Lectures on nonlinear analysis / Pavel Drábek, Jaroslav Milota. Plzeň : Vydavateľstvo servis, 2004
Nonlinear differential equations and dynamical systems / Ferdinand Verhulst. Berlin : Springer, 1990
Nelineární diferenciální rovnice / Svatopluk Fučík, Alois Kufner. Praha : Státní nakladatelství technické literatury, 1978
Continuous assessment: handwriting
Exam: oral
Original rating scale: A 90%, B 80%, C 70%, D 60%, E 50%
1. Differential calculus in Banach spaces.
2. Local nonlinear analysis: Uniform contraction theorem and implicit function theorem.
3. Bifurcation theory: Lyapunov - Schmidt reduction.
4. Continuous methods for solving nonlinear equations.
40/60
Fundamentals of nonlinear analysis, differential calculus in Banach spaces, bifurcation theory and continuous methods.
B. Dacorogna: Direct methods in the calculus of variations, Springer, Berlin - Heidelberg 2008.
M. Struwe: Variational methods, Springer, Berlin - Heidelberg 2008.
J.L. Troutman: Variational calculus and Optimal Control, Springer, New York 1996.
G. Buttazzo, M. Giaquinta, S. Hildebrandt: One-dimensional variational problems, Clarendon Press, Oxford 1998.
Preliminary grading: homeworks.
Exam: written and oral.
Grading: A 90%, B 80%, C 70%, D 60%, E 50%.
English
Differentiability of the Nemytskii mapping, basic existence theorem for global extrema, necessary and sufficient conditions for local extrema,
constrained extrema, the Euler and Jacobi equations, necessary and sufficient conditions for strong and weak extrema of one-dimensional integrals, investigation of critical points of particular functionals.
20/80
The students will learn to differentiate variational integrals and related Nemytskii mappings, they will be able to verify necessary and sufficient conditions guaranteeing the existence of global and local extrema of particular functionals, to find extrema in the case of one-dimensional integrals and find out, whether these extrema are weak or strong.
General topology / Stephen Willard. Mineola : Dover, 1970
Topology / James R. Munkres. Upper Saddle River : Prentice-Hall , 2000
Final evaluation: oral exam
Rating scale: A 90%, B 80%, C 70%, D 60%, E 50%
Slovak, English
Topological spaces and continuous functions. Basic topological constructions (subspace, topological sum and product, quotient space).
Countability axioms and separation axioms (Hausdorff, regular, completely regular and normal spaces). Connected and linearly connected spaces. Compact and locally compact spaces. Metric space, metrizable spaces.
http://msleziak.com/vyuka/vstop.html
100% final exam
Students will understand basic notions of general topology, properties of topological spaces and their subsets, basic topological constructions. They will be able to apply topological results in further areas of mathematical analysis, topology and geometry.
M. Hirsch, Differential Topology. Springer-Verlag, New York 1976.
J. Milnor, Topology from the Differential Viewpoint, The Univ. Press of Virginia, Charlottesville 1965.
I. Singer, J. Thorpe, Lecture Notes on Elementary Topology and Geometry, Scott, Foresman and Co., Glenview, Illinois 1967.
F. Warner, Foundations of Differentiable Manifolds and Lie Groups. Springer-Verlag, Berlin 1983.
Exam: written and oral
Indicative assessment scale: A 90%, B 80%, C 70%, D 60%, E 50%
English
A review of selected basic notions of general topology. Differentiable manifolds and differentiable maps. Tangent vector space. The differential of a differentiable map at a point. Tangent bundles. Submanifolds. Immersions and embeddings of manifolds. Inverse Function Theorem and its corollaries; transversality. Regular and critical points, regular and critical values, Sard’s Theorem. Proof of the fundamental theorem of algebra.
Subject aim: to acquaint students with basic ideas, methods and some applications of differential topology.
A. Hatcher, Algebraic Topology. Cambridge University Press 2002
A. Kriegl, Algebraic Topology. Lecture Notes. University of Vienna, Vienna 2008, accessible at http://www.mat.univie.ac.at/~kriegl/Skripten/alg-top.pdf
W. Massey, A Basic Course in Algebraic Topology. Springer-Verlag, New York 1991
E. Spanier, Algebraic Topology. Springer-Verlag, New York 1995
Exam: written and oral
Indicative assessment scale: A 90%, B 80%, C 70%, D 60%, E 50%
English
The problem of homeomorphy. Constructions of new topological spaces by forming quotient spaces. Attaching a cell to a topological space. Surfaces and topological manifolds. Path-connectedness. Homotopy. Fundamental group. Basic homology theory. Homology groups of spheres and their applications. Cohomology groups, cohomology ring, and applications.
Subject aim: to acquaint students with basic ideas, methods and some applications of algebraic topology.
Algebra a príbuzné disciplíny / Milan Kolibiar ...[et al.]. Bratislava : Alfa, 1992
Categories for the working mathematician / Saunders Mac Lane. New York : Springer, 1997
Abstract and Concrete Categories/Jiří Adámek, Horst Herrlich, George E. Strecker. http://katmat.math.uni-bremen.de/acc/acc.pdf
Continuous assessment: homework and 1 presentation
Indicative evaluation scale: A 90%, B 80%, C 70%, D 60%, E 50%
Slovak, English
Categories, functors and natural transformations. Special morphisms and objects. Subcategories. Limits and colimits. Factorization systems.
100/0
Students will master selected basic concepts and methods of category theory and will be able to apply them in topology and algebra.
Algebra a príbuzné disciplíny / Milan Kolibiar ...[et al.]. Bratislava : Alfa, 1992
Categories for the working mathematician / Saunders Mac Lane. New York : Springer, 1997
Abstract and Concrete Categories/Jiří Adámek, Horst Herrlich, George E. Strecker. http://katmat.math.uni-bremen.de/acc/acc.pdf
Continuous assessment: homework and 1 presentation
Indicative evaluation scale: A 90%, B 80%, C 70%, D 60%, E 50%
Slovak, English
Adjoint functors, existence theorems, reflective and coreflective subcategories. Generators and cogenerators of categories and subcategories. Application of category theory methods in topology and algebra.
100/0
Students will master selected basic concepts and methods of category theory and will be able to apply them in topology and algebra.
The aim of this lecture, based on principles and methods of the traditional geometry and the computational synthetic geometry, is to deepen the knowledge of the students useful in technical applications of geometry and machine vision. The lecture will also supply the necessary geometric basis for the theory of computer vision and image recognition. The students will also find inspiration for creating new algorithms or improving effectiveness of the traditional algorithms in computer graphics.
R. Hartley, A Zisserman: Multiple View Geometry, Cambridge University Press 2002
O. Faugeras, Q – T. Luong ( T. Papadopoulo) Geometry of Multiple Images, The MIT Press, Cambridge, Massachusetts, London 2001
Final exam (oral exam with written preparation 100%). Rough evaluation scale: A 90%, B 80%, C 70%, D 60%, E 50%
Synthetic constructions of curves, surfaces and solids for technical applications. Viewing methods and traditional methods of the realistic imaging (illumination, shadowing, isophotes). The use of computers and professional software in constructions and photo-realistic imaging. Geometric photogrammetry and its use in creating virtual cities. Single view geometry and camera models. Mathematical and geometric principles of multiple view geometries. Two-view and epipolar geometry. Projections used in cartography or related fields.
The aim of this lecture, based on principles and methods of the traditional geometry and the computational synthetic geometry, is to deepen the knowledge of the students useful in technical applications of geometry and machine vision. The lecture will also supply the necessary geometric basis for the theory of computer vision and image recognition. The students will also find inspiration for creating new algorithms or improving effectiveness of the traditional algorithms in computer graphics.
examination
1. S. Bosch: Algebraic Geometry and Commutative Algebra, Springer, 2013
2. M. F. Atiyah, I. G. MacDonald: Introduction to commutative algebra: Advanced book program.Oxford : Westview, 1969
3. D. Eisenbud: Commutative algebra with a view toward algebraic geometry. New York: Springer,2004
4. H.Matsumura: Commutative Ring Theory, Cambridge University Press, Cambridge, 1989
Homeworks (written solutions of problems and their consulting 50%), final exam (oral exam with written preparation 50%). Rough evaluation scale: A 90%, B 80%, C 70%, D 60%, E 50%
English
Commutatiove rings and modules. Theory of noetherian rings. Integral extensions of rings. Extensions and restrictions of coefficients. Homological methods: Ext and Tor.
Homeworks/ final exam: 50/50
PhD. student masters selected methods of modern commutative algebra with emphasis on application in other areas, especially in algebraic geometry.
1. S. Bosch: Algebraic Geometry and Commutative Algebra, Springer, 2013
2. D. Eisenbud: Commutative algebra with a view toward algebraic geometry. New York: Springer,2004
3. D. Eisenbud, J. Harris: The Geometry of Schemes, Springer, 2000
4. U. Görtz, T. Wedhorn: Algebraic Geometry I: Schemes, Springer, 2020
Homeworks (written solutions of problems and their consulting 50%), final exam (oral exam with written preparation 50%). Rough evaluation scale: A 90%, B 80%, C 70%, D 60%, E 50%
English
Affine schemes and their basic constructions. Techniques of global schemes.
Homeworks / Final evaluation: 50/50
PhD. student masters basic notions and methods of modern algebraic geometry in order to read contemporary literature in the area.
This is a follow-up to the master course in algebraic topology, an elaboration of homology and cohomology theories at advanced levels.
Topology and geometry / Glen E. Bredon. New York : Springer, 1993
Algebraic topology / Edwin H. Spanier. New York : Springer, 1966
Algebraic topology / Allen Hatcher. New York : Cambridge University Press, 2001
Exam: written and oral
Indicative evaluation scale: A 90%, B 80%, C 70%, D 60%, E 50%
Homology and cohomology theories, the universal coefficient theorems and Kuenneth fomulae, products, Steenrod cohomology operations, duality.
This is a follow-up to the master course in algebraic topology, an elaboration of homology and cohomology theories at advanced levels.
examination
An elaboration of higher homotopy theory and basic facts from the theory of spectral sequences.
Topology and geometry / Glen E. Bredon. New York : Springer, 1993
Algebraic topology / Edwin H. Spanier. New York : Springer, 1966
Algebraic topology / Allen Hatcher. New York : Cambridge University Press, 2001
Exam: written and oral
Indicative evaluation scale: A 90%, B 80%, C 70%, D 60%, E 50%
Higher homotopy groups, the Hurewicz homomorphism, homotopy properties of CW-complexes, homology and cohomology spectral sequences of fibrations and their applications.
Elaboration of higher homotopy theory and basic facts from theory of spectral sequences.
examination
An elaboration of the advanced theory of smooth manifolds and vector bundles.
Topology and geometry / Glen E. Bredon. New York : Springer, 1993
Differential topology / Morris W. Hirsch. New York : Springer, 1997
Exam: written and oral
Indicative evaluation scale: A 90%, B 80%, C 70%, D 60%, E 50%
The Morse-Sard theorem, transversality, vector bundles, immersions and embeddings of manifolds in Euclidean spaces, the degree of a map, the Euler characteristic, basic facts from Morse theory.
An elaboration of the advanced theory of smooth manifolds and vector bundles.
examination
Topology and geometry / Glen E. Bredon. New York : Springer, 1993
Diferenciálna geometria a Lieove grupy pre fyzikov / Marián Fecko. Bratislava : Iris, 2004
Differential geometry and Lie groups for physicists / Marián Fecko. Cambridge : Cambridge University Press, 2006
Carter, Roger, Segal, Graeme, and MacDonald, Ian, Lectures on Lie Groups and Lie Algebras, Cambridge University Press, 1995.
Exam: written and/or oral examin
Indicative grading scheme: A: 90%, B: 80%, C: 70%, D: 60% , E:50%
English, Slovak
The notion of Lie group, examples. The action of a Lie group on a manifold. Homogeneous spaces. Classical Lie groups. Invariant vector fields. Basic information on representations. Fundamentals of the theory of Lie algebras.
0/100
Students will learn the basic concepts, methods and results of the theory of Lie groups and algebras and will be able to apply them in solving problems in geometry and topology.
To acquaint the students with basic notions, methods and results of the different-ial geometry on manifolds.
Foundations of differential geometry : Volume 2 / Shoshichi Kobayashi, Katsumi Nomizu. New York : John Wiley, 1969
A comprehensive introduction to differential geometry : volume 1 / Michael Spivak. Berkeley : Publish or Perish, 1979
A comprehensive introduction to differential geometry : Volume 2 / Michael Spivak. Berkeley : Publish or Perish, 1979
A comprehensive introduction to differential geometry : Volume 3 / Michael Spivak. Berkeley : Publish or Perish, 1979
A comprehensive introduction to differential geometry : Volume 4 / Michael Spivak. Berkeley : Publish or Perish, 1979
A comprehensive introduction to differential geometry : Volume 5 / Michael Spivak. Berkeley : Publish or Perish, 1979
Kobayashi, S., Nomizu, K.: Foundations of Differential Geometry I. Interscience Publishers N. York, 1996.
Final exam (oral exam with written preparation 100%). Rough evaluation scale: A 90%, B 80%, C 70%, D 60%, E 50%
Differentiable manifolds, smooth mappings, tangent vectors. Tensors and tensor fields. Covariant derivative, affine connection. Geodesics. Riemannian metric, the Levi-Civita connection. Homogeneous spaces, invariant connections.
The students will master basic ideas and results of the global differential geometry of manifolds.
examination
Knots / Gerhard Burde, Heiner Zieschang, Michael Heusener. New York : Walter de Gruyter, 2013
Algebraic topology / Allen Hatcher. New York : Cambridge University Press, 2001
Algebraic topology / Edwin H. Spanier. New York : Springer, 1966
Knots, Links, Braids and 3-manifolds: An Introduction to the New Invariants in Low-Dimensional Topology / V. V. Prasolov, A. B. Sossinsky: AMS, Providence, 1996
Exam: written and oral exam
Indicative grading scheme: A: 90%, B: 80%, C: 70%, D: 60% , E:50%
English, Slovak
The contents of the course will be adjusted, to some extent, to the interests of the students. The topics covered in the course will include mainly the following:
Basic notions, methods and results of knot and link theory; results from the topology of 3-dimensional manifolds: examples of manifolds, lens spaces, surgery, torus decompositions;
results on 4-dimensional manifolds: examples of manifolds, algebro-topological invariants, complex surfaces, the Kirby calculus.
0/100
The students will master classical results, as well as selected outcomes of the modern low-dimensional topological research.
Symplectic geometry, grupoids, and integrable systems / Pierre Dazord, Alan Weinstein. New York : Springer, 1991
Algebraic topology / Edwin H. Spanier. New York : Springer, 1966
Introduction to Symplectic Topology / Dusa McDuff, Dietmar Salamon: Oxford Science Publications, 1998
Exam: written and/or oral exam
Indicative grading scheme: A: 90%, B: 80%, C: 70%, D: 60% , E:50%
English, Slovak
The contents of the course will be adjusted, to some extent, to the interests of the students. The topics covered in the course will include mainly the following:
basic notions, methods and results of symplectic topology, tools and analytical background of theory of J-holomorphic curves, the Gromov-Witten invariants, applications of the gauge theory in the topology of 3-dimensional and 4-dimensional manifolds.
0/100
Students will master classical results, as well as selected outcomes of the current research in symplectic topology, topological applications of gauge theories etc.
Examination (A: 90%, B: 80%, C: 70%, D: 60% , E:50% )
Geometric incidence structures, projective and affine planes. Coordinatization of projective and affine planes and the relations between geometric and corresponding coordinate algebraic structures. Finite geometries and geometries over the field. Ordered geometry. Absolute geometry as the starting point for introduction of hyperbolic non-euclidean geometry. Riemann's non-euclidean geometry. Fundamental principles for construction of four-dimensional geometry. Selected chapters of Euclidean geometry (special properties of triangle, isometries and similarities in Euclidean plane and space, two-dimensional crystallography, geometry of circles and spheres, Platonic solids, golden section, phyllotaxis).
The PhD students learn some interesting but little known properties of geometric planar and spatial objects, as well as the fundamental principles and methods in the axiomatic approach to classical geometry related to some geometric and algebraic structures and formation of non-euclidean geometries. They will be then able to use the knowledge obtained to solve problems in geometry and topology.
A comprehensive introduction to differential geometry : volume 1 / Michael Spivak. Berkeley : Publish or Perish, 1979
A comprehensive introduction to differential geometry : Volume 2 / Michael Spivak. Berkeley : Publish or Perish, 1979
A comprehensive introduction to differential geometry : Volume 3 / Michael Spivak. Berkeley : Publish or Perish, 1979
A comprehensive introduction to differential geometry : Volume 4 / Michael Spivak. Berkeley : Publish or Perish, 1979
A comprehensive introduction to differential geometry : Volume 5 / Michael Spivak. Berkeley : Publish or Perish, 1979
Lectures on classical differential geometry / Dirk J. Struik. Cambridge : Addison-Wesley Press, 1950
Final exam (oral exam with written preparation 100%). Rough evaluation scale: A 90%, B 80%, C 70%, D 60%, E 50%
Curves: Analytic expression. Tangent lines and osculating planes. Natural parametrization. Curvature and torsion, the Frenet formulas. Natural equations of curves.
Surfaces: Analytic expression. Curves on surfaces. Tangent planes and normals. Developable surfaces. The first fundamental form of a surface. Mappings between surfaces. The second fundamental form of a surface. The normal curvature of a surface. Directions on a surface. Principal directions and principal curvatures. The Gaussian curvature of a surface.
Geometry on surfaces: Geodesics, geodetic coordinates. Surfaces with constant curvature. Non-euclidean geometry.
The PhD students master important notions, methods and results of the classical differential geometry of curves and surfaces. They will be able to apply their knowledge to problems in geometry and topology.
Solid modeling by computers : From theory to applications / edited Mary S. Pickett, John W. Boyse. New York : Plenum Press, 1984
Level set methods and dynamic implicit surfaces / Stanley Osher, Ronald Fedkiw. New York : Springer, 2003
Michael Mortenson : Geometric Modeling. John Wiley & Sons, Inc. New York, NY, 3rd Edition 2006
Final exam (oral exam with written preparation 100%). Rough evaluation scale: A 90%, B 80%, C 70%, D 60%, E 50%
Mathematical methods in geometric modeling. Extended methods in paramteric modeling (Coons body construction, bodies as special hypersurfaces in E4). Geometric modeling using splines, especially in rational form. Recursive subdivision and refinement in modeling. Fundamentals of implicit modeling of curves and surfaces. F-rep. Implicitization. Selected elimination methods. Polar forms. Shape modification tools and fitting. Mesh in geometric modeling. Effective methods of tesselation for smooth surfaces and boundaries.
0/100
The students are supposed to acquire modern trends in parameteric, implicit and subdivision modeling of curves, surfaces and volumes. They should be able to solve tasks connected with constructive modelling requirements of technical praxis as well as contemporary problems of modeling in computer graphics, entertainment industry and mass media.
Real-time rendering / Tomas Akenine-Möller, Eric Haines, Naty Hoffman. Wellesley : A. K. Peters, 2008
Study materials in Slovak and selected recent papers and monographs in Visual Computing research.
individual work 100%, examination 0%
Slovak and English
The course content can be (partially) individualized with regard to the dissertation topic.
Methodology of science, methodology of mathematical modeling and structured engineering design in computer graphics and image processing. Mathematical models relevant to the field of Visual Computing. Digital Processing of Visual Information with regard to the application of projective and affine geometry. Theory of HCI (Human Computer Interface).
(Applications.) CAD / CAM. Real-time rendering, visual effects and computer games. Advanced techniques of special modeling and 3D computer animation. International standardization (philosophy of the MPEG and SEDRIS standards, standardization for geodata and biodata). Medical informatics.
The PhD students will acquire the necessary general and specific methodological theoretical knowledge on trends and applications of computer graphics and they will be able to apply them to solve relevant theoretical and practical problems.
Image processing, analysis, and machine vision / Milan Sonka, Vaclav Hlavac, Roger Boyle. [Stamford] : Cengage Learning, 2008
Počítačové videnie / Elena Šikudová, Zuzana Černeková, Wanda Benešová, Zuzana Haladová, Júlia Kučerová. Praha: Wikina 2013.
https://vgg.fiit.stuba.sk/kniha/Pocitacove%20Videnie%20-%20Detekcia%20a%20Rozpoznavanie%20Objektov.pdf
Study materials in Slovak and selected recent papers and monographs in Visual Computing research.
individual work
Examination 100% (A: 90%, B: 80%, C: 70%, D: 60% , E:50% )
1. Digital image and its properties (overview)
2. The image preprocessing (advanced method)
3. Segmentation (advanced method)
4. Pattern recognition (advanced method)
5. Image understanding
6. 3D vision, geometry and radiometry
7. Uses of 3D vision
8. Motion Analysis
9. Case studies (selected topics)
The PhD students receive an overview of recent advanced methods in computer vision, which reflect the current state of knowledge in the field (preprocessing, segmentation, image recognition and understanding), with an emphasis on the most challenging ideas in 3D vision. They will be able to apply the acquired knowledge in solving theoretical and practical problems of computer vision.
The Visual Display of Quantitative Information / Edward R.Tufte. Graphics Press 2001.
Virtual Space / Lars Qvortrup et al. Springer-Verlag London 2002 2002.
The Data Science Design Manual / Steven S. Skiena. Cham: Springer Nature 2017.
individual work 100%, examination 0%
Slovak and English
The course content can be (partially) individualized with regard to the dissertation topic.
Methodology of scientific and technical visualization. Information visualisation. Visualization techniques and scenarios for geodata and medical data. Special representation (point-based graphics, implicit surfaces, volume graphics). Selected applications.
Virtual environments by Qvortrup. Cyberspace and virtual navigation, interaction and cooperation. Computer games, visual effects and their programming in real time.
Digital storytelling.
The PhD student receives theoretical and practical knowledge of visualization and virtual environments. If it is appropriate and possible, the students will participate in solving problems in a cooperating company, thus achieving practical applications of their theoretical knowledge.
General topology / Stephen Willard. Mineola : Dover, 1970
Topology / James R. Munkres. Upper Saddle River : Prentice-Hall , 2000
Modern general topology / Jun-Iti Nagata. Amsterdam : North-Holland, 1968
Exam: written and oral
Indicative evaluation scale: A 90%, B 80%, C 70%, D 60%, E 50%
Compact spaces and compactifications, compactly generated spaces, perfect mappings, paracompact spaces, topologies on sets of continuous mappings, compact - open topology, metrizable spaces, metrization theorems, uniform spaces, selected topical themes.
To master selected notions and methods of general topology and their applications in geometry and topology, mathematical analysis and algebra.
Categories for the working mathematician / Saunders Mac Lane. New York : Springer, 1997
Algebra a príbuzné disciplíny / Milan Kolibiar ...[et al.]. Bratislava : Alfa, 1992
Abstract and Concrete Categories/Jiří Adámek, Horst Herrlich, George E. Strecker. http://katmat.math.uni-bremen.de/acc/acc.pdf
Exam: written and oral
Indicative evaluation scale: A 90%, B 80%, C 70%, D 60%, E 50%
Abstract and concrete categories and functors, adjoint functors, existence of adjoints, reflective and coreflective subcategories, factorization structures, topological categories and functors, selected topical themes.
To master selected category-theoretical methods used in topology and algebra.
Bochnak, J.; Coste, M.; Roy, M.-F., Real algebraic geometry. Berlin: Springer. ix, 430 p., (1998)
Basu, S.; Pollack, R.; Roy, M.-F., Algorithms in real algebraic geometry. 2nd ed. Berlin: Springer, 662 p., 2006
Examination (A: 90%, B: 80%, C: 70%, D: 60% , E:50% )
Real closed fields. Semialgebraic sets, their properties and decomposition. Real and complex algebraic sets. Properties, examples, constructions. Real roots of polynomial systems and their localization – methods and algorithms.
The student should master basic qualitative results and computational methods of work with real (semi)algebraic varieties. The student learns typical examples in spaces of dimensions 1, 2, 3, 4 and becomes able to use them in applications based on real semialgebraic objects, e.g. in geometric modeling, visualization etc.
Examination (A: 90%, B: 80%, C: 70%, D: 60% , E:50% )
An active individual study of the literature (mostly a monograph or its selected parts) prescribed by the individual plan of study.
The student masters the subject of individual study and is able to apply the knowledge obtained in solving open questions of geometry and topology.
Examination (A: 90%, B: 80%, C: 70%, D: 60% , E:50% )
An active individual study of the literature (mostly a monograph or its selected parts) prescribed by the individual plan of study.
The student masters the subject of individual study and is able to apply the knowledge obtained in solving open questions of geometry and topology.
An active individual study of the literature (mostly a monograph or its selected parts) prescribed by the individual plan of study.
The student masters the subject of individual study and is able to apply the knowledge obtained in solving open questions of geometry and topology.
Examination (A: 90%, B: 80%, C: 70%, D: 60% , E:50% )
An active individual study of the literature (mostly a monograph or its selected parts) prescribed by the individual plan of study.
The student masters the subject of individual study and is able to apply the knowledge obtained in solving open questions of geometry and topology.
The seminar talk.
Seminar talks on selected topics of contemporary geometry and topology.
The student will be able to give a public talk about their own or other scientific theories and concrete results, as well as to react to questions and criticisms.
Examination 0%
Achieving new scientific results in the area of student’s PhD study. Writing a scientific manuscript and its publication.
A publication on the top interational level, in a journal (conference proceedings) covered by the database WoK or SCOPUS; in internationally renowned congress (conference) proceedings published by IFAC, covered in SCOPUS; a monograph or a chapter in monograph published by an internationally renowned publishing house (Elsevier, Springer). The number of credits will be 0.P times 35 if the student’s participation on the publication is P%
Achieving new scientific results in the area of student’s PhD study. Writing a scientific manuscript and its publication.
A publication in a journal covered by Mathematical Reviews, Zentralblatt MATH, Referativnyi Zhurnal, INSPEC; in fully peer reviewed proceedings of an international conference held in an international language, with a large international participation, reviewed by title in Mathematical Reviews, Zentralblatt MATH, Referativnyi Zhurnal; in proceedings of an internationally renowned organization (IFAC) or publisher (Springer, Elsevier) if it is not of category A; a monograph or a chapter in monograph in an international language published by an international publisher if it is not of category A. The number of credits will be 0.P times 25 if the student’s participation on the publication is P%.
Achieving new scientific results in the area of student’s PhD study. Writing a scientific manuscript and its publication.
A publication reviewed, but not by title, in Mathematical Reviews, ZbMATH, Referativnyi Zhurnal; in peer reviewed proceedings of an international conference with an international organizing committee, if it is not of categories A or B; a monograph or a chapter in monograph published by a Slovak publishing house in an international language, exceptionally also in Slovak, reviewed in Mathematical Reviews, ZbMATH, Referativnyi Zhurnal, if it contains new original results by the student. The number of credits will be 0.P times 20 if the student’s participation on the publication is P%.
Achieving new scientific results in the area of student’s PhD study. Writing a scientific manuscript and its publication.
A scientific publication by the student that cannot be classified as of type A, B, or C. The number of credits will be 0.P times 10 if the student’s participation on the publication is P%.
Preparations for a lecture or talk. Delivery of a lecture or talk at a scientific conference or seminar.
The students are able to deliver a lecture or talk about results of their own scientific research abroad, at a conference or university scientific seminar.
Preparations for a lecture or talk. Delivery of a lecture or talk at a scientific conference.
The students are able to deliver a lecture about results of their own scientific research at a conference in Slovakia with domestic and foreign participants.
Preparations for a lecture or talk. Delivery of a lecture or talk at a scientific conference.
The students are able to deliver a lecture about results of their own scientific research at a conference with no foreign participants.
Talk at seminar
Individual research activity of the student. Preparations for a public presentation of the results . Delivery of a talk.
The student proves to be able to present mathematical results to an expert audience and to discuss the topic presented in the talk.
Scientific research and elaboration of the results in a written form.
The student completes the corresponding part of the research related to the dissertation and achieves original results.
Scientific research and elaboration of the results in a written form.
The student completes the corresponding part of the research related to the dissertation and achieves original results.
Scientific research and elaboration of the results in written form.
The student completes the corresponding part of the research related to the dissertation and achieves original results.
Preparations for a grant project. Getting a grant.
The student gets a grant from Comenius University in Bratislava.
Participation in preparations for a grant project. Membership in an international research team supported by a grant agency.
The student becomes a member of an international research team supported by a grant agency.
Participation in preparations for a grant project. Membership in a research team supported by a Slovak grant agency.
The student becomes a member of a research team supported by a Slovak grant agency.
Finding and recording a citation of the specified type.
A scientific work of the student is cited in a publication covered by Web of Knowledge or SCOPUS (autocitations are excluded).
Finding and recording a citation of the specified type.
A scientific work of the student is cited in a monograph (auto-citations are excluded).
Finding and recording a citation of the specified type.
A scientific work of the student is cited in a publication with at least one foreign author (autocitations are excluded).
Finding and recording a citation of the specified type.
A scientific work of the student is cited in a publication without foreign authors (autocitations are excluded).
Preparations. Indroduction of a novel experimental method in relation to the topic of the dissertation.
The student introduces an experimental method of new kind, related to the topic of the dissertation.
Preparations; completion and documentation of a new software product related to the topic of the dissertation thesis.
The student develops an original software product related to the topic of the dissertation thesis.
Preparations for teaching. Teaching.
The student gains a personal experience as part of the training for teaching at a university.
Preparations for teaching. Teaching.
The student gains a personal experience as part of the training for teaching at a university.
Preparations. Supervision of a BSc (undergraduate) diploma thesis.
The PhD-student supervises a BSc diploma thesis.
Preparations. Supervision of a student.
The PhD-student supervises writing and submitting a paper for the Students‘ Conference.
Preparations. Work in the organising committee of a scientific conference.
The student demonstrates organizational capabilities in co-organising a scientific conference as a member of its organising committee.
Preparations for producing a new teaching aid or text. Production of a new teaching aid or text.
The student produces a new teaching aid or text.
Preparations; choosing a suitable foreign scientific institution; completing the study stay.
The student completes a scientific study stay in the corresponding area of study at an accredited foreign university or other scientific institution.
Reading of the Bc-degree thesis in question. Writing a referee report on it.
The student writes a referee report on a Bc-degree thesis.
Preparations for the assistance. Performing the assistance.
The student assists, in a verifiable manner, a colleague directing a Master Thesis.
State examination.
Written part and oral part of the state exam.
By completing this subject, the student fulfils a necessary condition for
finishing the learning period and beginning the research period of the study.
State examination.
Preparations for the defense. Defense of the dissertation thesis.
The student defends originality and scientific value of the results presented in the dissertation thesis.