1. Carroll, B. W., Ostlie, D. A., An Introduction to Modern Astrophysics, Addison-Wesley Publishing Company, Reading, Massachusetts, 1996;

2. Contopoulos, D. Kotsakis, Cosmology, the structure and evolution of the Universe, Springer, 1984;

3. Pasachoff, J.M., Filippenko, A., The Cosmos: Astronomy in the New Millennium, Cambridge University Press, 2013;

4. Vanýsek, V., Základy astronomie a astrofyziky, Academia, Praha,1980;

5. Čeman, R., Pittich, E., Vesmír 1 - Slnečná sústava, MAPA Slovakia, Bratislava, 2002;

6. Čeman, R., Pittich, E., Vesmír 2 - Hviezdy - Galaxie, MAPA Slovakia, Bratislava, 2003;

Basic knowledge of physics.

To successfully complete the course, the student must demonstrate sufficient understanding of the basic knowledge of the structure and evolution of the universe. Knowledge of the basic properties of stars and methods of their determination, the structure, evolution and energy sources of stars, the structure of matter in the universe and its evolution is required. The condition for obtaining credits is passing a written or oral exam, preparation, and presentation of a semester essay. The credit evaluation of the course considers the following student workload: direct teaching (1 credit) and assessment (1 credits). The minimum threshold for completing the course is to obtain at least 50% of the total score, using the following rating scale: A (90-100%), B (80-89%), C (70-79%), D (60- 69%), E (50-59%), Fx (0-49%).

Slovak, English

Structure of matter in the universe

Basic properties of stars and methods of their determination: Masses, dimensions and distances of stars. Radiation flux, apparent and absolute magnitude. The temperature of stars, black body radiation, spectra of atoms and molecules, non-thermal radiation. Spectral classification, luminosity classes, HR diagram. (1st - 2nd week)

The structure and evolution of stars: Basic equations of stellar structure, production and transfer of energy in stars, fusion reactions. The origin of stars, interstellar matter, Jeans’ criterion, protostars, main sequence stars, giants and final stages of stellar evolution - white dwarfs, neutron stars and black holes. Planetary systems. (3rd - 5th week)

Structure of matter in the universe: Galaxy, its structure, dynamics and evolution. Types of galaxies, quasars, intergalactic matter. Local Group of galaxies, clusters and super-clusters of galaxies. The large-scale structure of the universe. Dark matter and dark energy. (6th - 7th week)

Evolution of the universe

Introduction to Cosmology: Historical development of views on the universe, Olbers paradox, gravitational paradox. Cosmological principle. Isotropy and homogeneity of the universe, cosmic background radiation, expansion of the universe. Steady-state theory. (8th - 9th week)

Relativistic Cosmology: Cosmological solutions of Einstein's equations, models of the universe and their properties. Theory of the expanding universe, the Big Bang, the age of the universe. (10th - 11th week)

The origin of the universe: The initial stages of the expansion of the universe, inflationary expansion and nucleogenesis. The formation of galaxies and galaxy clusters. The arrow of time, the future of the universe. Anthropic principle.(12th - 13th week)

1. Basic properties of stars and methods of their determination: radiation flux, apparent and absolute magnitude, distances of stars, colors of stars.

2. Temperature of stars, black body radiation, spectra of atoms and molecules, non-thermal radiation.

3. Spectral classifications, luminosity classes, HR diagram, masses of stars.

4. Structure of stars: basic equations of stellar structure, transfer of energy by radiation and convection, production of energy in stars, fusion reactions.

5. Evolution of stars: interstellar matter and formation of stars and stellar systems, Jeans’ criterion, protostars.

6. Evolution of stars: main sequence stars, giants, final stages of star evolution - white dwarfs, neutron stars and black holes.

7. Distribution of matter in the universe: Milky Way, its structure, dynamics, and evolution, types of galaxies, quasars, intergalactic matter, local group of galaxies.

8. Clusters and super-clusters of galaxies, large-scale structure of the universe, dark matter, and dark energy.

9. Evolution of the universe: historical development of views on the universe, Olberson's paradox, gravitational paradox, Cosmological principle.

10. Isotropicity and homogeneity of the universe, relic radiation, expansion of the universe. Steady state theory.

11. Relativistic cosmology: cosmological solutions of Einstein's equations, models of the universe and their properties, theory of the expanding universe, the Big Bang, the age of the universe.

12. Origin of the universe: the initial stages of the expansion of the universe, inflationary expansion and nucleogenesis, the formation of galaxies and galaxy clusters.

After completing the lectures, the student will master the basic knowledge about the properties of stars and methods of their determination, structure, evolution and energy sources of stars, the structure of matter in the universe and its evolution. It will also have sufficient physical knowledge and mathematical apparatus to enable independent solving of a various tasks related to astrophysical research.

Slovak and Czech mathematics textbooks for secondary education. National mathematics

curriculum of Slovakia, Czech republic and USA.

Active participation - 40% of assessment

Seminar works - 60% of assessment

Slovak

The concept of function in mathematics, its aspects, and definitions. The concept of function in

the school curriculum, knowledge of the structure of mathematics with respect to the concept of

function. Proximal formative assessment, knowledge of the characteristics of learning mathematics.

Instrumented formative assessment with a focus on the use of digital technologies for assessment

in mathematics. Selection of tasks and digital tools for teaching functions. MTSK model as a tool

for teacher self-reflection.

The student understands the term function and its various aspects also in the context of different definitions of the term function. He looks critically at the school curriculum from the point of view of the development of the concept of function. It characterizes high-quality formative assessment and can react differently to correct and incorrect student solutions. He applies the acquired knowledge in the design of the lesson plan. He knows the MTSK model and knows how to use it as a tool for his self-reflection.

e- version of schoolbook Physics for lower secondary school

Analysis of the fundamental Physics Education problems.

The analysis of teaching units based on the current state educational currculum.

Planning of the teaching lesson.

Design of the educational activity and tools for gaining feedback.

semester work:

elaborated online assignments in lms.upjs.sk

analysis of model methodologies

elaboration and presentation of own educational activity

oral examination:

clarification of two topics from subject didactics

clarification of the thematic unit

presentation of model methodology

Slovak, English

..

Within the Didactics of Physics subject the core problems of physics education are introduced and case studies of their solving are interpreted. Strategies on design and implementation of educational activities, their evaluation and the use of modern media are introduced and corresponding skills are trained.

..

Knowledge and skills in the field of Physics education, overview about the problems of Physics education, basic skills necessary to prepare and quide educational activities, school experiments, problem solving and to use modern media for physics education.

Vaníček, J.: Počítačové kognitivní technologie ve výuce geometrie, Pedagogická fakulta Univerzity Karlovy, 2009

Stahl, G.: Dynamic-Geometry activities with GeoGebra for Virtual Math Teams, The Math Forum at Drexel University, 2012.

De Villiers, M., D.: Rethinking proof with the Geometer's Sketchpad. Key Curriculum Press, 2003.

Master the concept of dynamic geometric systems and commands for creating and modifying dynamic constructions. To be able to use dynamic geometric systems in the study of the properties of geometric shapes and the discovery of geometric patterns. To be able to effectively use the commands of dynamic geometric systems for modeling various situations, solving geometric problems, exploring geometric transformations, exploring graphs of functions, data processing.

Rating:

Test requiring the solution of geometric problems using classical tools and the use of a dynamic geometric system - 16 b.

Elaboration of a project focused on the use of a dynamic geometric system in solving geometric problems on a selected topic - 16 b.

Classification scale:

A: 91 % - 100 %, B: 81 % - 90 %, C: 71 % - 80 %, D: 61 % - 70 %, E: 51 % - 60 %, FX: 0 % - 50 %.

Slovak

1.-4. Constructions and investigation of properties and geometric relations in triangles, quadrilaterals, circles and their use in solving construction problems. Menelaos's theorem, Ceva's theorem, Varignon's theorem, Ptolemy's theorem, cyclic and tangential quadrilaterals, center of gravity of triangles and quadrilaterals.

5. Investigation of sets of points with a given property.

6. Discovering and testing geometric relationships.

7. Composing congruent transformations. Use of congruent and similar transformations and circular inversion for solving tasks.

8. Mathematical modeling, investigation of functional dependencies between quantities, solving problems to find extremes.

9.-10. Constructions of bodies, mutual positions of geometric shapes in space, sections of bodies, intersection of a line with a body.

Skills to create dynamic constructions in a dynamic geometric system and to use commands usable in solving geometric problems. Knowledge and skills to effectively use geometric, algebraic and other types of tools in experimenting with geometric objects and their attributes, in discovering invariant properties of geometric shapes and geometric relationships between objects in triangles, quadrilaterals, conic sections and in basic types of spatial bodies. Be able to use geometric transformations in solving more complex constructing tasks.

1. Brunovský, P. , Diferenčné a diferenciálne rovnice (vysokoškolský učebný text), FMFI UK, 2011

http://www.iam.fmph.uniba.sk/skripta/brunovsky/ddrtext.pdf

2. L. Kluvánek, I. Mišík, M. Švec: Matematika II, SVTL, Bratislava, 1961.

3. N. M. Matvejev: Zbierka príkladov z obyčajných diferenciálnych rovníc, ALFA, Bratislava,

4. Stuart, A.M.; Humphries, A.R. (1996), Dynamical Systems and Numerical Analysis, Cambridge University Press

5. Jacques M. Bahi and Christophe Guyeux. 2013. Discrete Dynamical Systems and Chaotic Machines: Theory and Applications. CRC Press, Inc., Boca Raton, FL, USA. 1970.

6. Kelley, C. T. (1995). Iterative Methods for Linear and Nonlinear Equations. SIAM.

7. Kelley, C.T. (1999) Iterative Methods for Optimization. In: Frontiers in Applied Mathematics, Vol. 18, SIAM

Ongoing evaluation takes the form of a written test during the semester. The overal evaluation is based on a result of mid-term evaluation (60%) and the result of final written and oral examination (40%).

Slovak

1. Basic notions of the theory of dynamical systems and their properties.

2. Differential equations of n-th order and systems of differential equations - their relationship, methods of solution.

3. Difference equations and systems - methods of solution.

4. Existence, uniqueness and continuation of Cauchy problem.

5. Applications of dynamical systems.

The course provides students deep knowledge of the theory of dynamical systems from the theoretical and practical point of view (their modeling, their properties and numerical simulation). Emphasis is put on an interdisciplinary approach and hte usage of software.

A general introductory course in solid state physics and material science.

H. Ibach, H. Lüth: Solid-State Physics. Springer - Verlag, Berlin, 1993.

Ch. Kittel: Introduction to Solid State Physics. John Wiley & Sons, Inc. 1976.

Sucessfull passing the course requires presentation of adequate knowledge of concepts, phenomena and laws from Condensed Matter Physics. Knowledge of structural, mechanic, electric, thermal, transport and magnetic properties of solids and potetail possibilities of their practical applications. The number of credits reflects the extent of the course (2 hours of lectures) and the fact that the contents of the course represents part of state exam in magister degree.

During semester students will prepare two written works on the given topic and they will actively participate in the final debate on the topics which are identical to the content of the lectures. Treshold for for sucessfull passing the course is 50 % of the sum of obtained scores from the tests and oral exam. Maximal total score from both tests represents 30 % from the total score.

The scale of the total score is defined as follows:

A 100-91%

B 90-81%

C 80-71%

D 70-61%

E 60-50%

Fx 49-0%

Slovak, English

The course is given in attendance form, if a need arises, online form using MS Teams can be adopted.

1.week: Structure of crystals. Amorphous materials. Space and crystal lattice, elementar cell. Bravais lattices and crystallographic systems. Directions and planes in a crystal lattice – Miller´s indexes. Reciprocal lattice.

2. week Methods of structural analysis. Diffraction of X-ray radiation on crystals. Bragg´s equation and Laue´s condition, relation between them. Ewald´s construction for different experimental techniques.

3. week: Mechanical properties of solids and perturbations in crystal lattice. Classification of solids according to nature of bonding among elements in crystal lattice. Basic types of bondings (ion, covalent, metal, Van der Walls, hydrogen)

4. week: Thermal properties of solids – Einstein and Debye theory of specific heat. Eletrical properties of solids.

5. week: Sommerfield´s theory. Density of electronic states. Influence of temperature on the distribution of free electrons. Fermi – Dirac distribution function.

6. week: Electron in periodic potential. Energy spectrum of electrons in crystal. Kronig – Penney´s model. Effective mass of electron.

7. week: Concept of holes. Semiconductors. Electrical conductivity of metals and semiconductors adopting properties of energy spectrum of electrons.

8. week: Transport properties in metals and semiconductors – Hall effect, magnetoresistance, photoconductivity, contact phenomena, quantum Hall effect.

9. week: Macroscopic quantum phenomena: Superconductivity and Superfluidity.

10. week: Magnetic properties of solids – orbital and spin magnetic moment of atom. Definition of basic magnetic quantities (magnetization, polarization, susceptibility, permeability). Vector model of atom.

11. Classification of magnetic materials according to nature of magnetic interactions. Diamagnetic and paramagnetic systems.

12 week: Basic properties of ferromagnets. Magnetic hysteresis, coercitive field. Domain structure, physical reasons ledaing to the domain structure.

Sucessfull passing the course will significantly contribute to the expertise of the teacher in physics. Student will learn basic concepts in Condensed matter physics and understand phenomena in solids. He will also learn selected theoretical approaches and used experimental techniques in Condensed matter physics. In addition, he will also be able to interpret simple experimental observations based on quantum-mechanical phenomena.

oral examination

1. M. Sekanina et al, Geometry 2, SPN, 1988 (in slovak).

2. O. Šedivý et al, Geometry 2, SPN, 1987 (in slovak).

3. H.S.M. Coxeter, Introduction to geometry, Wiley, 1989.

4. J.T. Smith, Methods of geometry, Wiley, 2000.

In the covered areas of geometry, the ability to formulate definitions and statements, to present proofs of statements, to explain individual steps in proofs and to solve selected problems related to given topics is required. During the semester (continuous assessment) two tests take place, from which 50% of points can be obtained, and from the oral exam alike 50% can be obtained. Evaluation: A ... at least 90%, B ... at least 80%, C ... at least 70%, D ... at least 60%, E ... at least 50%, FX ... less than 50%

Slovak

- (week 1-2) Quadric surfaces (circular and general quadric surfaces)

- (week 3-7) Affine transformations (associated transformation, matrix representation, affinities, fixed points and lines, pseudo-reflections)

- (week 8-10) Isometric transformations (matrix representation, isometries, classification in the plane, composiion of reflections)

- (week 11-12) Similarity transformations (matrix representation, similarities, homothety, composition of homotheties)

- (week 13-14) Geometry of circles (the power of a point with respect to a circle, radical axis of two circles, pencils of circles)

Acquired knowledge of the properties of affine, isometric and similarity transformations, understanding of important statements and methods, knowledge of the use of isometric and similarity transformations in construction and optimization problems and the ability to solve other problems in this area.