G. Dorren: Babel. Around the World in 20 Languages. Profile Books, 2019
S. Pinker: Language Instinct. Brilliance Audio, 2014
S. Pinker: The Stuff of Thought. Language as a Window Into Human Nature. Penguin Books 2008
S. Pinker: Words and Rules. The lngredients of Language. Basic Books 2015
Continuous assessment: presentations, bonus assignments
Indicative assessment scale: A 90%, B 80%, C 70%, D 60%, E 50%
Slovak, English
The course focuses on the most important aspects of natural language research (the most complex cognitive function): basic properties of language (arbitrariness, generative productivity, dynamism, structuring at many levels), mechanisms of speech production and perception, language acquisition, innate and acquired factors of language development.
http://dai.fmph.uniba.sk/~rybar/
100/0
Acquisition of the most important current theories and methods of studying natural language and cognitive processes.
S. Blackmore, E.T. Troscianko: Consciousnes. An Introduction. Routledge, third edition 2018.
M.S. Gazzaniga, R.B. Ivry, G.R. Mangun: Cognitive Neuroscience. The Biology of the Mind. W.W. Norton & company, fifth edition 2019.
J. Friedenberg, G. Silverman: Cognitive Science. An Introduction to the Study of Mind. Sage 2012.
T. Metzinger: The Ego Tunnel. The Science of the Mind and the Myth of the self. Basic Books 2009.
Continuous assessment: presence (30%), presentation (40%), bonus assignments (30%)
Indicative assessment scale: A 90%, B 80%, C 70%, D 60%, E 50%
Slovak, English
The subject of the course is the human mind and brain from the perspective of neuroscience, computer science, psychology, and philosophy. It is mainly focused on the interdisciplinary study of consciousness: its neural correlates, neuroscience and behavioral research methods, and major theories.
100/0
The course objectives are to make the students familiar with major theories and methods of mind/brain research.
CogLab / Greg Francis, Ian Neath, Daniel R. VanHorn. Thomson/Wadsworth, 2014
Interim evaluation: presentations
Indicative assessment scale: A 90%, B 80%, C 70%, D 60%, E 50%
Slovak, English
Demonstration of 40 standard experiments in the fields of neurocognition, mechanisms of perception, attention systems, memory processes, speech production and perception, knowledge representation (concepts and mental ideas), judgment and decision-making processes.
http://dai.fmph.uniba.sk/~rybar/
100/0
Acquisition of methods for studying various cognitive phenomena (data collection and analysis) using an online cognitive laboratory.
Continuing evaluation: homework assignments (50%), project (50%)
Indicative rating scale: A 90%, B 80%, C 70%, D 60%, E 50%
slovak, english
An introduction to the practical use of the Python programming language and the Pandas data processing library. The matplotlib library. Advanced plotting of graphs using the seaborn library (statistical distributions, confidence intervals, "heat maps", ...). Interactivity in data visualization using the Plotly library. Visualization of high-dimensional data. Methods for visualization of textual data. Data visualization in the context of machine learning.
Students will be able to analyze datasets of different sizes, pre-process them into a visualizable form as well as identify and practically apply different methods of data visualization using the Python programming language.
Students should gain basic knowledges and skills of the Mathematical Analysis in the below listed Subjests.
Rudin, Walter: Principles of mathematical analysis, ISBN 0-07-054235-X
Hildebrandt, Stefan: Analysis I, ISBN 3-540-42838-0
Forstter, Otto: Analysis I, ISBN 3-528-57224-8
Neubrunn, Tibor a Vencko, Jozef: Mathematical Analysis I, textbook of FMFI UK
Kubáček, Valášek: Cvičenia z Matematickej analýzy 1,2
6 times 45 minutes tests and individual tasks
Continuous assessment: 4 written examinations during the semester, 10 points each, homework evaluated twice per semester, active participation in seminars
Examination: written and oral examination
Indicative assessment scale: A 92%, B 84%, C 76%, D 68%, E 60%
Slovak and English
I. Introduction
II. The Real and Complex Number Systems
Ordered Sets, Fields, The Real Field, The Extended Real Number System, The Complex Field.
III. Basic Topology
Finite, Countable, and Uncountable Sets, Compact Sets.
IV. Numerical Sequences and Series
Convergent Sequences, Subsequences, Cauchy Sequences, Upper and Lower Limits, Some Special Sequences, Series, Series of Nonnegative Terms, The Number e, The Root and Ratio Test, Power Series, Absolute Convergence, Addition and Multiplication of Series, Elementary Functions.
V. Continuity
Limits of Functions, Continuous Functions, Continuity and Compactness, Dicontinuities, Monotonic Functions, Infinite Limits and Limits at Infinity.
60/40
After completing the course, students will master the basics of mathematical analysis of the functions of one real variable. Thus, they will be able to investigate the course of a function, calculate the limits and derivatives of functions of one variable.
final 90 minutes test and oral examination
Michael Baye: Managerial Economics and Bussines Strategy.
Continuous test.
Final test-
Slovak, English
Market forces - demand, supply.
Costs, cost function.
Basic market models.
Perfect competition.
Monopoly.
Monopolistic competition.
Oligopoly markets.
Pricing.
The role of government in a market economy.
40/60
Students will understand the basics of neoclassical, textbook economics.
Linear algebra and its applications / Gilbert Strang. Belmont : Thomson Brooks/Cole, 2006
Lineárna algebra a geometria : Cesta z troch rozmerov s presahmi do príbuzných odborov / Pavol Zlatoš. Bratislava : Albert Marenčin, 2011; electronic version available at http://thales.doa.fmph.uniba.sk/zlatos/la/LAG_A4.pdf
Introduction to linear algebra / Gilbert Strang. Wellesley : Wellesley - Cambridge Press, 2009
Pěstujeme lineární algebru / Luboš Motl, Miloš Zahradník. Praha : Karolinum, 2002
Linear algebra done right / Sheldon Axler. New York : Springer, 1997
Work during the semester: 2 midterm exams (each 18%), homework (14%)
Final exam: written exam, oral exam (15 points needed to pass the written exam)
Approximate grade scheme: A 85%, B 75%, C 65%, D 55%, E 45%
English, Slovak
Systems of linear equations and their geometry, Gaussian elimination, matrix representation, vectors, matrix operations, inverse matrix, vector spaces, linear dependence / independence, base, dimension, matrix rank, linear transformation, kernel, image, scalar product, orthogonality, projection, orthogonal complement, Gram-Schmidt orthogonalization, matrix determinant, Laplace's expantion, Cramer's rule, determinant as volume, permutations.
http://thales.doa.fmph.uniba.sk/niepel/LA/linalg.html
50/50
Upon completion of this course, students will master basic computational skills of linear algebra: solving linear systems, determining linear dependence / independence, determining spatial dimension, finding orthogonal complement, projection and projection matrix, finding a matrix of a linear mapping, calculating matrix determinants, determining whether a mapping is linear, finding the kernel and the image of a mapping.
Students will improve their skills in proving propositions and deducing the properties of mathematical objects and advance their argumentation in the language and the style of university mathematics.
Students should gain basic knowledges and skills of the Mathematical Analysis in the below listed Subjests.
Rudin, Walter: Principles of mathematical analysis, ISBN 0-07-054235-X
Hildebrandt, Stefan: Analysis I, ISBN 3-540-42838-0
Forstter, Otto: Analysis I, ISBN 3-528-57224-8
Neubrunn, Tibor a Vencko, Jozef: Mathematical Analysis I, textbook of FMFI UK
Kubáček, Valášek: Cvičenia z Matematickej analýzy 1, 2
6 times 45 minutes tests and individual tasks
Continuous assessment: 4 written examinations during the semester, 10 points each, homework evaluated twice per semester, active participation in seminars
Examination: written and oral examination
Indicative assessment scale: A 92%, B 84%, C 76%, D 68%, E 60%
Slovak and English
VI. Differentiation
The Derivative of a Real Function, Mean Value Theorems, The Continuity of Derivatives, L'Hospital's Rule, Derivatives of Higher Order, Taylor's Theorem,
VII. The Riemann Integral
Definition and Existence of the Integral, Properties of the Integral, Integration and Differentiation, Rectifiable Curves.
VIII. Sequences and Series of Functions
Discussion of Main Problem, Uniform Convergence, Uniform Convergence and Continuity, Uniform Convergence and Integration, Uniform Convergence and Differentiation, Power Series.
60/40
After completing the course, students will master the basics of the integral number of functions of one real variable. Thus, to determine the primitive function, to compute certain integrals of the functions of one variable, to investigate the convergence of the series.
final 90 minutes test and oral examination
Olivier Blanchard: Macroeconomics
Mid-term test, final test.
Slovak, English
Gross domestic product. Total demand in the economy. IS-LM model. Government fiscal policy. Central bank monetary policy. Labor market. Total supply in the economy. Inflation. AS-AD model. Open economy.
40/60
Understanding the basics of how the country's economy as a whole works. The role of government and central bank.
Mastering of more advanced techniques of linear algebra, overview of applications - eigenvalues and eigenvectors, diagonalization, quadratic forms.
Linear algebra and its applications / Gilbert Strang. Belmont : Thomson Brooks/Cole, 2006
Lineárna algebra a geometria : Cesta z troch rozmerov s presahmi do príbuzných odborov / Pavol Zlatoš. Bratislava : Albert Marenčin, 2011; electronic version available at http://thales.doa.fmph.uniba.sk/zlatos/la/LAG_A4.pdf
Introduction to linear algebra / Gilbert Strang. Wellesley : Wellesley - Cambridge Press, 2009
Pěstujeme lineární algebru / Luboš Motl, Miloš Zahradník. Praha : Karolinum, 2002
Linear algebra done right / Sheldon Axler. New York : Springer, 1997
Linear Algebra and Geometry I. (1-EFM-121) or equivalent course.
Work during the semester: 2 midterm exams (each 18%), homework (14%)
Final exam: written exam, oral exam (15 points needed to pass the written exam)
Approximate grade scheme: A 85%, B 75%, C 65%, D 55%, E 45%
English, Slovak
Eigenvectors, eigenvalues, characteristic polynomial, applications of matrix diagonalization to difference and differential equations, Schur's lemma, minimal polynomial, Jordan Form, quadratic forms, Sylvester's criterion, Sylvester's law of inertia, conics.
http://thales.doa.fmph.uniba.sk/niepel/LA/linalg2.html
50/50
Upon completion of this course students will master the more advanced computational skills of linear algebra: finding eigenvalues and eigenvectors of a matrix, diagonalization of a matrix and finding its exponential, finding the minimum polynomial of a matrix, the generalized eigenvectors, deciding whether two matrices are similar, finding the Jordan canonical form, quadratic forms, describing a conic corresponding to a quadratic form.
Students will improve their skills in proving propositions and deducing the properties of mathematical objects and advance their argumentation in the language and the style of university mathematics.
Differential and integral calculus in R^n with applications in theoretical economics and finance.
Online zbierka príkladov a úloh a základov teórie:
Martin Kollár, Ľubica Kossaczká, Daniel Ševčovič: Diferenciálny a integrálny počet funkcií viac premenných v príkladoch
Knižničné a edičné centrum FMFI UK, 192 pp. (in Slovak). ISBN: 978-80-89186-54-9
http://www.iam.fmph.uniba.sk/institute/sevcovic/knihy/
BARNOVSKÁ M., SMÍTALOVÁ K.: (1991) Matematická analýza III, Skriptá UK, Bratislava.
BARNOVSKÁ M., SMÍTALOVÁ K.: (1984) Matematická analýza IV, Skriptá UK, Bratislava.
KLUVÁNEK, I., MIšÍK, L., ŠVEC M.: (1961) Matematika I, II, SVTL Bratislava.
DEMIDOVIČ, B.P.: (1977) Sbornik zadač i upražnenij po matematičeskomu analizu, Moskva Nauka (v ruštine).
exercises, homeworks
Continuous assessment: 2 tests, evaluation of oral presentations
Examination: written and oral examination
Indicative assessment scale: A 90%, B 80%, C 70%, D 60%, E 50%
Slovak and English
Class syllabus:
Topic 1: Normed vector spaces (NVS).
• Norm and its properties.
• Equivalent norms.
• Examples of norms in general NVS.
• Euclidean space. Scalar product.
• Cauchy-Schwartz inequality, Young's and Minkowski inequality.
• Linear mappings and functionalities.
Topic 2: Topological properties of NVS.
• Open and closed sets in a NVS.
• Boundary of a set.
• Convergence of sequences in NVS.
• Compact sets, criteria for compactness, Heine-Borel theorem.
• Complete normed spaces, Banach and Hilbert space.
• Completions of a normed space.
• Lebesgue space.
• Contiguous set.
• Convex set in the NVS.
Topic 3: Continuity in NVS.
• Limits of functions. The definition of continuity of a function in NVS.
• Extremal properties of continuous functions on compact and contiguous subsets.
• Contractive mapping and Banach theorem on the existence of a fixed point and its applications
Topic 4: Multivariate functions.
• Relationship between multiple limit and limits of functions of more variables.
• Graph over a function of several variables.
• Convex and concave function.
• Level sets of convex functions.
Topic 5: Differentiability of functions of several variables.
• Partial derivatives of functions of several variables and their geometric interpretation.
• Partial derivatives of higher order, interchangeability of the order of differentiation.
• The derivative of a multivariate function and its geometrical interpretation.
• Relationship between derivative of a function and its partial derivatives, Jacobi matrix.
• Derivative of a composite function. Derivatives of higher order.
Topic 6: Properties of differentiable functions.
• Taylor series for multivariate function.
• Differential of a function and its use to determine the approximate value of a function.
• Gradient of a function and directional derivatives.
• Relationship between gradient and level set of a differentiable function.
• Convexity criterion for functions of several variables.
Topic 7: Extremal properties of multivariate functions.
• Tangent plane to a graph of a functions.
• Maximum and minimum of a multivariate function, local extremes. Saddle points.
• Necessary conditions for local extremes of functions of several variables.
• Sufficient conditions for local extremes and Hessian matrix of second derivatives.
• Global extremes and methods for their determination.
• Applications that lead to finding extremes of unconstrained functions.
Topic 8: Functions given implicitly.
• Examples of importance of implicit functions.
• The existence of an implicit function.
• Derivative of implicit function.
• Existence of an inverse function.
Topic 9: Extremes of a constrained multivariate function.
• Importance and application of extremes of a constrained multivariate function.
• Geometric interpretation of the extreme of a constrained multivariate function and Lagrange multipliers.
• Lagrangian.
• Necessary conditions for the existence of an extreme of a constrained function.
• Methods for determining the extreme type, some simple sufficient conditions for finding constrained minimum/maximum.
• General sufficient condition for an extreme of a constrained function and bounded Hessian.
40/60
To master the basics of the differential calculus of functions of several variables with emphasis on the methods used in the economic sciences. Upon completion of the course, students will acquire key competences in the field of vector mathematical analysis and finite-optimization methods.
final examination
To master basic linear programming.
Mária Trnovská: Lineárne programovanie, online text.
Lineárne programovanie / Ján Plesník, Jitka Dupačová, Milan Vlach. Bratislava : Alfa, 1990
Robert J. Vanderbei: Linear programming: Foundations and extensions, Kluwer Academic Publishers, 2000.
class activity, home works, project presentation
Continuous assessment: exercises: 20%, project: 20%, Exam: 60%.
The student must obtain at least half of the points for the exercises in order to pass the final written exam.
Grading: A (100-91), B (90-81), C (80-71), D (70-61), E (60-51), Fx (50-0).
Slovak, English
Geometric approach to solving linear programming problems. Practical problems formulation in the form of LP. Fundamentals of convex analysis (convex set, polyhedrons, extreme points, separation theorems, theorems of alternatives). Basic solutions and connection with extreme points. Simplex method (basic idea, two-phase and dual simplex method). Duality theory (duality and complementarity theorems) and its applications and economic interpretation. Basic idea of interior point methods for linear programming, central path. Modern applications of linear programming.
40% / 60%
Student master the basics of linear programming (simple models of real problems, relevant geometry, duality theory and some of simplex methods, the idea of interior point methods). They are able to prove the statements. At the same time, they will gain an overview of possible applications of linear programming in other scientific fields, or in practice.
examination
F. Zhang - Matrix theory, Springer Verlag New York, 1999
C.D. Meyer Matrix analysis and applied linear algebra, SIAM, 2001,
David C. Lay Linear algebra and its applications, Pearson Education, 2016,
S.L. Campbell, Carl D. Meyer Generalised inverses of linear transformation, SIAM, 2009,
W. Ford Numerical linear algebra with applications using MATLAB, Elsevier 2014
Activity, homework, passing the test. Grading A (100-91), B (90-81), C (80-71), D (70-61), E (60-51), Fx (50-0).
slovak, english
Partitioned matrices, Schur complement, various matrix classes and their properties (positive semi-definite matrices, hermitian, unitary and orthogonal matrices, stochastic matrices, permutation matrices, tri-diagonal and circulant matrices, nilpotent and unipotent matrices, normal matrices etc.), matrix norms, (condition number Frobenius norm, vector norm induced matrix norms and their properties), singualr values and singular value decomposition, other matrix decompositions, pseudo-inverse matrices and their properties.
100% / 0%
Students become familiar with fundamental knowledge of matrix calculus useful in other fields of mathematics.
C.D. Meyer Matrix analysis and applied linear algebra, SIAM, 2001,
David C. Lay Linear algebra and its applications, Pearson Education, 2016,
S.L. Campbell, Carl D. Meyer Generalised inverses of linear transformation, SIAM, 2009,
W. Ford Numerical linear algebra with applications using MATLAB, Elsevier 2014
Activity, homework (100%). Grading A (100-91), B (90-81), C (80-71), D (70-61), E (60-51), Fx (50-0).
Slovak and English
See: Matrix calculus
100% /0%
Acquisition of knowledge and practice of tasks from the subject Matrix calculus.
Brealey, R. A., Myers, S.C.: Principles of Corporate Finace, McGraw Hill, 13th Edition, 2020
Brealey, R. A., Myers S.C.: Teorie a praxe firemních financí, Computer Press, Praha, 2000
Damodaran, A.: Corporate Finance, John Wiley and Sons, 2001
Ross, A. R., Westerfield, R.W., Jaffe, J.: Corporate Finance, McGraw Hill, 5th Edition, 1999
Continuous assessment: Presentation of a project on a given topic.
Examination: Written test
Grading scale: A 91%, B 81%, C 71%, D 61%, E 51%
Slovak, English
Introduction to issues in corporate finance. Financial ratios. Time value of money, compounding and discounting. Valuation of stocks and bonds. Investment criteria, sensitivity analysis, decision trees. Yield and risk. Portfolio theory, Capital Asset Pricing Model (CAPM). Capital Structure. Tax Shield. Financial distress and bankruptcy. Dividend policy.
https://sites.google.com/view/podnikovefinancie2020/home
30/70
By the end of this course, students should be able to demonstrate an understanding of the basic principles of investment and financial decision making processes of the firm.
Differential and integral calculus in R^n with application in theoretical economics and finance.
M. Barnovská, K. Smítalová, Matematická analýza IV, Skriptum UK v Bratislave, 1984.
V. Ďurikovič, Mat. Analýza 4, Integrálny počet v R^n, UK, 1997.
Online zbierka príkladov a úloh a základov teórie:
Martin Kollár, Ľubica Kossaczká, Daniel Ševčovič: Diferenciálny a integrálny počet funkcií viac premenných v príkladoch
Knižničné a edičné centrum FMFI UK, 192 pp. (in Slovak). ISBN: 978-80-89186-54-9
http://www.iam.fmph.uniba.sk/institute/sevcovic/knihy/
BARNOVSKÁ M., SMÍTALOVÁ K.: (1991) Matematická analýza III, Skriptá UK, Bratislava.
BARNOVSKÁ M., SMÍTALOVÁ K.: (1984) Matematická analýza IV, Skriptá UK, Bratislava.
KLUVÁNEK, I., MIšÍK, L., ŠVEC M.: (1961) Matematika I, II, SVTL Bratislava.
DEMIDOVIČ, B.P.: (1977) Sbornik zadač i upražnenij po matematičeskomu analizu, Moskva Nauka (v ruštine).
exercises, homeworks
Continuous assessment: 2 written tests, evaluation of oral presentations
Examination: written and oral examination
Indicative assessment scale: A 90%, B 80%, C 70%, D 60%, E 50%
Slovak and English
Class syllabus:
Topic 1: Fourier series.
• Decomposition of a function into Fourier series.
• Formulas for the Fourier coefficients
• Complex form of trigonometric series.
• Periodic extension of a functions.
• Pointwise convergence of Fourier series. Fejer kernel.
• Bessel inequality and Parseval equality.
• Odd and even extentions of functions and their decomposition into Fourier series.
• Applications of the Fourier series.
• Solution to the boundary value problem for ordinary differential equations using Fourier series.
Topic 2: Parametric integrals.
• Definition of a parametric integral.
• Examples of parametric integrals.
• Continuity and differentiability of parametric integrals.
• Parametric integrals of unbounded functions.
• Parametric integrals on unbounded intervals.
• Method of calculation for parametric integrals.
• Gamma, Beta functions and their properties.
Topic 3: Riemann integral of multivariate function.
• Riemann integral on a bounded area.
• Properties of the integral of a multivariate function.
• Fubini theorem.
Topic 4: Substitution method for integrating functions of several variables.
• Linear and non-linear coordinate transformation.
• Jacobi matrix of a transformation and the geometric interpretation of its determinant.
• Substitution theorem for integrals of multivariate functions.
• Polar and spherical coordinates.
• Method of calculation of multidimensional integrals by transformation of variables.
Topic 5: Curve and surface integrals.
• Integrating functions defined on curves.
• Curve integral: kind I. and II..
• Integrating functions defined on surfaces.
• Surface integrals.
• Relationship between, curve, surface and volume integrals.
• Green's formula of integration by parts.
• Ostrogradskij-Gauss theorem and Stokes formula.
40/60
To master the basics of the integral calculus of functions of multiple variables, with emphasis on the methods used in financial mathematics. Upon completion of the course students will acquire key competences in the field of vector mathematical analysis.
final examination
A Course in Game Theory / Martin J. Osborne, Ariel Rubinstein. Cambridge, Mass. : MIT Press, 1994
Extensive games with complete information. / Levent Kockesen and Efe A. Ok, New York University 2007
Game Theory: An Introduction, Steven Tadelis. Princeton University Press 2013
Homework, midterm test, final test, experiments.
Grade policy A 100-90%, B 89-80%, C 79-70%, D 69-60%, E 59-50%
Slovak, English
Strategic games with complete information. Dominance. Nash equilibrium. Applications (Cournot oligopoly, Bertrand oligopoly, voting games, deterrence wars, auctions). Nash equilibrium in mixed actions.
Extensive games with complete information. Associated game. Nash equilibrium, subgame perfect equilibrium.
Extensive games with perfect and imperfect information.
100/0
Students will be able to analyze correctly strategic situations, being able to make the right decisions
laying foundations of monetary policy and commercial banking
Study guide for money, banking and financial intermediation / Gary Smith. Lexington : D. C. Heath, 1991
Hubbard, R.G.: Money, the Financial System and the Economy, Addison-Wesley, 1999
written test
Exam: exam
Indicative assessment scale: A 90%, B 80%, C 70%, D 60%, E 50%
Slovak, English
Money, interest rate, money demand, money supply, monetary policy, IS-LM model, AS-AD model and inflation, monetary policy in an open economy, commercial banking.
0/100
The student masters the basics of monetary policy and commercial banking.
examination
To teach students basic methods of the modeling of dynamic processes with discrete and continuous time with particular focus on economic applications.
P. Brunovský: Dynamické systémy a diferenciálne rovnice, text MFFUK www.iam.fmph.uniba.sk/skripta/brunovsky
M. Greguš, V. Šeda, M. Švec: Obyčajné diferenciálne rovnice, Alfa 1985
J. T. Sandefur: Discrete dynamical systems. Clarendon 1990
G. Gandolfo: Economic Dynamics, Springer
written exam and homework
Continuous assessment: Written exam and homework
Exam: Written and oral exam
Approximate rating: A 90%, B 80%, C 70%, D 60%, E 50%
Slovak, English
Difference equations: One-dimensional and higher-dimensional linear equations, affine and nonlinear equations, solutions and their stability.
Differential equations: One-dimensional linear, affine and nonlinear equations. Higher-dimensional linear equations. General theory of differential equations. One-dimensional and two-dimensional autonomous equations. Integrals of differential equations, conservative systems with one degree of freedom.
20/80
Students master basic methods of modelling the dynamical processes with discrete and continuous time variable using difference and differential equations, with special regard to their application in economics and finance.
examination
Nelineárne programovanie, teória a algoritmy / Milan Hamala, Mária Trnovská. Bratislava : EPOS, 2013
S. Boyd, L. Vandenberghe: Convex Optimization, Cambridge University Press, 2004.
Continuous assessment: project: 20%,
Exam: 80%. Grading: A (100-91), B (90-81), C (80-71), D (70-61), E (60-51), Fx (50-0).
Slovak and English
Lagrange function and its properties, Lagrange duality, Transformations of optimization problems, Generalization of Lagrange function, Roode axioms, Min-max theorem, General principle of duality, Convex, quasiconvex and strong convex functions, Optimality conditions, Lagrange and Kuhn-Tucker theorem, Duality thoery in convex programming, Slater theorem, Interior point methods - introduction.
20% / 80%
Student has mastered the basics of nonlinear programming theory and methods.
Milan Hamala, Mária Trnovská: Nelineárne programovanie, teória a algoritmy. Bratislava : EPOS, 2013
S. Boyd, L. Vandenbergne: Convex optimization, Cambridge University Press, 2000.
Activity, homework, passing the test.
Grading
A (100-91), B (90-81), C (80-71), D (70-61), E (60-51), Fx (50-0).
Slovak, English
See the syllabus for the Non-Linear programming course.
100/0
Students improve the knowledge required to pass the Non-Linear Programming course.
Casella G, Berger R: Statistical inference. 2nd ed. Cengane Learning 2001;
Anděl J: Základy matematické statistiky. Matfyzpress 2005.
Probability and statistics (2) 1-MAT-282
written exam
Approximate grade thresholds: A 90%, B 80%, C 70%, D 60%, E 50%
Slovak, English
Properties of sample mean and sample variance. t-tests and F-tests. Basic confidence intervals and the Bonferroni method. How to create a test? How to measure test quality? Neyman-Pearson's lemma and UMP tests for compound hypotheses. How to measure the quality of estimates? BLUE. BUE and its uniqueness. Fisher information and Cramér-Rao inequality. Asymptotic properties of maximum likelihood estimates & tests. Wald test and score test. Bootstrap and jackknife.
http://www.iam.fmph.uniba.sk/ospm/Somorcik/teaching.htm
0/100
Students will be able to apply some basic methods of mathematical statistics, while understanding their principles. They will also understand some general statistical techniques and they will be able to apply them.
Dalgaard P: Introductory Statistics with R. Springer 2008.
Anděl J: Statistické metody. Matfyzpress 2007.
Venables W N et al.: An Introduction to R. The R Foundation 2021.
Probability and statistics (2) 1-MAT-282 or Probability and statistics 2-INF-175
project (teaching period), written exam using computer
Approximate grade thresholds: A 90%, B 80%, C 70%, D 60%, E 50%
Slovak, English
History of R and comparison with other systems. Arithmetic, logical operators. Data import and visualization, descriptive statistics. Tests of normality. Tests about location parameters, proportions, and correlation coefficients. Linear regression: estimates, tests, confidence regions, submodels, diagnostic. ANOVA. Modern methods of statistics (cluster and discriminant analysis, Monte Carlo).
http://www.iam.fmph.uniba.sk/ospm/Somorcik/teaching.htm
20/80
Using the software "R" students will be able to perform basic statistical analysis of real data.
To teach students the basics principles of microeconomics and practice their economic thinking.
P. Brunovský: Mikorekonómia, Material available online on the course's web page.
H. Varian: Microeconomic Analysis. Norton 1992
A. Mas-Collel, M. D. Whinston, J. R. Green: Microeconomic Theory. Oxford 1995
R. Pindyck and D. Rubinfeld: Microeconomics, Pearson Series in Economics, 2012.
tests and homeworks
Continuous assessment: tests and homeworks
Examination: written test and oral exam
Grading scale: A 100-91%, B 90-81%, C 80-71%, D 70-61%, E 60-51%
Slovak, English
Theory of firm. Consumer theory. Perfect competition. Effect of taxes and subsidies. Imperfect competition. Price discrimination. General Equilibrium in a Pure Exchange Economy. Uncertainty and risk. Economics and Information. Asymmetric information.
https://sites.google.com/view/mikroekonomia2021/sylabus-predmetu?authuser=0
30/70
Students will gain knowledge of the basic principles of consumer and producer decision-making and their interactions.
written test and oral exam
J. Babušíková, M. Slodička, J. Weisz: Numerické metódy, Bratislava: Univerzita Komenského, 2000
J. H. Mathews, K. K. Fink: Numerical Methods Using Matlab, Pearson, 2004
P. Guba: Numerické metódy, skriptá, FMFI UK, 2021
Interim assessment during the semester has a weight of 40% (homeworks 30%, bonus exercises 10%). The two semester exam papers have a total weight of 60% (the first paper taken in the middle of the semester, the second paper taken at the end of the semester). The student must obtain at least half of the points from each semester exam paper. The final evaluation can be adjusted by an oral exam (theoretical questions, written preparation).
Grading: A (100-91), B (90-81), C (80-71), D (70-61), E (60-51), FX (50-0)
Slovak, English
Representation of real numbers and computer arithmetics. Stability. Examples of instability: Recurrent relations and their use. Gronwall lemma. Evaluation of functions. Numerical methods for solving algebraic and transcendental equations. Numerical solution of systems of linear equations: Jacobi method, Gauss--Seidel method, Conjugate gradient method. Numerical solution of systems of nonlinear equations: Bisection method, Newton's method. Interpolation, optimal selection of interpolation nodes. Linear and cubic splines. The least squares method. Numerical differentiation and quadrature.
40/60
The student has basic numerical mathematical methods that are necessary for solving problems using current computers and available software.
Familiarize students with basic elements of the financial mathematics: theory of interest rates, portfolio theory and pricing of derivatives.
Baxter M., Rennie A.: Financial Calculus
Hull J.: Options, Futures and Other Derivatives
Luenberger D.: Investment Science
Project, written test, activity during semester
Evaluation during the semester: Project, written test, activity during exercises
Written exam. Voluntary oral examination to improve the final evaluation.
Informative evaluation scale: A 90%, B 80%, C 70%, D 60%, E 50%
English, Slovak
Coupon and zero-coupon bonds, term structure of interest rates, bootstrap method, yield to maturity, forward rates, duration.
Risk aversion, properties of utility functions, utility functions and mean-variance analysis, the problem of Markowitz, Capital Asset Pricing Model (CAMP).
Binomial tree model, risk-neutral probabilities, risk-neutral pricing formula, Black-Scholes formula, pricing of american options.
50/50
After completing the course, students will understand the basic principles of interest rate theory and bond investment management. They will also get acquainted with the principles of stock portfolio management. In the last part of the lecture, they will learn to price derivatives of the European and American type using binomial trees and will also get acquainted with Black-Scholes formulas for pricing put and call options.
oral examination
Johnston J, DiNardo J: Econometric methods 4th ed. McGraw Hill 1997;
Greene W: Econometric Analysis 8th ed. Pearson 2017;
Zvára K: Regrese. MatfyzPress, 2008.
Statistical methods 1-EFM-330 or Statistical methods 1-DAV-303 or Computer statistics 2-MMN-106
Continuing evaluation: project (10%) and test (20%); at least 10% out of 30% are needed to proceed to the final exam
Exam: written exam
Approximate grade thresholds: A 90%, B 80%, C 70%, D 60%, E 50%
Slovak, English
Linear regression, the geometry behind it, and LS-estimators of parameters. Decomposition of the Total Sum of Squares, coefficients of determination, and the Akaike information criterion. Properties of the parameter estimators and of the error term variance estimator. Gauss-Markov theorem. Tests of linear hypotheses about parameters. Restricted regression. Model specification errors and their diagnostic. Dummy variables. Generalized least squares. Heteroscedasticity: testing for and dealing with. Autocorrelation: testing for and dealing with.
http://www.iam.fmph.uniba.sk/ospm/Somorcik/teaching.htm
30/70
Students are able to perform standard linear regression analysis and also are able to apply it in real econometric research. They also understand the mathematics behind these methods, being a necessary condition for further studies in this subject.
O. Blanchard. S. Fischer: Lectures on Macroeconomics
D. Romer: Advanced Macroeconomics
Examination: Final test: A 88%, B 78%, C 68%, D 58%, E 48%
Slovak, English
Aggregated demand, aggregate supply, business cycles. Inflation, unemployment, monetary policy of the central bank. Labor markets and policies of the economic side. Monetary policy of the central bank. Government fiscal policy. Theory of private consumption and investment. Money and financial markets. Open economy in the short term. Inflation and Unemployment in an Open Economy. Shocks and responses of the government and the central bank.
0/100
Students will understand the current macroeconomic theory in relation to its use in the real policy of central banks and governments.
To exercise the subject-matter of Mathematical analysis (1) thoroughly.
Kubáček, Valášek: Cvičenia z matematickej analýzy I
solving problems on the blackboard, presentations of students' homework, written homework controlled 3-4 times during semester, 3 essay form tests
Continuous assessment: 2 tests of 10 points, active participation in seminars, homework checked twice a semester
Slovak and English
I. Introduction: 1. Basic concept of sets and logic, function, relations. 2. Definition of real numbers, supremum of a bounded set.
II. Sequences: 1. Limit of a sequence, limes superior a inferior, limit point. 2. Relationship between convergence and boudedness, Cantor set, Bolzano-Cauchy criterion.
III. One variable functions: 1. Limit of a function, continuous functions, basic theorems of limits, Heine definition of limit, uniform continuity. 2. Differential calculus, mean value theorems, monotonic functions, local maxima and minima, convex functions, asymptotic behaviour, Taylor polynomial.
100/0
After completing the course, students will master the basics of mathematical analysis of the functions of one real variable. Thus, investigate the course of the function, calculate the limits and derivatives of functions of one variable.
none
Kubáček, Z, Žabka, J: Seminár z matematiky, Zbierka úloh s riešeniami, 1. časť. , 2017.
Kubáček, Z, Žabka, J: Seminár z matematiky, Zbierka úloh s riešeniami, 2. časť., 2018.
P.J. Eccles An introduction to mathematical reasoning, Cambridge University Pres, 2007.
D. Solow, How to Read and Do Proofs, Wiley, 2014
Continuous assessment: warm-ups (1/3 of the assessment) and homework (2/3 of the assessment) during the semester. It is necessary to obtain at least 50% from each assignment.
Indicative assessment scale: A 90%, B 80%, C 70%, D 60%, E 50%
Slovak
Classes give an introduction to logic, proof techniques and a variety of example problems that illustrate different aspects of mathematical proof. Particular emphasis is given to teaching fundamentals of how to communicate thoughts rigorously: both in an oral fashion and in a written form. Classes also enable students to consolidate their learning and mathematical background to help follow the Mathematical Analysis and Linear Algebra courses. Topics cover also algebraic expression, linear and quadratic function, real functions of one variable and their properties.
100/0
Students will learn to formulate their own thoughts, argue and prove claims mathematically accurately orally and verbally. They will also consolidate and supplement the knowledge of high school mathematics needed in their further studies.
Kubáček, Z, Žabka, J: Seminár z matematiky, Zbierka úloh s riešeniami, 2. časť., 2018.
Kubáček, Z, Žabka, J: Seminár z matematiky, Zbierka úloh s riešeniami, 3. časť., 2020.
D.G. Zill, P.D. Shanahan Comlex analysis, Jones and Bartlett Publishers, 2003.
D. Solow, How to Read and Do Proofs, Wiley 2014.
Continuous assessment: warm-ups and homework during the semester. It is necessary to obtain at least 50% from each assignment.
Indicative assessment scale: A 90%, B 80%, C 70%, D 60%, E 50%
Slovak
Classes enable students to consolidate their learning and mathematical background to help follow the Mathematical Analysis and Linear Algebra courses. Particular emphasis is given to teaching fundamentals of how to communicate thoughts rigorously: both in an oral fashion and in a written form. Topics cover analytical geometry, curves of the second order, classification of the curves of the second order, equivalence relations, complex numbers and their properties, polar form of complex numbers, powers and roots of complex numbers
100/0
Students will learn to formulate their own thoughts, argue and prove claims mathematically accurately orally and verbally. They will also consolidate and supplement the knowledge of high school mathematics needed in their further studies.
Linear algebra and its applications / Gilbert Strang. Belmont : Thomson Brooks/Cole, 2006
Algebra a teoretická aritmetika 1 / Tibor Katriňák ... [et al.]. Bratislava : Univerzita Komenského, 1999
Grading: homework, semester exams, activity in the class.
Slovak, English
See the syllabus of the subject Linear algebra and geometry (1).
http://www.iam.fmph.uniba.sk/institute/trnovska/linalg.html
100/0
Students are able to solve various problems required to pass the course Linear algebra and geometry (1).
To exercise the subject-matter of Mathematical analysis (2) thoroughly.
Kubáček, Valášek: Cvičenia z matematickej analýzy II
solving problems on the blackboard, presentations of students' homework, written homework controlled 3-4 times during semester, 3 essay form tests
Continuous assessment: 2 tests of 10 points each, active participation in classes, homework checked twice a semester
Indicative assessment scale: A 92%, B 84%, C 76%, D 68%, E 60%
Slovak and English
I. Functional sequences and series: 1. Sequences of functions, point and uniform convergence. 2. Numbers and functions series, convergence criterions, power expansions. 3. Taylor series of the functions.
II. Integral calculus: 1. Primitive function, Newton integral, integration by parts and substitution methods, reduction to the parial fractions. 2. Riemann integral, integrability of monotonic and continuous functions, mean value theorems, Newton-Leibniz formula, applications of integral (area of planar regions, lehght of a curve, volume and surface area of solids). 3. Functions with bounded variation, Riemann-Stieltjes integral.
100/0
After completing the course, students will master the basics of the integral number of functions of one real variable. Thus, to determine the primitive function, to compute certain integrals of the functions of one variable, to investigate the convergence of the series.
none
Linear algebra and its applications / Gilbert Strang. Belmont : Thomson Brooks/Cole, 2006
Algebra a teoretická aritmetika 1 / Tibor Katriňák ... [et al.]. Bratislava : Univerzita Komenského, 1995
Grading: homework, semester exams, activity in the class.
Slovak, English
See the programme of the subject Linear algebra and geometry (2).
100/0
Students are able to solve various problems required to pass the course Linear algebra and geometry (2).
To exercise the subject-matter of Mathematical analysis (3) thoroughly.
Zbierka úloh z vyššej matematiky : 3. časť / Jozef Eliaš, Ján Horváth, Juraj Kajan. Bratislava : Slovenské vydavateľstvo technickej literatúry, 1967
Sbornik zadač i upražnenij po matematičeskomu analizu / B. P. Demidovič. Moskva : Fizmatgiz, 1963
Martin Kollár, Ľubica Kossaczká, Daniel Ševčovič Diferenciálny a integrálny počet funkcií viac premenných v príkladoch Knižničné a edičné centrum FMFI UK, 192 pp. (in Slovak). ISBN: 978-80-89186-54-9
M. Barnovská, K. Smítalová, Matematická analýza III, Skriptum UK v Bratislave, 1983
solving problems on the blackboard, presentations of students' homework, 2 essay form tests
Continuous assessment: 3 written exams, class activity
Indicative assessment scale: A 92%, B 84%, C 76%, D 68%, E 60%
Slovak and English
Metric spaces. Limit and continuity of a multivariable function. Differentiation of _ mappings, total differential and total derivative. Partial derivative, Taylor formula. Local and global extrema of multivariable function. Implicit functions.
100/0
After completing the course, students will master the basics of differential calculus of functions of several real variables. They will be able to determine local and bound local extremes of functions of several real variables.
none
to make students familiar with internationally accepted principles of accounting
Financial Accounting and Reporting : A Global Perspective / Hervé Stolowy, Michel J. Lebas. London : Thomson Learning, 2006
Hervé Stolowy and Michel J. Lebas: Financial Accounting and Reporting. A global perspective
Anna Šlosárová a kolektív: Analýza účtovnej závierky
IASB Framework for the Preparation and Presentation of Financial Statements
Zákon o účtovníctve č. 431/2002 Z.z. v znení neskorších predpisov
individual tasks, tests
Continuous assessment: individual problem solving, continuous testing
Indicative assessment scale: A 90%, B 80%, C 70%, D 60%, E 50%
Slovak, English
Accounting as the language of business, introduction to financial statements, accounting process, accounting principles, detailed characterization of the main balance sheet accounts, cash flow statement, financial statement analysis.
The course is based on the approach adopted in the international accounting standards IAS/IFRS
100/0
The student masters the basics of internationally accepted accounting principles.
closing test
To exercise the subject-matter of Mathematical analysis (4) thoroughly.
Zbierka úloh z vyššej matematiky : 4. časť / Jozef Eliaš ... [et al.]. Bratislava : Alfa, 1979
Sbornik zadač i upražnenij po matematičeskomu analizu / B. P. Demidovič. Moskva : Fizmatgiz, 1963
Martin Kollár, Ľubica Kossaczká, Daniel Ševčovič Diferenciálny a integrálny počet funkcií viac premenných v príkladoch Knižničné a edičné centrum FMFI UK, 192 pp. (in Slovak). ISBN: 978-80-89186-54-9
M. Barnovská, K. Smítalová, Matematická analýza IV, Skriptum UK v Bratislave, 1984.
Eliaš J., Horváth J., Kajan J., Zbierka úloh z vyššej matematiky, 4. časť, Bratislava, Alfa, 1972.
solving problems on the blackboard, presentations of students' homework, 2 essay form tests
Continuous assessment: 2 written exams, class activity
Indicative assessment scale: A 92%, B 84%, C 76%, D 68%, E 60%
Slovak and English
Multiple integrals. Line and surface integrals, Green's formula, Ostrogradskij and Stokes theorem. Parametric integrals. Fourier series.
100/0
After completing the course, students will master the basics of the integral number of functions of several real variables. They will be able to compute multidimensional definite integrals and curve integrals.
none
Jílek, J. [2013] Finance v globální ekonomice. Grada, 2013
1-EFM-280/00 Money and Banking
Interim evaluation: Active participation / presentation
Concluding evaluation: Written exam
Approximate rating scale: A 90%, B 80%, C 70%, D 60%, E 50%
Slovak
Money, the ECB's monetary system and policy, Balance of payments, Risks - Slovak and global context, Financial cycle, Financial crisis, Financial stability, Macro-prudential policy.
60/40
Student controls the main principles of the international financial system, imbalances affecting financial stability and tools to mitigate systemic risk
Data envelopment analysis : A comprehensive Text with Models, applications, references and DEA- Solver software / William W. Cooper [et al.]. Boston : Kluwer , 2004
M. Halická: Učebné texty k predmetu DEA modely dostupné na www.iam.fmph.uniba.sk/institute/halicka/text/TextDEA35.pdf
Continuous assessment: project 30%, small written exams or homeworks 20% , a necessary condition to obtain at least 10% of the 30% evaluation for the project
Examination: written 50%, possible oral exam (improvement or deterioration of the achieved evaluation by one degree)
Indicative assessment scale: A 90%, B 80%, C 70%, D 60%, E 50%
Slovak, English
Introduction to DEA modelling, different approaches to DEA modeling, efficiency and effectiveness, CCR model, BCC model, range efficiency, additive model, basic model properties, model invariance, monotonous efficiency, input / output additions, returns to scale, superefektivity, rules for correct application of DEA models, SBM model, AR model.
50/50
Upon completion of the course students will understand the fundamentals of DEA models and will be able to use them for evaluating the effectiveness of units within a given group.
Nelineárne programovanie, teória a algoritmy / Milan Hamala, Mária Trnovská. Bratislava : EPOS, 2013
Algorithms for Optimization, Kochenderfer, Wheeler, MIT Press, 2019
Optimization Theory and Methods, Nonlinear programming, Sun, Yuan, Springer 2006
Continuous assessment: exercises: 20%, project: 20%, Exam: 60%. The student must obtain at least half of the points for the exercises in order to pass the final written exam. Grading: A (100-91), B (90-81), C (80-71), D (70-61), E (60-51), Fx (50-0).
Slovak, English
Introduction to the subject, Classification of optimization problems, Methods of minimizing the function of one variable (Interval approximation methods, Interpolation methods), Classical methods for minimizing n-variable function (Classification of methods and basic algorithmic schemes, Cauchy's method (steepest descent), coordinate descent Newton’s method and modified Newton's method), Modern methods for minimizing the function of n variables (Conjugate gradient method, Quasi Newton method, Broyden class and other parametric classes of Quasi Newton formulas)
40% / 60%
Students master classical and modern methods of unconstrained optimization methods for functions of one and several variables, theoretical and practical aspects of these methods and their significance for solving nonlinear programming problems with boundaries. They also become familiar with some practical problems, that can be solved using unconstrained optimization methods.
Continuous assessment: warm-ups (1/3 of the assessment) and projects (2/3 of the assessment) during the semester. It is necessary to obtain at least 50% from warm-ups and each project.
Indicative assessment scale: A 90%, B 80%, C 70%, D 60%, E 50%
Slovak, English
1. Vectors, matrices
2. Data import and export
3. Visualization - plotting functions
4. Systems of Nonlinear Equations
5. Optimization (linear and nonlinear)
6. LaTex - scientific text writing, mathematical formulas, tables, images
100/0
Following the courses Programming (1) and (2) students learn the basics of numeric computing relevant for their specialization and master writing scientific texts in LaTeX.
Experimental economics introduces the subject matter, methods, and results of experimental economics. It will stress interaction of theory and experiment, seeking to relate questions in the theories of markets, games, and decisions to issues in experimental design and the analysis and the interpretation of results. These themes will be developed by discussing series of related experiments.
The Handbook of experimental economics / Editors John H. Kagel, Alvin E. Roth. Princeton : Princeton University Press, 1995
Theodore Bergstrom - John H. Miller: Experiments with Economic Principles: Microeconomics, McGraw-Hill, 2000.
Homeworks, Participation on Experiments
Continuous assessment: based on the evaluation of written protocols from the performed experiments
Indicative assessment scale: A 100-90%, B 89-80%, C 79-70%, D 69-60%, E 59-50%
Slovak, English
1. Competitive Markets (Supply and Demand. Shifting Supply.)
2. Market Intervention and Public Policy (A Sales Tax. Prohibition. A Minimum Wage.)
3. Imperfect Markets (Externalities. Monopolies and Cartels.)
4. Firms a technology (Entry and Exit. Network Externalities. Measuring Productivity. Comparative Advantage.)
5. Information, Auctions, Bargaining (Adverse Selection. Auctions. Bargaining.)
100/0
Students will be able to verify the principles on which economic theory is built. They can construct an experiment to support / refute new hypotheses in further research.
Gruber, J. 2016. Public Finance and Public Policy. Macmillan.
Harris, J. M., and Roach, B. 2018. Environmental and Natural Resource Economics: A Contemporary Approach. ME Sharpe.
Schotter, A. 2009. Microeconomics: A Modern Approach. Cengage Learning.
Evaluation of the course consists of the final exam (60%), homework (30%) and exercises during lectures (10%). In addition, it is necessary to obtain a minimum of 50% from both the interim assessment and the final exam.
Grading scale: A 100-91%, B 90-81%, C 80-71%, D 70-61%, E 60-51%
English, Slovak
The course is a part of the cooperation of the EFM study program with CERGE-EI on their Distance learning program. The course will be conducted in a partially cumulative form: (3P+1C) per week during 6 weeks from the beginning of the semester. The final exam will be held the week after the end of the course, the make-up exam a week later. Lectures on the subject will take place in electronic form in English, exercises in person.
The the course aims to provide a deeper theoretical insight into the issue of economic externalities, such as global warming. The course will introduce several classic economic tools that are used to solve externalities in the field of public finances (Pigou's tax, cap-and-trade programs, subsidies, etc.). The second part of the course will be devoted to the issue of decarbonization technologies, such as heat pumps or electric cars. In the context of solving the problem of global warming, we will evaluate the economic benefit of these technologies and present the current progress in the field.
40/60
The student will gain an overview of economics of decarbonization technologies and teconomic instruments suitable for addressing externalities.
Internal regulation no. 5/2010 Directive of the Rector of Comenius University in Bratislava, on the basic requirements for final and qualification theses, their bibliographic registration, control of originality, storage and access to Comenius University in Bratislava, www.uniba.sk
Teacher's electronic texts provided to students
Current evaluation: Bachelor thesis project
Indicative evaluation scale: if the student submits the project in the prescribed structure and content A (it is also possible to re-correct the project), otherwise FX
Slovak and English
Meetings with potential supervisors of bachelor theses and selection of bachelor thesis topic. Basic requirements for content and formal aspects of the bachelor thesis. Thesis objective. Structure of work. Citation technique and ethics. Methods of creating a bibliography.
100/0
: The student is informed about the basic regulations and requirements for content and formal aspects of bachelor thesis, citation technique and ethics. He/she has a thought-out structure of his bachelor thesis and a pre-established list of used literature.
1. P. Zlatoš: Algebra a geometria, skriptá http://thales.doa.fmph.uniba.sk/zlatos/la/LAG_A4.pdf
G. Strang: Linear algebra and its applications, 1976 (ruský preklad 1980);
R. A. Horn, Ch. Johnson: Matrix Analysis, 1990.
2. T. Neubrunn, J. Vencko: Matematická analýza I, II. Skriptá UK Bratislava;
M. Barnovská, K. Smítalová: Matematická analýza III, IV. Skriptá UK Bratislava
Z. Kubáček, J. Valášek: Cvičenia z matematickej analýzy I, II. Skriptá UK Bratislava
(www.iam.fmph.uniba.sk/skripta/kubacek);
M. Barnovská, K. Smítalová: Matematická analýza III, IV. Skriptá UK Bratislava
M. Kollár, Ľ. Kossaczká, D. Ševčovič: Diferenciálny a integrálny počet funkcií viac premenných v
príkladoch, Knižničné a edičné centrum FMFI UK, 2012, tretie doplnené vydanie,
(www.iam.fmph.uniba.sk/institute/sevcovic/skripta/difint)
M. Barnovská a kol.: Cvičenia z matematickej analýzy III. Skriptá UK Bratislava
(www.iam.fmph.uniba.sk/skripta/maiii);
3. P. Brunovský: Diferenčné a diferenciálne rovnice, Skriptá UK Bratislava,
(www.iam.fmph.uniba.sk/skripta/brunovsky); S. H. Strogatz: Nonlinear Dynamics and
Chaos, Addison-Wesley/CRC Press, 2000;
J. Eliaš, J. Horváth, J. Kajan: Zbierka úloh z vyššej matematiky, 3.časť, Alfa, Bratislava, 1980;
4. K. Janková, A. Pázman: Pravdepodobnosť a štatistika, Univerzita Komenského Bratislava 2011;
R. Harman, E. Honschová, J. Somorčík: Zbierka úloh zo základov teórie pravdepodobnosti,
PACI, Bratislava 2009;
T. Amemiya: Introduction to Statistics and Econometrics. Harvard Univ. Press, 1994;
Examination: written and oral in front of the state commission
Slovak, English
1. Linear algebra and matrix calculus
Vector spaces: Linear dependence and independence of vectors, basis and dimension, linear envelope, subspaces, intersection, sum and direct sum of subspaces, projections, coordinate transformations.
Linear mappings: Matrix, kernel and image of linear mapping, coordinate transformations and similarity of linear representation matrices, eigenvalues and eigenvectors, invariant subspaces, characteristic polynomial, criteria of diagonalizability of matrices, Cayley-Hamilton theorem, Jordan normal form.
Bilinear and quadratic forms: Matrix of bilinear form in various bases, symmetric and cososymmetric forms, canonical form of quadratic form, Lagrange's method, Sylvester's law of inertia, positive definite quadratic forms and their matrices, properties of positive definite matrices.
Vector spaces with scalar product: Euclidean vector space, Gram matrix, basic metric concepts, relation of norm and scalar product, Gram-Schmidt orthogonalization process, orthonormal basis.
Gaussian elimination method and LU matrix decomposition, Fredholm alternative, orthogonal matrices and QR-decomposition, orthogonal projections and least squares method, normal system of linear equations.
Complexification of real vector space, realization of complex vector space, complex extension of real linear representation, real matrix of complex linear representation. Hermitian vector space, special complex matrices, Schur decomposition, unitary equivalence of matrices and normal matrices, spectral decomposition of matrices.
2. Mathematical analysis
Functions of one and more variables: Limit, continuity, differentiability, derivation, directional derivation, total differential. Functions specified implicitly, implicit function theorem. Inverse function theorem. Higher order derivatives. Sufficient conditions for the existence of a local extreme of functions of one and more variables.
Numerical series and function series, convergence criteria of numerical series (D’Alembert, Cauchy, Raabe, integral), uniform convergence of function series, Weierstrass's majority criterion. Power series, Taylor evolution of a function of one or more variables. Analytical functions. Fourier series and the criterion of their point convergence. Bessel's inequality and Parseval's equality.
Multivariate function optimization: Free and bounded extremes of multivariate functions. Necessary and sufficient conditions. Lagrange's theorem and Lagrange multipliers
Convex functions. Convexity criteria of functions of one and more variables.
Integration theory: Riemann integral of functions of one and more variables. Integral as a function of the upper bound. Parametric integrals. Continuity and differentiability of parametric integrals. Gamma function and its basic properties. Multidimensional integrals and substitution theorem. Curve integrals. Independence of the curve integral from the integration path, vector field potential. Green's formula of per partes integration for multidimensional integrals.
Standard spaces, complete spaces, open, closed and compact sets. Banach's fixed point theorem and its applications. Properties of continuous functions on compact sets (Weierstrass theorem).
3. Differential and difference equations
Discrete dynamical systems: Equilibrium states and their stability. Trajectory calculation.
Linear differential equations: Solution of autonomous homogeneous equations. Solving nonhomogeneous equations by the method of indefinite coefficients. Stability. Classification of two-dimensional autonomous equations. Fixed point and its stability.
Nonlinear differential equations: Equilibrium states and their stability. Trajectories of autonomous equations. Phase portraits of two-dimensional autonomous equations.
4. Probability and mathematical statistics.
Classical and axiomatic definition of probability. Conditional probability, Bayesian formula.
Random variable: probability distribution, distribution function of a random variable and its properties.
Discrete probability distributions: binomial, hypergeometric, Poisson, geometric. Continuous random variables: density and basic types of distributions: uniform, exponential, normal, mean and dispersion of random variables. Independence of random variables and uncorrelation. Correlation coefficient and its basic properties.
Central limit theorem and the law of large numbers.
Random vectors, mean and covariance matrix of a random vector. Marginal and conditional distributions, convolution of densities. Distributions derived from the normal: chi square, Student's distribution.
Linear model, parameter estimation, least squares method, maximum likelihood method.
0/100
The result will be the completion of the final state examination in the subject of the Mathematical Basis. This means that the student demonstrates an understanding of the basics of each subject in the subject syllabus in their interdisciplinary contexts.
1. J. Plesník, J. Dupacova, M. Vlach: Lineárne programovanie. Alfa, Bratislava 1990
2. M. Hamala, M. Trnovská: Nelineárne programovanie, EPOS, Bratislava 2013.
3. P. A. Samuelson, W. D. Nordhaus: Ekonómia I, II. Bradlo, Bratislava 1992;
B. Felderer, S. Homburg: Makroekonomika a nová makroekonomika. Elita, Bratislava, 1995.
P. Brunovský: Mikroekonómia, učebný text (http://www.iam.fmph.uniba.sk/skripta/brunovsky2)
4. I. Melicherčík, L. Olšarová, V. Úradníček: Kapitoly z finančnej matematiky, EPOS, Bratislava 2005
5. G. Casella a R. L. Berger: Statistical inference (2nd edition). Cengane Learning, 2001.
J. Johnston, J. DiNardo: Econometric Methods. McGraw-Hill, 1997.
Examination: written and oral in front of the state commission
Slovak, English
1. Linear programming
Convex analysis of sets: convex sets and their properties, extreme points of convex sets, supporting hyperplane theorem, theorems on the separation of convex sets, Farkas' lemma.
Simplex method: Geometric idea. Simplex table and algorithm. Two-phase simplex method. Finite simplex method, anticyclic method. Dual simplex method.
Duality theory: General form of a dual problem. Weak theorem about duality and its consequences. Strong duality theorem. Complementarity theorem. optimality verification.
2. Nonlinear programming and free optimization methods
Optimization methods (Overview and basic principles): Minimization of the function of one variable (interval approximation methods and interpolation methods). Minimization of the function of n-variables (gradient method, cyclic coordinate reduction method, Newton's method, combined gradients method and quasi-Newtonian methods).
The concept of Lagrange function, the vector of Lagrange multipliers, the relation of the optimal solution and the associated vector of multipliers with the saddle point of the Lagrange function, nonlinear programming methods using the Lagrange function, generalizations of the Lagrange function, Lagrange's dual problem.
Necessary conditions of optimality: Lagrange's theorem and theorem on sensitivity for the classical problem to a bounded extreme. Kuhn-Tucker theorem for mathematical programming problem (with mixed boundary type), construction of Kuhn-Tucker conditions for general problems.
Overview of basic types of extremes and saddle points. Existence theorems for extreme and saddle point type "minmax". General principle of duality in extremal problems: General concept of dual problem. (Application of Roode's theorem and the "minmax" theorem.)
Convex analysis of functions: definition of convexity, conditions of the 1st and 2nd order of convexity, convexity criteria, operations preserving convexity, quasi-convex functions, strongly convex functions.
Convex programming: Kuhn-Tucker theorem for the convex programming problem. Weak and strong duality theorem. Wolfe's dual problem, Slater's condition and Slater's theorem.
3. Selected chapters of economic theory
Basic macroeconomic variables: gross domestic product, unemployment rate, inflation rate. Commodity market. Aggregate demand and its composition. Equilibrium output of the economy. Commodity market dynamics. Financial markets. Money and bonds. Demand for money, money supply and equilibrium interest rate. The role of the central bank and commercial banks. IS-LM model, balance of goods and financial markets. Fiscal and monetary policy. Expectations and macroeconomic policy. Commodity market in an open economy. Equilibrium output and trade balance. IS-LM model in the case of open economy. Exchange rates. The effectiveness of macroeconomic policy.
Labor market. Wage and pricing. Natural unemployment rate. Aggregate demand and aggregate supply. Inefficiency of monetary policy in the long run. The effectiveness of fiscal policy. Changes in the natural rate of unemployment. Philips curve. Inflation, expected inflation and unemployment. Economic growth. Saving, capital accumulation and economic output. Technological progress and growth.
Consumer: Preferences and utility function. Consumer balance. Marshall and Hicks demand function: Slutsky's equation.
Company: Technological set and production function. Company balance and cost function.
Equilibrium in a sub-market in perfect competition: Short-term equilibrium and equilibrium with free market entry. Impact of taxes and subsidies. Consumers and producers surplus.
Imperfect competition: The balance of the monopoly and its inefficiency. Cournot's equilibrium oligopoly. Cartel instability.
Equilibrium of the complete market: Walras 'law, Walras' equilibrium and its Pareto optimality. Externalities and property rights.
4. Financial mathematics
Interest rates: Coupon and zero-coupon bonds. Time structure of interest rates. Construction of the time structure of interest rates using bond market prices (bootstrapping). Net present value. Yield to maturity. Forward interest rates. Duration and change in the value of the bond portfolio with a parallel shift in interest rates.
Portfolio theory: Utility function, risk aversion, optimal portfolio selection by maximizing the mean value of the utility function. Markowitz model. Risk minimization with fixed return, optimization of the portfolio containing risk-free securities, market price of risk. Capital Asset Pricing Model as Equilibrium Model, Capital Market Line, Security Market Line.
Fundamentals of derivative valuation theory: Binomial tree model, calculation of risk-neutral probabilities and values of derivatives based on them. Self-financed strategies and derivatives replication.
5. Statistical methods and econometrics
Properties of diameter and selective dispersion. Student's t-tests and F-test of dispersion equality. Confidence intervals for mean and dispersion. UMP-tests and the Neyman-Pearson lemma. Estimates of BUE and Cramér-Ra inequality. MLE estimation properties. Wald's test
0/100
The result will be the completion of the final state exam in the subject: Mathematical Methods. This means that the student demonstrates an understanding of the basics of each subject in the subject syllabus in their interdisciplinary contexts.
Literature as recommended by the supervisor and the student's own discretion. The student will list all used literature in the bachelor's thesis in the list of used literature.
Continuous assessment: submission of bachelor thesis
Exam: oral, in the form of defending a bachelor's thesis before a state commission
Slovak, English
The student works on the topic of the final work under the guidance of the supervisor of his work. The results of the work are processed into written form according to prescribed standards. He submits the thesis and prepares for the defense. They will get acquainted with the testimonials of their work and prepare answers to them. He responds to the commission with comments and questions from the opinions, and participates in a discussion about the significance and main results of his work.
0/100
The result of successful completion of the state subject will be a defended bachelor's thesis. Defending the thesis means that the student has demonstrated the ability to creatively apply the knowledge and skills acquired during the study to solve a given problem.
Salanci, L.: www.salanci.sk - web page with lectures and exercises
Active work on practice lessons at which a student solve assigned tasks is required. At least 80% of completed practice lessons are need to be admitted to the final examination. During the final examination, the student solves a practical assignment on a computer and according to obtained score, he/she receives a grade: A (90%), B (80%), C (70%), D (60%), E (50%) or FX (less than 50%).
Slovak, English
Expressions and variables.
Loops.
Program branching.
Subroutines and functions.
List.
Solving mathematical and geometrical problems.
User interaction.
https://www.edu.fmph.uniba.sk/~salanci/Python/index.html
0/100
Students are able to solve problems algorithmically, to process large number of data and to communicate with the user using basic constructions and data types of programming language Python.
-
Salanci, L.: www.salanci.sk - web page with lectures and exercises
Programming 1
Active work on practice lessons at which a student solve assigned tasks is required. At least 80% of completed practice lessons are need to be admitted to the final examination. During the final examination, the student solves a practical assignment on a computer and according to obtained score, he/she receives a grade: A (90%), B (80%), C (70%), D (60%), E (50%) or FX (less than 50%).
Slovak, English
Strings.
Objects.
Many objects.
Turtle graphics.
Recursion.
Files,
Solving mathematical and geometrical problems.
User interaction.
https://www.edu.fmph.uniba.sk/~salanci/Python/index.html
0/100
Using object-oriented programming in the Python programming language, students are able to solve problems algorithmically, process structured data and interact with the user.
-
The study of elements of probability and statistics
Janková, K., Pázman, A.: Pravdepodobnosť a štatistika, Vydavateľstvo UK 2011
Harman, R., Honschová, E., Somorčík, J.: Zbierka úloh zo základov teórie pravdepodobnosti, Paci Bratislava 2009
G.R.Grimmett, D. Stirzaker: Probability and Random Processes. Oxford University Press 2001
test
Preliminary semester evaluation: a test
Examination: written examination
Approximate grade thresholds: A 90%, B 80%, C 70%, D 60%, E 50%
Slovak, English
Probability space. Classical probability models. Random variable and distribution function. Elementary discrete and continuous distributions, expectation and variance. Independence and correlation. Normal distribution and the central limit theorem. Random sample, sample mean, sample variance. Sampling normal distribution. Estimation of parameters, maximal likelihood, confidence intervals for the mean of a normal distribution.
50/50
After completing the course the student will be able to use classical probability models, axiomatic approach to the definition of probability. He will master one dimensional discrete and continuous random variables. He will be given an introduction to selected statistical procedures: point and interval estimates of parameters sampling normal distribution.
written exam
Introduction of elementary concepts and relations in probability and mathematical statistics.
Janková, K., Pázman, A.: Pravdepodobnosť a štatistika, Vydavateľstvo UK 2011
K. Zvára, J. Štěpán: Pravděpodobnost a matematická statistika, Matfzypress 1997
Harman, R., Honschová, E., Somorčík, J.: Zbierka úloh zo základov teórie pravdepodobnosti, Paci Bratislava 2009
G.R.Grimmett, D. Stirzaker: Probability and Random Processes. Oxford University Press 2001
test
Preliminary assessment: test
Examination: written examination
Approximate final assessment: A 90%, B 80%, C 70%, D 60%, E 50%
Slovak, English
Multiple random variables, their distribution and characteristics. Elementary introduction to Lebesgue integral. Marginal and conditional distributions and densities. Independence, sums of independent random variables. Characteristic functions and their applications. Convergence of sequences of random variables, central limit theorems and weak law of large numbers. Statistical inference: estimation of parameters, maximal likelihood estimates, hypothesis testing. Neyman Pearson lemma. Regression models: least squares and maximal likelihood estimation of parameters. Goodness of fit tests.
30/70
After completing the course the student will master multivariate discrete and continuous distributions. He will be able to calculate distributions of sums, products and ratios of independent random variables. He will know the technique of characteristic functions and will be able to apply it to the multidimensional normal distribution. The knowledge of probability methods will be applied to selected statistical problems of parameter estimation and hypotheses testing.
Life Insurance Mathematics / Hans U. Gerber. Heidelberg : Springer, 1997, ISBN 978-3-662-03460-6;
Modely v životnom a neživotnom poistení / Rastislav Potocký. Bratislava : STATIS, 2012, ISBN 978-80-85659-71-9;
study materials of the lecturer.
The course assessment consists of one tests (100%), which is usually written during the final weeks of the semester. To successfully complete the course, it is necessary to obtain at least half of the points on the test.
Grade thresholds: A: at least 90.00%; B: 89.99% – 80.00%; C: 79.99% – 70.00%; D: 69.99% – 60.00%; E: 59.99% – 50.00%; Fx: 49.99% – 0.00%.
Slovak, English
Introduction to insurance business. Compounding and discounting. Life tables, biometric (mortality) risk. Life insurance: the deterministic approach and the equivalence principle. Assets and liabilities of the insurance company. Basic and some other types of life insurance: pure endowment, term insurance, endowment, insurance with a fixed-period payout. Whole life insurance, term insurance and deferred insurance. Life annuities: present value of life annuities, annuity-due and immediate annuity, annuities with linearly increasing or linearly decreasing benefits. Temporary and lifetime annuities. Single premium and level premium. Net premium and gross premium. Net premium reserves, expense-loaded premium reserves, gross premium, adequate reserves Calculations of premium reserves in the case of single premium or level premium.
Practical work during semester 100% / final exam 0%.
After completing the course, the student receives an overview of the basics of insurance business, classical life insurance products, net and gross premium calculation and methods of reserving. The student will be able to valuate basic life insurance products.
Basic practising and improving of locomotive faculties in the particular chosen sports. Developing harmonic personality in the sense of "kalokagatia" - cultivate his/her mental and physical values.
Grades: A 90%, B 80%, C 70%, D 60%, E 50%
Slovak, English
Introduction to the basic history of the selected sport, with the basic principles of compensation of one-sided psychological burden of the individual's body. Development of basic motor skills with a stop to all kinds of endurance, coordination, increasing the level of joint mobility. Training of individual game activities in collective sports games. In individual sports disciplines, practice of basic techniques of individual elements.
100/0
Orientation in the history of the selected sports discipline, mastering the basic principles of compensation of mostly mental burdens of the individual. Creating a positive, lasting relationship to physical education and sports in the sense of calocagation. Mastering the demands for the development of motor abilities, skills, proper technique of performing individual movements in individual sports, individual game activities in collective sports games.
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 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.
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.
Acquisition and improving of locomotive faculties in the particular sport. Development of the harmonic personality in the intention of "kalokagatia". To build up and increase resilience of the youth against different vicious and dangerous factors.
Grades: A 90%, B 80%, C 70%, D 60%, E 50%
Slovak, English
Completing a positive lasting relationship to physical education and sport. Development of motor skills with a focus on the development of strength, with an emphasis on dynamic strength and endurance in strength. In collective sports games, improving individual game activities, practicing basic game combinations, playing with modified rules, tasked games. In individual sports disciplines, the development of motor abilities and skills necessary for the acquisition of more complex elements of lower difficulty techniques.
100/0
Addressing a positive and lasting relationship with physical education and sport by understanding the importance of physical development and maintaining its optimal level throughout life. The use of strength and other motor skills to more rationally manage the game activities of the individual, while improving the acquisition of more complex elements of technology. In everyday life in providing basic necessities.
The objective of the subject is to provide the students with experience and knowledge of technical English and thus make them ready to use English sources of information for later study and professional career.
Anglický jazyk pre študentov FMFI UK : Kurz pre mierne pokročilých / Alena Zemanová.
Učebnica je nepublikovaná, k dispozícii v elektronickej podobe na webovej stránke KJP.
Anglický jazyk pre študentov FMFI UK : Aplikovaná matematika / Alexandra Maďarová, Ľubomíra Kožehubová.- učebnica publikovaná online
Anglický jazyk pre študentov FMFI UK : Matematika: Alexandra Maďarová, Eva Foltánová.
Učebnica je nepublikovaná, k dispozícii v elektronickej podobe na webovej stránke KJP.
Anglický jazyk pre študentov FMFI UK : Fyzika / Alena Zemanová.
Učebnica je nepublikovaná, k dispozícii v elektronickej podobe na webovej stránke KJP.
Anglický jazyk pre študentov FMFI UK : Informatika / Elena Klátiková.
Učebnica je nepublikovaná, k dispozícii v elektronickej podobe na webovej stránke KJP.
test, essay, presentation
Grades: A 93%, B 85%, C 77%, D 70%, E 65%
Course prerequisites:
https://fmph.uniba.sk/microsites/kjp/katedra-jazykovej-pripravy/poziadavky-na-udelenie-priebezneho-hodnotenia-aj1aj2aj3-ostatne-kurzy/
Slovak, English
On entering the first semester, students´ knowledge of English is tested and they are divided into groups according to the results of the placement test. In the groups of pre-intermediate and intermediate students, fundamentals of technical English are taught. Advanced students take classes of technical English for their field of study: English for mathematics, for physics, for computer science, English for management and economic and financial mathemathics.
100/0
The objective of the subject is to provide the students with experience and knowledge of technical English and thus make them ready to use English sources of information for later study and professional career.
The objective of the subject is to provide the students with experience and knowledge of technical English and thus make them ready to use English sources of information for later study and professional career.
Anglický jazyk pre študentov FMFI UK : Kurz pre mierne pokročilých / Alena Zemanová.
The textbook has not been published. It is at students' disposal in an electronic format.
test, essay, presentation
Grades: A 93%, B 85%, C 77%, D 70%, E 65%
Course prerequisites:
https://fmph.uniba.sk/microsites/kjp/katedra-jazykovej-pripravy/poziadavky-na-udelenie-priebezneho-hodnotenia-aj1aj2aj3-ostatne-kurzy/
Slovak, English
This is a continuation of the course English (1) designed for pre-intermediate students. Fundamental vocabulary is presented through selected topics in mathematics, physics and informatics. The lessons also contain revision of elementary grammar. Generally, it is a necessary preliminary to advanced programs.
100/0
The objective of the subject is to provide the students with experience and knowledge of technical English and thus make them ready to use English sources of information for later study and professional career.
Study materials are created by the teacher and available in electronic form.
Raymond Murphy: Essential Grammar in USe, Cambridge University Press, 1998
Michael McCarthy, Felicity O'Dell: English Vocabulary in Use, Cambridge University Press, 1994
tests, homework
English
Texts dealing with the most important topics for FMPI majors combining grammar revision with vocabulary needed to pass the A4 English exam.
100/0 credit - ongoing evaluation
Minimum 65 percent of the total points for the assigned work is needed to pass the course. Points can be awarded for attendance, completed homework tasks, and short tests assigned during the course.
A 100-93 %
B 92-85 %
C 84-77 %
D 76-70 %
E 69-65 %
Course prerequisites:
https://fmph.uniba.sk/microsites/kjp/katedra-jazykovej-pripravy/poziadavky-na-udelenie-priebezneho-hodnotenia-aj1aj2aj3-ostatne-kurzy/
Study materials are created by the teacher and available in electronic form. Raymond Murphy: Essential Grammar in USe, Cambridge University Press, 1998 Michael McCarthy, Felicity O'Dell: English Vocabulary in Use, Cambridge University Press, 1994
tests, homework
English
Texts dealing with the most important topics for FMPI majors combining grammar revision with vocabulary needed to pass the A4 English exam.
100/0 EN
credit - ongoing evaluation Minimum 65 percent of the total points for the assigned work is needed to pass the course. Points can be awarded for attendance, completed homework tasks, and short tests assigned during the course. A 100-93 % B 92-85 % C 84-77 % D 76-70 % E 69-65 %
Course prerequisites:
https://fmph.uniba.sk/microsites/kjp/katedra-jazykovej-pripravy/poziadavky-na-udelenie-priebezneho-hodnotenia-aj1aj2aj3-ostatne-kurzy/
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.
By means of physical education and sports to effectively act and advance a physical ability, fitness, performance and health of students.
Slovak, English
To practise game combinations, tactical - mechanical elements in basketball, volleyball, soccer, floorball, ice hockey, badminton, competition rules in the sports specialization.
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 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.
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 material 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.
To strengthen the procedural side of the physical education and sports with the emphasis on health and psychological value as well as to enhance the physical condition of students.
Slovak, English
Preparation for sport championships of the Faculty in the chosen sport at modified rules. The selection of talented students into the teams of the University and Faculty leagues and other faculty sport events.
100/0
The objective of the classes is to provide the students with knowledge of technical English in their field of study and experience with technical English sources sufficient to make the able to use technical language for their later study and professional purposes.
Anglický jazyk pre študentov FMFI UK : Kurz pre mierne pokročilých / Alena Zemanová.
Učebnica je nepublikovaná, k dispozícii v elektronickej podobe na webovej stránke KJP.
Anglický jazyk pre študentov FMFI UK : Aplikovaná matematika / Alexandra Maďarová, Ľubomíra Kožehubová.- učebnica publikovaná online
Anglický jazyk pre študentov FMFI UK : Matematika: Alexandra Maďarová, Eva Foltánová.
Učebnica je nepublikovaná, k dispozícii v elektronickej podobe na webovej stránke KJP.
Anglický jazyk pre študentov FMFI UK : Fyzika / Alena Zemanová.
Učebnica je nepublikovaná, k dispozícii v elektronickej podobe na webovej stránke KJP.
Anglický jazyk pre študentov FMFI UK : Informatika / Elena Klátiková.
Učebnica je nepublikovaná, k dispozícii v elektronickej podobe na webovej stránke KJP.
test, essay/presentation
Grades: A 93%, B 85%, C 77%, D 70%, E 65%
Course prerequisites:
https://fmph.uniba.sk/microsites/kjp/katedra-jazykovej-pripravy/poziadavky-na-udelenie-priebezneho-hodnotenia-aj1aj2aj3-ostatne-kurzy/
Slovak, English
The subject continues the program of English (2). Students take classes of special English for their field of study: English for mathematics, English for physics, English for computer science, English for management and economic and financial mathemathics.
The subject requires advanced knowledge of general English.
100/0
The objective of the classes is to provide the students with knowledge of technical English in their field of study and experience with technical English sources sufficient to make the able to use technical language for their later study and professional purposes.
The objective of the classes is to provide the students with knowledge of technical English in their field of study and experience with technical English sources sufficient to make them able to use technical language for their later study and professional purposes.
Anglický jazyk pre študentov FMFI UK : Kurz pre mierne pokročilých / Alena Zemanová.
Učebnica je nepublikovaná, k dispozícii v elektronickej podobe na webovej stránke KJP.
Anglický jazyk pre študentov FMFI UK : Aplikovaná matematika / Alexandra Maďarová, Ľubomíra Kožehubová.- učebnica publikovaná online
Anglický jazyk pre študentov FMFI UK : Matematika: Alexandra Maďarová, Eva Foltánová.
Učebnica je nepublikovaná, k dispozícii v elektronickej podobe na webovej stránke KJP.
Anglický jazyk pre študentov FMFI UK : Fyzika / Alena Zemanová.
Učebnica je nepublikovaná, k dispozícii v elektronickej podobe na webovej stránke KJP.
Anglický jazyk pre študentov FMFI UK : Informatika / Elena Klátiková.
Učebnica je nepublikovaná, k dispozícii v elektronickej podobe na webovej stránke KJP.
Examination: an examination consisting of a written and an oral part.
Grades: A 93%, B 85%, C 77%, D 70%, E 65%
Course prerequisites:
https://fmph.uniba.sk/microsites/kjp/katedra-jazykovej-pripravy/skuska-z-predmetu-anglicky-jazyk-4/
Slovak, English
Students take classes of special English for their field of study: English for mathematics, English for physics, English for computer science, English for management and economic and financial mathemathics.
0/100
After completing the course, students will be able to work independently with professional literature in English
written and oral examination
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.
To optimize the programmes of the sport recreational activities as a basic precondition of health strengthening, acquirement of physical capability, fitness, regaining of working energy and readiness of body to confront stress situations and dangerous factors.
Slovak, English
Preparation and participation of individuals and teams in the system of university sport competitions and sport events.
100/0
To mediate information and instructions from different fields of physical education and sports to students, to broaden know-how of sport performance in free time.
Slovak, English
Using the communication in the physical education and sport and organizing the sport championships to achieve expressive motion of the sport and health in a valuable orientation the students.
100/0
- Lechta, V. (ed): Inkluzivní pedagogika. Praha: Portál, 2016, ISBN 978-80-262-1123-5
- Slowík, J.: Komunikace s lidmi a postižením. Praha: Portál, 2010, ISBN 978-80-7367-691-9
- Kol. autorov: Od integrácie k inklúzii. VÚDPaP: Bratislava, 2018, ISBN 978-80-89698-27-1
Continuous assessment: active participation in class (elaboration of assigned tasks, participation in discussions)
An exam: -
Indicative assessment level: e.g. A 90%, B 80%, C 70%, D 60%, E 50%
Slovak
- Characteristics of basic concepts.
- Disability models.
- Disability legislation.
- Human, communication, information and architectural barriers.
- Impact of disability on education.
- Segregation - integration - inclusion.
- Information access technologies for people with disabilities.
- Possibilities and limits of creating equal conditions for the education of pupils with specific educational needs.
- Inclusive school - education for all.
- The importance of education for the social inclusion of people with disabilities.
100/0
The student:
- They will get acquainted with the basic characteristics of types of health disadvantage (HR) and will know the consequences of HR on education.
- Gain personal experience from meetings with people with disabilities and will be able to explain and apply the rules of communication with them.
- Can characterize the forms of education of students with SEN and assess the possibilities of their pedagogical, technical and human support, which positively affect the success of education.
Microsoft Excel 2016 step by step Curtis Frye / Frye C, Redmond: Microsoft Press, 2015
Preliminary evaluation: tests (60%), project (40%)
Rating scale: A 90%, B 80%, C 70%, D 60%, E 50%
Slovak, English
Maximum number of students: 24.
MS Excel environment, basic mathematical functions, cell formatting. Creating and working with tables. Data processing and cleaning, working with missing data. Basic types of graphs (bar, pie, histogram, etc.). Basics of VBA.
100/0
After completing the course, students will be able to use MS Excel, they will be able to use basic and more advanced functions for data processing and basic visualization, and they will get acquainted with the VBA language.
Poisťovníctvo a účtovníctvo poisťovní / Jitka Meluchová. Bratislava : Iura Edition, 2004;
Riziko ve financích a pojišťovnictví: Basel III a Solvency II / Tomáš Cipra. Praha : Ekopress, 2015;
Collection of Laws of the Slovak Republic;
EUR-Lex: EU law, the official online database of European Union law;
study materials of the lecturer.
During the semester the student can get 100% points for one written test, which is usually written sometime during the last two weeks of the semester.
Grade thresholds: A: at least 90.00%; B: 89.99% – 80.00%; C: 79.99% – 70.00%; D: 69.99% – 60.00%; E: 59.99% – 50.00%; Fx: 49.99% – 0.00%.
Slovak, English
Basic terms used in the banking and insurance sector. Origin and development of banking and insurance in the world. Commercial banking and insurance market in Slovakia. Acts (in their current and complete wording) regulating the commercial insurance industry in Slovakia: Act on Insurance, Act on Compulsory Contractual Motor Vehicle Third Party Liability Insurance and other laws. Social and pension security in Slovakia. Legal regulations regulating the commercial banking sector in Slovakia in their current and complete wording. Solvency and financial stability of commercial banks and insurance companies in Slovakia and the European Union, the Basel III and Solvency II regulatory frameworks. International Financial Reporting Standards (IFRS) for commercial banks and insurance companies.
Practical work during semester 100% / final exam 0%.
After completing the course, the student will master the history and basic concepts of banking and insurance, as well as some parts of the law governing commercial banking and insurance business in Slovakia.
Pravdepodobnosť a štatistika / Katarína Janková, Andrej Pázman. Bratislava: Univerzita Komenského, 2011
Štatistika v Exceli 2007 / Jozef Chajdiak. Statis, Bratislava 2009
Preliminary evaluation: tests (40%), project (60%)
Rating scale: A 90%, B 80%, C 70%, D 60%, E 50%
Slovak, English
Mathematical functions in MS Excel. Probability distributions. Processing and visualization of the data. Excel VBA introduction. Descriptive statistics. Parameter estimation, hypothesis testing, regression analysis.
Probability distributions in MS Excel (probability, distribution, quantile functions, data generation). Descriptive statistics in MS Excel environment (sample characteristics). Advanced data vizualization methods (eg box plot, time series vizualization), Power BI. Basics of inference statistics (parameter estimation, hypothesis testing, linear regression analysis). Solver and Data Analysis add-ins.
100/0
After completing the course the students will be able to use the MS Excel environment for processing, visualizing and analyzing real data.
Jíří Anděl: Matematika náhody. Praha, MatfyzPress, 2000.
the basics of the R language, or good skill in programming in another language
Assessment during the term: homework (60%), test (40%).
Grading: A: 90 and more, B: [80, 90), C: [70, 80), D: [60, 70), E: [50, 60), FX: less than 50
Slovak, English
Combinatorial probability, conditional probabilities, Bayes theorem. Discrete and continuous random variables and random vectors - computation of probabilities, moments, transformations, computer simulations, applications. Selected statistical methods.
100/0
Student gains skills in applying the knowledge from probability and statistics to solve problems, including real life applications.
Pravdepodobnosť a štatistika / Katarína Janková, Andrej Pázman. Bratislava : Univerzita Komenského, 2011
Zbierka úloh zo základov teórie pravdepodobnosti / Radoslav Harman, Erika Hönschová, Ján Somorčík. Bratislava : PACI, 2009
Preliminary evaluation: tests.
Slovak, English
Random vectors and their characteristics. Marginal and conditional distributions. Characteristic functions. Multidimensional normal distribution and its properties. Convergence of the sequence of random variables. Central limit theorem, laws of large numbers. Statistical inference, parameter estimation, maximum likelihood method, statistical hypothesis testing.
100/0
Students will practice working with multidimensional discrete and continuous probability distributions. They will be able to apply the acquired knowledge in solving selected statistical problems.
Pravdepodobnosť a štatistika / Katarína Janková, Andrej Pázman. Bratislava : Univerzita Komenského, 2011
Zbierka úloh zo základov teórie pravdepodobnosti / Radoslav Harman, Erika Hönschová, Ján Somorčík. Bratislava : PACI, 2009
Preliminary evaluation: tests.
Slovak, English
Probability space. Classical probability models and discrete distributions. Random variable and its distribution function. Basic types of discrete and continuous random variables. Expected value and variance. Independence and correlation coefficient. Normal distribution and central limit theorem. Random sample, its mean, sample variance. Random sample from normal distribution. Point estimates of unknown parameters, maximum likelihood estimation. Confidence intervals for the mean of the normal distribution.
100/0
After completing the course, students will be able to solve the problems of one-dimensional discrete and continuous random variables. Furthermore, students will be able to solve some statistical problems.
- S. Russell: Human compatible. Artificial intelligence and the problem of control. Viking, 2019.
- J. Havens: Heartificial intelligence. Embracing our humanity to maximize machines. Penguin, 2016.
- P. Boddington: Towards a code of ethics for artificial intelligence. Springer, 2017.
- M. Shanahan: The technological singularity. MIT Press, 2015.
- C. MacKellar, C.: Cyborg Mind: What Brain–Computer and Mind–Cyberspace Interfaces Mean for Cyberneuroethics. Berghahn Books, 2019.
- G. Bel, J. Gemmell: Total Recall, How the e-Memory Revolution will change everything. Dutton, 2009.
- S. Zuboff: The Age of Surveillance Capitalism: The Fight for a Human Future at the New Frontier of Power. PublicAffairs, 2019.
- C. O'Neil: Weapons of Math Destruction: How Big Data Increases Inequality and Threatens Democracy. Crown Publishers, 2016.
- M. Tegmark: Life 3.0. Allen Lane, 2017.
Semestral evaluation: active participation
Final evaluation: essay
Weight of the final evaluation: 60%
To achieve an A, 90% is needed, for B at least 80%, for C 70%, for D, 60% and for an E, at least 50% of overall assessment.
English
Big data: privacy, politics and power,
Internet of things, it usefulness and threats,
Assistant AI and its place in future society,
Job market and inequality,
Enhancements and human rights and the right to change self and others,
Initiatives for responsible research,
Artificial minds,
Hybridization between species and between AI and organic minds,
Future of minds and trans-humanism,
Artificial emotional intelligence,
An after human era.
http://dai.fmph.uniba.sk/courses/STH/
The students will gain awareness of the contemporary and potential future challenges posed by scientific and technological innovations and their impact on human behaviour, culture and society.