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Sylabus predmetu D1-KVST - Quantum structures (FCE - 2019/2020 - post-graduate studies)

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University: Slovak University of Technology in Bratislava
Faculty: Faculty of Civil Engineering
Course unit code: D1-KVST
Course unit title: Quantum structures
Mode of delivery, planned learning activities and teaching methods:
workshop2 hours weekly / 26 hours per semester of study (on-site method)

Credits allocated: 5
Recommended semester/trimester: Applied Mathematics - doctoral (semi-compulsory), 1. year
Applied Mathematics (in english language) - doctoral (semi-compulsory), 1. year
Level of study: 3.
Prerequisites for registration: none
Assesment methods:
seminar project, exam
Learning outcomes of the course unit:
The aim of the subject is to bring the basic knowledge in the area of modern quantum theory of mathematical structures. It deals with non-compatible events and with their applications. It helps to understand the basic connections between the classical probability theory (all events are compatible) and quantum probability theory (accepting also non-compatible systems of events). More, it deals with the conditional probabilites in the framework of quantum probability theory.
Course contents:
- Orthomodular lattice (OML) as a basic model for non-compatible events.
- Observables (analogy of distribution functions in probability theory) for non-compatible events.
- Compatibility, centre, partitions into direct products, blocks, atoms.
- States and conditional states; asymmetric dependence and independence.
- Connections between the time dependent classical probability theory and the asymmetric distributions on orthomodular lattices.
Recommended or required reading:
CHOVANEC, F. Diferenčné posety a ich grafická reprezentácia. Liptovský Mikuláš : Akadémia ozbrojených síl generála M.R. Štefánika, 2013. 250 p. ISBN 978-80-8040-479-6.
KLEMENT, E P. -- MESIAR, R. -- PAP, E. Triangular Norms. Dordrecht : Kluwer Academic Publishers, 2000. 385 p. ISBN 0-7923-6416-3.

Language of instruction: slovak and english or english
Courses evaluation:
Assessed students in total: 0

Name of lecturer(s): prof. RNDr. Martin Kalina, PhD. (examiner, instructor, lecturer, tutor) - slovak, english
prof. RNDr. Radko Mesiar, DrSc. (person responsible for course)
Last modification: 31. 10. 2017
Supervisor: prof. RNDr. Radko Mesiar, DrSc. and programme supervisor

Last modification made by Ing. Peter Korčák on 10/31/2017.

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