. Modular arithmetic, polynomial rings. Ideals, ring factorization, homomorphisms of rings. Field extensions. Rings with unique factorization, Gauss primes, etc.
Semester 25% (homework assignments)/Final exam 75%
Students will gain familiarity with examples of mathematical objects (symmetries, permutations, linear maps) which can be described by using an axiomatic approach. They will be able to use these definitions and deduce basic properties, analyze examples and identify various algebraic structures, such as groups and fields.
Grafové algoritmy / Ján Plesník. Bratislava : Veda, 1983
Grafy a jejich aplikace / Jiří Demel, Academia, 2002
Konec záhady hlavolamů / Stanislav Vejmola, SPN 1989
Peliminary evaluation: homeworks
Exam: oral
Indicative evaluation scale: A 90%, B 80%, C 70%, D 60%, E 50%
slovak,english
Some basic concepts and results from graph theory, searching graphs reachability and connectivity, trees and spanning trees, planar graphs, hard problems in graph theory.
50/50
Students will get acquainted with basic concepts of graph theory. At the same time, they will learn to transform different types of problems into graph theory problems and solve them algorithmically.
Geometria 1 : Pre študentov matematiky učiteľského štúdia na univerzitách a pedagogických fakultách / Milan Hejný, Valent Zaťko, Pavel Kršňák. Bratislava : Slovenské pedagogické nakladateľstvo, 1985
Analytická teorie kuželoseček a kvadrik / Josef Janyška, Anna Sekaninová. Brno : Masarykova univerzita, 2001
Analytická geometria kužeľosečiek / Leo Boček. Bratislava : Slovenské pedagogické nakladateľstvo, 1978
Continuous assessment: homework (50%).
Final assessment: written exam (50%).
At least half of the points from the continuous assessment must be admitted to the exam.
Grading: A [100-90], B (90-80], C (80-70], D (70-60], E (60-50], Fx (50-0].
Slovak, English
1. Conics in the Euclidean plane: definition and representation; asymptotic vectors; regular, singular point; the center of the conic; polarity; tangents; principal vectors; axes and vertices of the conics; affine and metric classification of conics; focal points and directrices. Applications.
2. Fundamentals of the theory of quadratic surfaces in the Euclidean three-dimensional space: regular linear and non-linear quadratic surfaces; singular quadratic surfaces; quadratic surfaces such as cylindrical surfaces over the conic sections; quadratic surfaces obtained by affine transformation of a conic. Intersection points of a line (plane) with a quadratic surface.
50/50
Course graduate:
1. Knows basic affine and metric properties of conic sections in the Euclidean plane and quadratic surfaces in the Euclidean three-dimensional space, using mainly the analytical method.
2. Is aware of the crucial role of polarity in the theory of quadratic forms. Is informed about quadrics in the Euclidean space of any dimension.
3. Is acquainted with synthetic constructions of real regular conic sections and practical applications and interpretations of their properties.
Helmut Pottmann, Andreas Asperl, Michael Hofer, Axel Kilian, Daril Bentley: Architectural Geometry, Bentley Institute Press, 2007
Lectures on classical differential geometry / Dirk J. Struik. Cambridge : Addison-Wesley Press, 1950
Elektronické učebné texty predmetu
The student can get 100% for written homeworks.
Grading: A (100-91), B (90-81), C (80-71), D (70-61), E (60-51), Fx (50-0).
Slovak, English
Gear wheels, milling, 3D printing, exceptional structures, maps, typography, painting, and sculpture from the perspective of objects, methods, and representations in differential geometry.
Preliminary assessment 100% for written homework assignments.
By completing the course, the student will gain deeper knowledge about the properties of curves and surfaces. They will become familiar with their fundamental applications in practical disciplines such as modern design, engineering, construction, cartography, and art.
Dějiny matematiky / Dirk J. Struik ; přeložili Jaroslav Folta, Luboš Nový. Praha : Orbis, 1963
Dějiny matematiky ve starověku / Arnošt Kolman. Praha : Academia, 1968
Dějiny matematiky ve středověku / Adolf P. Juškevič. Praha : Academia, 1977
Dejiny matematiky / Ján Čižmár. Bratislava : Perfekt, 2020
The history of mathematics / Roger L. Cooke. Hoboke, NJ : John Wiley, 2003
The history of mathematics / David M. Burton, New York : McGraw-Hill, 2011
Ongoing evaluation: presentation of the prepared lesson (20 points), preparation of the written exam for other participants (10 points), active participation in the evaluation of presentations and written exams of other participants (30 points).
Grading: A (56-60 points), B (51-55 points), C (46-50 points), D (41-45 points), E (36-40 points), Fx (0-35 points).
Weight of the ongoing / final assessment: 100/0
Slovak, English
Mathematics of ancient Egypt and Babylonia. Pre-Euclidean mathematics in ancient Greece. Euclid´s Elements.
100/0
Student will gain an overview of the various periods of development of mathematics in antiquity, including examples of problems solved in individual basic works.
Matematika v proměnách věků III / Editori Jindřich Bečvář, Eduard Fuchs. Praha : Výzkumné centrum pro dějiny vědy, 2004
Dějiny matematiky / Dirk J. Struik ; přeložili Jaroslav Folta, Luboš Nový. Praha : Orbis, 1963
Dějiny matematiky ve starověku / Arnošt Kolman. Praha : Academia, 1968
Dějiny matematiky ve středověku / Adolf P. Juškevič. Praha : Academia, 1977
Dejiny matematiky / Ján Čižmár. Bratislava : Perfekt, 2020
The history of mathematics / Roger L. Cooke. Hoboke, NJ : John Wiley, 2003
The history of mathematics / David M. Burton, New York : McGraw-Hill, 2011
Ongoing evaluation: presentation of the prepared lesson (20 points), preparation of the written exam for other participants (10 points), active participation in the evaluation of presentations and written exams of other participants (30 points).
Grading: A (56-60 points), B (51-55 points), C (46-50 points), D (41-45 points), E (36-40 points), Fx (0-35 points).
Weight of the ongoing / final assessment: 100/0
Slovak, English
Students will choose from the following topics: Ptolemy. Apollonius. Chinese and Arabic mathematics. Fibonacci. Alcuin's problems. Cardano´s Ars Magna. Pascal's Arithmetic Triangle. Huygens´s De Ratiociniis in Ludo Aleae. Bernoulli's Ars Conjectandi. Cavalieri's Geometry of indivisibles. Euler's Introductio and Letters to a German Princess. Venn´s Symbolic Logic.
100/0
The student will gain an overview of the various periods of mathematics development, including examples of problems solved in individual basic works.
Mathematics and Art / Bruter (Ed.), Springer
Hudba ako zdroj námetov vo vyučovaní matematiky / M. Slavíčková, In. Matematika, informatika, fyzika. Roč. 21, č. 38 (2012), s. 3-8. ISSN 1335-7794
Chladniho obrazce / E. Dubajová, (časť diplomovej práce), dostupné na https://wilma.sk/dokumenty/ef0ed9b0f05bd757ddcf91b96794b0cf/show
The Science of Sound / T. D. Rossing, R. F. Moore, P. A. Wheeler, 3. vyd., Pearson, 2014
Music: A Mathematical Offering / D. Benson, Department of Mathematics, Meston Building, University of Aberdeen, UK. 2008
Continuous assessment: individual work of students, project
Indicative assessment scale: A 90%, B 80%, C 70%, D 60%, E 50%
slovak, english
To complete the course, it is recommended to have at least a basic knowledge of music theory (min. of 2 years music school)
Selected parts of music theory from the point of view of mathematics, connection to mathematics from lower secondary school to university, related to the teaching of mathematics, preparation of interdisciplinary projects and activities for direct inclusion in teaching and leisure activities.
100/0
By completing the course, the student will deepen and combine knowledge of basic mathematics courses in bachelor's studies in the study program mathematics teacher preparation in combination, build on knowledge of mathematics didactics and broaden horizons in the context of creating lessons using interdisciplinary relationships.
Dostupné učebnice Matematiky pre 5. – 9. ročník ZŠ a nižšie ročníky osemročných gymnázií / Ján Žabka, Pavol Černek / Ondrej Šedivý a kol. / Soňa Čeretková a kol. / Milan Hejný a kol.
Nový Pomocník z matematiky (5. – 9. ročník) / Iveta Kohanová a kol.
Dítě, škola a matematika: Konstruktivistické přístupy k vyučování / Milan Hejný, František Kuřina. Praha : Portál, 2001
Matematické cítenie / Jo Boalerová. Bratislava : Tatran, 2016
Moderní vyučování / Geoffrey Petty. Praha : Portál, 1993
Dvacet pět kapitol z didaktiky matematiky / Milan Hejný, Jarmila Novotná, Naďa Stehlíková (Eds.) Praha, 2004
Own electronic materials published via the subject's website (eg course in LMS Moodle)
Continuous assessment: output in front of the board, seminar work
Indicative assessment scale: A 94%, B 86%, C 79%, D 70%, E 60%, Fx <60%
slovak, english
The course will follow on from the compulsory course Didactics of Mathematics 2 and will deal in depth with specific adequate methods, forms and age-appropriate activities for teaching problematic units in mathematics at lower secondary school.
100/0
Metódy riešenia matematických problémov / L. C. Larson ; from the American original translated by Jaroslav Smítal. Bratislava : Alfa, 1990
Metódy riešenia matematických úloh / Tomáš Hecht, Zita Sklenáriková. Bratislava : Slovenské pedagogické nakladateľstvo, 1992
Tasks from Mathematical Olympiad and Mathematical correspondence seminars
Continuous assessment: Homework - individual work of students
Indicative assessment scale: A 90%, B 80%, C 70%, D 60%, E 50%
Slovak, English
Generally about solving mathematical tasks, basic methods of solving mathematical tasks –patterns identification and conclusion making, figural approaches to solving, formulating equivalent problems, modifying the problem, choosing effective marking, using symmetry, dividing the problem into several special cases, reverse procedure, indirect procedure, use of parity, mathematical induction, Dirichlet (Pigeon) principle.
100/0
After completing the course, students will master methods of solving various mathematical tasks from the curriculum of lower and upper secondary school and will be able to apply these methods in the teaching of mathematics.
Metódy riešenia matematických problémov / L. C. Larson ; from the American original translated by Jaroslav Smítal. Bratislava : Alfa, 1990
Metódy riešenia matematických úloh / Tomáš Hecht, Zita Sklenáriková. Bratislava : Slovenské pedagogické nakladateľstvo, 1992
Tasks from Mathematical Olympiad and Mathematical correspondence seminars
Continuous assessment: Homework - individual work of students
Indicative assessment scale: A 90%, B 80%, C 70%, D 60%, E 50%
Slovak, English
Equations, inequalities, systems of equations and inequalities, sets of points of given properties, analytical geometry, construction tasks, planimetric tasks, stereometric tasks, inequalities in geometry, number theory, diophantic equations, combinatorial geometry, sequences, recurrent relationships, trigonometry and complex numbers, probability.
100/0
After completing the course, students will master methods of solving various mathematical tasks from the curriculum of lower and upper secondary school and will be able to apply these methods in the teaching of mathematics.
Aj geometria naučila človeka myslieť / Milan Hejný. Bratislava : Slovenské pedagogické nakladateľstvo, 1990
Analýza řešení slovních úloh : Kapitoly z didaktiky matematiky. / Jarmila Novotná.. Praha : Univerzita Karlova,, 2000.
Dítě, škola a matematika : Konstruktivistické přístupy k vyučování / Milan Hejný, František Kuřina. Praha : Portál, 2001
Teória vyučovania matematiky 2 / Milan Hejný ... [et al.]. Bratislava : Slovenské pedagogické nakladateľstvo, 1990
Ongoing evaluation: homeworks
Indicative rating scale: A 90%, B 80%, C 70%, D 60%, E 50%
Slovak, English
Demonstrations of a transmissive and constructivist way of leading a lesson. Error preview. Textbook as a teacher's aid. Textbook as a student aid. (Topics will be documented in the curriculum of the second primary education stage).
100/0
Students will be prepared for the situations they will experience in the reality of teaching mathematics at the second primary education stage. They will know various teaching techniques, methods of interpretation, working with the textbook as well as supplementary materials, various forms of written and oral examinations, as well as methods of correcting children's solutions. They will learn to distinguish which statements help students and which harms them.
Aj geometria naučila človeka myslieť / Milan Hejný. Bratislava : Slovenské pedagogické nakladateľstvo, 1990
Dítě, škola a matematika : Konstruktivistické přístupy k vyučování / Milan Hejný, František Kuřina. Praha : Portál, 2001
Stavba planimetrie / Ján Gatial, Milan Hejný. Bratislava : Slovenské pedagogické nakladateľstvo, 1973
Teória vyučovania matematiky 2 / Milan Hejný ... [et al.]. Bratislava : Slovenské pedagogické nakladateľstvo, 1990
Analýza řešení slovních úloh : Kapitoly z didaktiky matematiky. / Jarmila Novotná.. Praha : Univerzita Karlova, 2000.
Ongoing evaluation: homeworks
Indicative rating scale: A 90%, B 80%, C 70%, D 60%, E 50%
Slovak, English
Evaluation and classification. Preparations, analysis and corrections of written works and tests (topics will be documented in the secondary school curriculum).
100/0
Students will be prepared for the situations they will experience in the school reality of teaching mathematics in secondary school. They will know various teaching techniques, methods of interpretation, working with the textbook as well as supplementary materials, various forms of written and oral examinations, as well as methods of correcting children's solutions. They will learn to distinguish which statements help students and which harms them.
Teória vyučovania matematiky 2 / Milan Hejný ... [et al.]. Bratislava : Slovenské pedagogické
nakladateľstvo, 1990
Učebné materiály pre vyučovanie matematiky / výber zostavili a preložili Monika Dillingerová, Lilla Koreňová, Peter Vankúš. Bratislava : Knižničné a edičné centrum FMFI UK, 2009
Geometrické úlohy z matematickej olympiády ZŠ / Monika Dillingerová. Bratislava : Metodicko-pedagogické centrum, 2005
Continuous assessment: homework (30 points)
Indicative assessment scale: A 90%, B 80%, C 70%, D 60%, E 50%
slovak, english
Basic features and historical development of constructivist teaching. Piaget, Kohlberg, Vygotsky, Bachelard. Creation of teaching material. Group and cooperative teaching. Didactic game, its use and creation. Stereometry cubes with paper scissors and glue. Stereometry of a circle, folding "other" origami. Project teaching, project assignment (to whom, what, how, when, for what time). Problem teaching, design of own problem teaching. Outdoor school - from organization to implementation. Mathematical afternoon at school in nature, creation of a program "out". Mathematical competitions - various forms of competitions, difficulty assessment and task creation.
100/0
After completing the course, the student knows the theories of various forms of teaching, some of which he has tried. He knows the root causes of the problems that students with a planar representation of space have - the question "Why don't students see it?". Can carry out various additional activities that develop students' mathematical competencies, e.g. competitions, games, fun afternoon.
1. Logic and sets
Logic (propositions, operations with propositions, logical conjunctions and quantifiers), sets (number of elements of unification of two and three sets, De Morgan's formulas for complement of unification and intersection), proofs and conclusions (direct and indirect proofs, proofs by dispute, mathematical induction, mode ponens, modus tollens).
2. Numbers, variables, numerical fields
Binomial theorem and Pascal's triangle, derivation of formulas a^n-b^n (including geometric interpretation for n = 2 and n = 3).
3. Number theory
Number of prime numbers, relation of largest common divisor and smallest common multiple of two numbers, prime decomposition number of number divisors, irrationality of the square root of a prime number, derivation of divisibility criteria 4, 5, 10, 100, 3, 6, 9.
4. Equations, inequalities and their system
Geometric interpretation of a system of two linear equations with two unknowns, conditions for the existence of solutions, equivalent and non-equivalent modifications and their relation to basic functions.
5. Function and its properties
Basic transformations of function graphs, definitions of basic properties of functions (domain of definition, domain of values, increasing and decreasing, extrema and local extrema - sharp and fuzzy, examples), inverse function and its graph.
6. Linear and quadratic function
Significance of coefficients k and q in the formula of the linear function y = kx + q, geometric meaning of the directive, quadratic function (derivation of the relation for calculating roots, coordinates of the vertex of the parabola .
7. Arithmetic and geometric sequence, infinite (geometric) series
Basic relationship management.
8. Polynomials, power functions and linear polynomials
Root factors and their relation to the roots of a polynomial equation, square roots as inverse functions to power functions, definition of a rational power of a positive number, linear polynomial function (derivation of asymptote equations and conditions why ad ≠ bc).
9. Exponential and logarithmic functions
Exponential functions (definition of power for natural, integer and rational exponent, basic properties of exponential function and their justification, simple and compound interest, regular deposits and withdrawals, loan repayments), definition of logarithm, rules for calculating logarithms and their connection with creation of exponential function , relationships between logarithms with different bases.
10. Trigonometric functions
Definition of trigonometric functions in a right triangle and using a unit circle and their mutual relation, values of trigonometric functions for basic angles, accounting formulas, formulas for double and half angle, relations for sum and difference of trigonometric functions.
11. Triangle
Consistency and similarity of triangles, Pythagorean and Euclidean theorems, different relations for the content of a triangle (Heron's formula, using sinus of angle, radius of inscribed and described circle), derivation of statements about intersections of angles, axes of sides, lines, heights, sine and cosine theorem.
12. Parallelograms and trapezoid
Derivation of formulas for the content of parallelograms and trapezoids, derivation of some of their properties the diagonals of a quadrilateral with sides a, b, c, d are perpendicular to each other just when a2 + c2 = b2 + d2).
13. Circle
Formula for the content of a circle and a paragraph, size in degrees and radians, center and circumferential angle, Tales' theorem, estimation of the number π using written and described n-gons, related to trigonometric functions.
14. Analytical geometry in the plane and in space
Vectors and operations with them, scalar product and its relation to the angle of two vectors, analytical expression of a line and a plane, various equations of a line, derivation of coordinates of the center of a line and a dividing line in a given ratio, center of a triangle, size of a line, derivation of a formula lines and from the plane, angle of two lines (using scalar product, using directives), angle of line and plane, normal vector.
15. Sets of points of given properties and their analytical expression
Derivation of "basic" sets of points of a given property (including a set of points from which a line can be seen at a given angle).
16. Conic sections
Definitions of conic sections (circle, ellipse, hyperbola and parabola) as sets of points of given properties and derivation of their equations.
17. Suitable and similar representations, construction tasks
Examples of design tasks solved by a combination of calculation and construction, the use of sets of points of given properties in design tasks, examples of design tasks solved using identical and similar representations.
18. Basic ways of displaying space in a plane
Basic properties of parallel projection, hint of their justification, linear perspective and its basic properties, layers and their basic properties.
19. Linear formations in space - positional problems
Use of basic statements about the intersections of a pair of parallel ones planes with another plane when constructing sections of bodies by a plane.
20. Solids
Cavalieri's principle and its application e.g. to calculate the volume of a sphere, a formula for calculating the volume of pyramids and cones, the idea of justifying the formula for the surface of a sphere.
21. Combinatorics
Combinatorial identities, basic combinatorial rules (sum, product), typical examples of their use, derivation of formulas for the number of variations, combinations, permutations (also with repetition), combinatorial derivation of basic relations in the Pascal triangle (symmetry, sum of minor elements).
22. Probability
Statistical and Laplace definition of probability, dependent and independent events, calculation of probability for independent events, geometric probability and an example of its use.
23. Statistics
Statistical set and position measures (modus, median, mean), basic properties of the arithmetic mean (sum of deviations from the mean is equal to 0), various possibilities of describing the "scatter" of the set, Chebyshev's inequality.
slovak, english
State final examination in the scope of master's study of mathematics didactics. The student should be able to include the task in the thematic unit, identify preconceptions and the necessary knowledge to solve it, determine the skills that the student will learn on it, respectively. concepts that allows you to discover. The student will demonstrate a model solution, point out problematic places in the solution with which students could have problems and how he would react to them as a teacher. After completing the task, the student should outline the activities that would follow and how he would close the lesson.
0/100
The graduate will be ready to perform the tasks assigned to a beginning math teacher.
Computer Aided Science Laboratory / Peter Demkanin et al .. Bratislava: Knižničné a edičné centrum, 2006
Evidence based teaching: A practical approach / Geoff Petty. Cheltenham: Nelson Thornes, 2006
Modern teaching: practical guide / Geoffrey Petty; translated from English by Štěpán Kovařík. Prague: Portal, 1996
Own electronic texts of the subject published through the subject's website.
Continuous assessment: 2 micro-appearances in front of the audience, evaluation of micro-appearances of classmates
Indicative assessment scale: A 90%, B 80%, C 70%, D 60%, E 50%
Slovak, English
student-supported guided research in science subjects, research teaching methods, interface, sensors, measurement with sensors, computer control (programming in Coach language), basics of laboratory safety, measurement of physical quantities and processing of measured values, measurement with sensors in chemistry teaching and biology, the use of the CMA Coach system in students' hobby work (within non-formal education), basic rules for the creation of instructional materials for students
100/0
Students will develop the ability to use the resources of a computer-assisted science laboratory in teaching their approbation subjects in primary and secondary school. They will be able to plan the student's activity and the teacher's activity in the student's experiment, they will be able to use the CMA Coach science laboratory system and they will be able to evaluate the students' work in this laboratory.
FONTANA, D. 2014. Psychology in school practice. Prague: Portal 2014. 384 p. ISBN 978-80- 262-0741-2
GAVORA, P. 2010. What are my students like? Nitra: Enigma, 2010. 224 p. ISBN 978-80-89132-91-1
JEDLIČKA, R. 2018. Pedagogical - psychological diagnostics (Chapter 7). In JEDLIČKA, R. et al. Educational psychology for teachers. Prague: Grada, 2018. p. 349-358. ISBN 978-80- 271-0586-1
DYTRTOVÁ, R. - KRHUTOVÁ, M. 2009. Teacher: příprava na profesi. Publisher information: Praha: Grada, 128 s. ISBN 978-80-247-2863-6
HRABAL, V. st. - HRABAL, V. Jr. 2004. Diagnostics: Pedagogical-psychological diagnostics of a pupil with an introduction to diagnostic application. Prague: Karolinum. 268 s. ISBN 80-246-0319-3
HELUS, Z. 2007. Social psychology for pedagogues. Prague: Grada, 2007. 280 p. ISBN 978- 80-247-1168-3
KOMPOLT, P. - TIMKOVÁ, B .: Pedagogical diagnostics and action research. Bratislava: UK, 2010. ISBN 978-80-223-2787-9
MIKULAJOVÁ, M. et al. 2012. Reading, writing and dyslexia. Bratislava: Slovak Association of Speech Therapy. 296 s. ISBN 978-80-89113-94-1
POKORNÁ, V. 2010. Theory and correction of learning and behavioral disorders. Prague: Portal. 336 s. ISBN 978-80-7376-817-3
MERTIN, V., KREJČOVÁ, L .: Methods and Procedures of Pupil Cognition. Pedagogical diagnostics. Wolters Kluwer CR, 2016;
GINNIS, P .: Effective Teaching Tools for Teachers. Universum Publishing House, 2019;
FLETCHER-WOOD, H .: Responsive Teaching. Cognitive sciences and formative assessment in practice. Universum, 2021.
The condition for successful completion of the course is to obtain at least 60% of the maximum possible evaluation of the course = active participation in classes (30%), homework (20%), reading literature (20%)
The course is completed by an exam (30%).
The rating is given on a scale:
A (100-91%, excellent - excellent results),
B (90-81%, very good - above average standard),
C (80-73%, good - normal reliable work),
D (72-66%, satisfactory - acceptable results),
E (65-60%, sufficient - results meet minimum criteria),
Fx (59-0%, insufficient - additional work required)
Slovak, Czech
Diagnosis as standard, resp. intuitive process of detailed cognition and evaluation of the pupil's personality, pupil groups, resp. family environment. Diagnosis as a "court" about a student (student groups), various types of diagnoses, including case studies. Diagnostic procedures and techniques (product analysis of pupils 'activities, performance tests, design techniques and traditional testing methods. The essence of school evaluation and its types. Evaluation of pupils' results, effects and school conditions. Action research as a specific professional activity of a teacher. Observation method. Interview method. Sociometers, self-diagnostics of pupils and teachers (self-evaluation, burnout diagnostics, diaries, questionnaires ...), diagnostics of classroom relationships, diagnosis of bullying.
70/30
Students will acquire key knowledge about the standard form of diagnostics, its basic stages and the formulation of diagnostic conclusions. They will acquire the necessary competencies in the use of diagnostic procedures and techniques for determining and evaluating students' performance in school conditions and in the reflection and evaluation of their own activities and professional growth.
own electronic texts published on the website, resp. in the Moodle environment
Qualitative research in pedagogical sciences / Švaříček, Roman and Klára Šeďová. Prague: Portal, 2007
Methods of pedagogical research: basics of quantitative research / Chráska, Miroslav. Prague: City, 2007
Guide to Qualitative Research Methodology / Peter Gavora. Bratislava: Comenius University, 2007
Basics of pedagogical-psychological research for student teachers / Martin Skutil et al .. Prague: Portal, 2011
Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research / John W. Creswell. Pearson 2011
Methodology of pedagogical research
individual work during the semester, focused on the research part of the diploma thesis - depending on the type of research and after a personal agreement with the teacher (60%) - min. 3 individual consultations
Exam: comprehensive research chapter of the future diploma thesis (40%)
Assessment scale: A 90%, B 80%, C 70%, D 60%, E 50%
Slovak, English
Course contents:
- Repetition of the basics of qualitative and quantitative research, processing and interpretation of empirical data.
- Implementation of procedures and selection of appropriate research techniques.
- Acquiring field data collection skills and solving related problems.
- Evaluation and consultation of the analysis of research results.
- Submission and presentation of the final work.
60 / 40
The student:
- deepen their knowledge of the basic stages and methods of empirical research of educational phenomena related to their research topic of the diploma thesis
- design, implement and evaluate at least part of the research problem of their thesis
- write a comprehensive chapter in his diploma thesis on research activities
own electronic texts published on the website, resp. in the Moodle environment
Qualitative research in pedagogical sciences / Švaříček, Roman and Klára Šeďová. Prague: Portal, 2007
Methods of pedagogical research: basics of quantitative research / Chráska, Miroslav. Prague: City, 2007
Guide to Qualitative Research Methodology / Peter Gavora. Bratislava: Comenius University, 2007
Basics of pedagogical-psychological research for student teachers / Martin Skutil et al .. Prague: Portal, 2011
Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research / John W. Creswell. Pearson 2011
Methodology of pedagogical research
individual work during the semester, focused on the research part of the diploma thesis - depending on the type of research and after a personal agreement with the teacher (60%) - min. 3 individual consultations
Exam: comprehensive research chapter of the future diploma thesis (40%)
Assessment scale: A 90%, B 80%, C 70%, D 60%, E 50%
Slovak, English
Course contents:
- Repetition of the basics of qualitative and quantitative research, processing and interpretation of empirical data.
- Implementation of procedures and selection of appropriate research techniques.
- Acquiring field data collection skills and solving related problems.
- Evaluation and consultation of the analysis of research results.
- Submission and presentation of the final work.
60 / 40
The student:
- deepen their knowledge of the basic stages and methods of empirical research of educational phenomena related to their research topic of the diploma thesis
- design, implement and evaluate at least part of the research problem of their thesis
- write a comprehensive chapter in his diploma thesis on research activities
PROKŠA, M., HELD, Ľ. et al .: Methodology of pedagogical research and its application in didactics of natural sciences. Bratislava: Comenius University, 2008.
CHRÁSKA, M .: Methods of pedagogical research.Prague, Grada, 2007.
SILVERMAN, D .: How to do qualitative research. Bratislava, Ikar, 2005.
GAVORA, P .: Introduction to pedagogical research. Bratislava: UK, 1996, 1999, 2001, 2008.
GAVORA, P .: A Guide to Qualitative Research Methodology. Bratislava: UK, 2007.
MAŇÁK, J. - ŠVEC, V .: Ways of pedagogical research. Brno: Paido, 2004.
PELIKÁN, J .: Basics of empirical research of pedagogical phenomena. Prague: Karolinum, 1998, 2004, 2007.
ŠVEC, Š. et al .: Methodology of educational sciences. Quantitative-scientific and qualitative-humanities approaches. Bratislava: Iris, 1996. 2nd ed. Brno: Paido, 2009.
GAVORA, P. et al. 2010. Electronic textbook of pedagogical research methodology. (Online). Bratislava: Comenius University in Bratislava, 2010. Available online. ISBN 978-80-223-2951-4.
STRAUSS, A., CORBINOVÁ, J. 1999. Basics of qualitative research. Procedures and techniques of grounded theory. Boskovice: Nakladatelství Albert, 1999, 196p. ISBN 80-85834-60-X.
ŠEĎOVÁ, K., ŠVAŘÍČEK, R., 2007. Qualitative research in pedagogical sciences. Prague: Portal, 2007, 377 p. ISBN 978-80-7367-313-0.
ŠVAŘÍČEK, R - ŠEĎOVÁ, K .. et al .: Qualitative research in pedagogical sciences. Game rules. Prague: Portal, 2007
J.W. CRESWELL: Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research: International Edition. Pearson Education (US) 2011
J.W. CRESWELL, V.L. Plano CLARK .: Designing and Conducting Mixed Methods Researc. SAGE Publications Inc, 2017
Attendance at lectures is not necessary, but recommended. (20%)
The exercises evaluate active work, solving tasks such as. coding, analysis and data collection, etc. and solving beds at home. (60%)
The course is completed by a research project (20%)
The condition for successful completion of the course is to obtain at least 60% of the maximum possible evaluation of the course. The rating is given on a scale:
A (100-91%, excellent - excellent results),
B (90-81%, very good - above average standard),
C (80-73%, good - normal reliable work),
D (72-66%, satisfactory - acceptable results),
E (65-60%, sufficient - results meet minimum criteria),
Fx (59-0%, insufficient - additional work required)
Slovak
Research of educational phenomena. Action research as a specific professional activity of a teacher. Stages of empirical educational research. Procedures and techniques of research of educational phenomena (experiment, observation, scales and scaling, interview, questionnaire, sociometry and measurement of social climate, method of content analysis of school documents).
Qualitative research (characteristics, principles, use), collection of qualitative data (tools, conditions, tool creation), processing and interpretation of qualitative data (transcription, coding, theory creation, use), quantitative research (characteristics, principles, use), collection of quantitative data data (tools, conditions, tool creation), processing and analysis of quantitative data. (statistical methods, types, application, use), objectivity, reliability and validity of research, designs of qualitative, quantitative and mixed pedagogical research
80/20
At the end of the semester, students will receive:
Knowledge of basic stages and methods of empirical research of educational phenomena, basic methodological concepts, stages, methods and principles of quantitative and qualitative pedagogical research.
Skills needed to study and analyze scientific studies in pedagogy.
The teacher is able to design his / her own educational research, survey or action research and, with the support of the trainer, to carry out an independent research effort.
Ability to choose appropriate and meaningful research topics, deftly develop a research project, collect and empirically correct analysis of research data. They can interpret, defend and publish research data meaningfully and creatively.
Ability to critically evaluate various pedagogical researches, their implementation and their results.
They can create and choose the right type of research, with regard to solving a problem in the teaching process. They are able to create, implement and evaluate a test of knowledge and skills, according to the rules of creation and with regard to educational goals.
FFinancie v praxi A / Peter Tóth, Monika Dillingerová, Bratislava : ABCedu, a.s. 2019
Financie v praxi B / Peter Samuel Tóth, Monika Dillingerová, Bratislava : ABCedu, a.s. 2021,
Financie v praxi C / Peter Samuel Tóth, Monika Dillingerová, Bratislava : ABCedu, a.s. will be printed soon
my own electronic texts published on a website in LMS Moodle
Continuous assessment: active participation in seminars / elaboration of assignments
An exam:
Indicative evaluation scale: e.g. A 90%, B 80%, C 70%, D 60%, E 50%
slovak
- National standard financial literacy
- Origin and development of money;
- Financial responsibility of consumers;
- Planning, receiving and working;
- Consumer decision-making and management;
- Credit and debt;
- Saving and investing;
- Risk management and insurance;
100/0
The student:
- knows the target requirements for a financially literate student
- propose activities and be able to assess their suitability
- can solve and prepare his / her own tasks in every topic of financial literacy.
- own electronic texts published on the website, resp. in the Moodle environment
- Cárová, T. and Kohanová, I. 2012. Global primary school education - mathematics - methodical manual. [online] Slovak AID, Human at Risk, 2012. ISBN: 978-80- 970900-4-3 Available on the Internet: https://globalnevzdelavanie.sk/globalne-vzdelavanie-na-zs-matematika/
- Kireš. M., Ješková, Z., Ganajová, M., Kimáková, K. Research activities in science education. Bratislava: ŠPÚ, 2016.
- outputs from the IT academy project, where digital technologies are implemented in various subjects.
Continuous assessment: Active participation in classes (50%), design and implementation of a project with the implementation of a cross-cutting theme (50%).
An exam: -
Indicative evaluation scale: e.g. A 90%, B 80%, C 70%, D 60%, E 50%
Weight of the mid-term / final evaluation: e.g. 100/0
Slovak
- Cross-cutting themes according to the official curriculum and the possibilities of their implementation in various subjects.
- Topics found in the intersection of various subjects.
- Authentic learning aimed at solving real problems of life.
- Design and implementation of a project with the implementation of a cross-cutting theme.
- Presentation of the results of the implemented project.
100 / 0
The student:
- is able to include cross-cutting themes in the teaching of their subject in an appropriate way (especially environmental, multicultural, regional and media education),
- learn about the possibilities of connecting approbation subjects in the form of project teaching,
- gets ideas and inspirations for interdisciplinary projects.
ANZENBACHER, Arno: Introduction to Philosophy. Prague: SPN, 1991. ISBN: 80-04-26038-1.
BREZINKA, Wolfgang: Filozofické základy výchovy. Prague: Zvon, 1996. ISBN: 80-7113-169-5
CORETH, Emerich: What is a human being? Fundamentals of philosophical anthropology. Prague: Zvon, 1994. ISBN: 80-7113-098-2
POPKIN, Richard. H., STROLL, Avrum: Philosophy for Everyone. Prague: Ivo Zelezny, 2000. ISBN: 80-240-0257-4
PELCOVÁ, Naděžda: Philosophical and pedagogical anthropology. Prague: Karolinum, 2000. ISBN: 80-246-0076-5
Complementary literature and literature that is not in AK UK will be presented at the beginning and during the semester. Teachers' presentations and non-AK UK literature are available at MS Teams.
During the teaching period of the semester: participation, activity, elaboration of assignments or final test. The test or assignments will be from the material covered during the semester. The student can get a maximum of 50 points, the minimum for successful completion of the course is 30 points.
Classification scale: A: 100-92%, B: 91-84%; C: 83-76%, D: 75-68%, E: 67-60% FX: 0-59%
Violation of academic ethics results in the cancellation of the obtained points in the relevant evaluation item. The teacher accepts max. 2 absences with proven documents.
Interim / final evaluation weight: 100% in the examination period
Slovak
1. The concept and structure of philosophy
2. Philosophical and pedagogical anthropology
3. Philosophical anthropology and axiology
4. Philosophy of education I.
5. Philosophy of education II.
6. Philosophy of culture and values
7. Ethical issues and perspectives of education
Upon successful completion of the course, students will know:
A: in the field of knowledge:
• What is philosophy, its basic structure, goals and mission
• What issues do philosophy of education and philosophical anthropology address, what are their goals and mission?
• What is the significance of philosophy for solving problems of theory and practice of education
B: in the field of skills:
• Orientation in basic philosophical problems, disciplines and concepts
• Ask questions and formulate answers regarding philosophical questions of education
• Think independently about philosophical issues of education
šeďová, K. et al .: Výukova komunikace, Masarykova Univerzita, Brno 2019.
Svoboda, M .: Psychosocial interaction training in pedagogical practice, University of West Bohemia in Pilsen, 2017.
Continuous assessment: active work in class (interactive presentation and practical solution of tasks - 50% of continuous assessment), submission and presentation of assignments (preparation for class and completion of lessons - 50% of continuous assessment).
Indicative assessment scale: A 90%, B 80%, C 70%, D 60%, E 50%
Slovak
- Key competencies of the teacher, influential theories about concepts in communication
- Verbal and nonverbal communication in the classroom
- Evaluation of verbal outcomes - SOLO taxonomy
- Argumentation as a part of critical thinking, conceptual comics
- Teacher questions
- Feedback
- Pupils' participation in learning communication
- Dialogue teaching
- Use of psychosocial interaction training in school practice
- Silent video as a means of developing communication skills
100 / 0
The student will be at the end of the semester:
- know specific activities focused on psychosocial interaction
- have experienced and practiced application of selected communication skills
- familiar with the rules and implications of best practices for effective communication
- know the rules and structure of arguments
- be able to appropriately apply the knowledge of solo taxonomy in evaluating the quality of verbal statements of the student
own electronic texts published on the website, resp. in the Moodle environment
GINNIS, P .: Effective Teaching Tools for Teachers. Universum Publishing House, 2019.
GORDON, T .: School without Losers. Malvern. 2015.
BREAUX, A .: Quick help for teachers. Portal. 2020.
SMETÁČKOVÁ, I., ŠTECH, S .: Učitelské vyhoření. Portal. 2020.
ČAPEK, R .: Lazy Teacher. How to teach well and effectively. Raabe. 2019
BUCHWALD, P .: Stress at school and how to manage it. Edika. 2013.
JANÍK, T .: Myths of False Error. About chibas in education and pedagogy. Masaryk University. 2020.
ČOKYNA, J .: And where are your edges? N Press. 2019
Continuous assessment: active participation in seminars + preparation for classes (80%), project / report (20%)
A 90%, B 80%, C 70%, D 60%, E 50%
Slovak, English
- first year of the teacher (holidays, payslips, attendance, introductory teacher, training, ...)
- work of subject commissions and pedagogical documentation
- class
- coordination of school activities and events
- communication with parents
- crisis situations at school
- professional development and mental health care
- toxic stress and inappropriate behavior
- bullying at school, mobing and bossing
- working with students with special educational needs
100 / 0
The student:
- gets a concrete idea of the teacher's responsibilities
- will be acquainted with the recommended procedures and effective ways of solving various situations in pedagogical practice
- propose activities and be able to assess their suitability for application to different problems with different groups of students
- can plan their own personal development in addition to professional development and take a critical approach to self-reflection
5 pillars of Mind / T.Tokuhama-Espinosa
The Learning Science / R.K.Sawyer
Course materials
During the semester, the student, based on information from lectures, prepares a proposal for a semester work (10 points) in the required structure, defends it (10 points) and implements it (20 points).
Indicative assessment scale: A 90%, B 80%, C 70%, D 60%, E 50%
Slovak in combination with English (study literature also in English).
Selected approaches to cognitive psychology. The theory of the 5 pillars of the mind. Knowledge-in-Pieces Theory. Principles and tenets of learning. Applying the acquired knowledge in design a series of teaching sequences in approbation subject.
100 / 0
The student knows selected approaches to current principles and tenets of learning formulated on knowledge of neuroscience results. In accordance with these principles and tenets can design a series of teaching sequences in his approbation.
Selection of literature according to the chosen topic of the thesis;
The current directive of the Rector of Comenius University on the basic requirements of theses;
KATUŠČÁK, D.: Ako písať záverečné a kvalifikačné práce. Nitra: Enigma 2007.
Active participation, ongoing reporting on work on the thesis. A 90%, B 80%, C 70%, D 60%, E 50%
Slovak, English
Choice of thesis topic.
Review of literature on the topic.
Basic material research and the procedure of its processing.
Methods of processing and producing the thesis (citation standards, manuscript editing, note-taking apparatus).
Presentation of a partial output (e.g. in the form of one chapter of the thesis).
100/0
Definition of the thesis topic, overview of the current state of problem solving, choice of the theoretical-methodological concept of the thesis and the ability to work selectively and correctly with secondary literature.
Creswell JW. Educational research: Planning, conducting, and evaluating quantitative. Prentice Hall Upper Saddle River, NJ; 2002.
Sources listed in the thesis assignment.
Sources available in databases (e.g. wos, scopus, researchgate).
Textbook on research methodology in science teaching recommended by the thesis supervisor.
active participation in the seminar, on time submission of assignments and presentation of preliminary results
A 90%, B 80%, C 70%, D 60%, E 50%
Slovak, English
Formulating the objectives of the thesis on the basis of its assignment; obtaining, sorting and using available resources; working with electronic information sources; formulating research questions, searching for research methods suitable for the topic of the thesis.
100/0
The graduate of the course is able to obtain and sort information from information sources, especially from monographs, journal articles, conference proceedings and university textbooks. The graduate is able to plan research in the area of the thesis.
Creswell JW. Educational research: Planning, conducting, and evaluating quantitative. Prentice Hall Upper Saddle River, NJ; 2002.
Sources listed in the thesis assignment.
Sources available in databases (e.g. wos, scopus, researchgate).
Textbook on research methodology in science teaching recommended by the thesis supervisor.
Active participation, ongoing reporting on work on the thesis.
A 90%, B 80%, C 70%, D 60%, E 50%
Slovak, English
Development of argumentation skills, causal thinking and creativity in the area of the thesis topic. Development of abilities to present the results of own work in the field of the thesis topic.
100/0
The graduate is able to elaborate the chosen topic at the level of a scientific study with a representative selection of literature, with appropriately chosen scientific procedures and hypotheses that can be verified. The graduate is able to formulate the contribution of his/her own work in the field of informatics/mathematics/physics teaching.
According to the topic of the master thesis.
Examination: state examination
Indicative assessment scale: A 90%, B 80%, C 70%, D 60%, E 50%
Slovak, English
1. The contribution of the final work for the given field of study depending on its nature and degree of study. The evaluation of the diploma thesis takes into account whether the student adequately processes the selected topic at the level of scientific study with a representative selection of professional literature, whether the chosen scientific procedures are appropriate and appropriate, and whether he adequately works with hypotheses that can be verified. The diploma thesis should be a clear contribution in the relevant field of study;
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 diploma thesis is usually 50 - 70 standard pages - 90,000 to 126,000 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
The student is able to work on the chosen topic at the level of scientific study with a representative selection of professional literature, with appropriately selected scientific procedures and hypotheses that can be verified. The diploma thesis is a contribution in the relevant field of study.