Main page | Study Branches/Specializations | Groups of Courses | All Courses | Roles                Instructions

A course is the basic teaching unit, it's design as a medium for a student to acquire comprehensive knowledge and skills indispensable in the given field. A course guarantor is responsible for the factual content of the course.
For each course, there is a department responsible for the course organisation. A person responsible for timetabling for a given department sets a time schedule of teaching and for each class, s/he assigns an instructor and/or an examiner.
Expected time consumption of the course is expressed by a course attribute extent of teaching. For example, extent = 2 +2 indicates two teaching hours of lectures and two teaching hours of seminar (lab) per week.
At the end of each semester, the course instructor has to evaluate the extent to which a student has acquired the expected knowledge and skills. The type of this evaluation is indicated by the attribute completion. So, a course can be completed by just an assessment ('pouze zápočet'), by a graded assessment ('klasifikovaný zápočet'), or by just an examination ('pouze zkouška') or by an assessment and examination ('zápočet a zkouška') .
The difficulty of a given course is evaluated by the amount of ECTS credits.
The course is in session (cf. teaching is going on) during a semester. Each course is offered either in the winter ('zimní') or summer ('letní') semester of an academic year. Exceptionally, a course might be offered in both semesters.
The subject matter of a course is described in various texts.

BI-VMM Selected Mathematical Methods Extent of teaching: 2P+2C
Instructor: Kalvoda T. Completion: Z,ZK
Department: 18105 Credits: 4 Semester: L

Annotation:
We start reviewing geometric properties of linear spaces with inner product. Next, we introduce and analyze the discrete Fourier transform (DFT) and its fast implementation (FFT). Further we deal with differential calculus of functions involving multiple variables. We present methods for the localization of extreme values of functions. For this purposes, we study normed linear spaces and quadratic forms. In addition, we introduce the least square method. The last part of the course is devoted to optimization and duality. The linear programming and the Simplex method is analyzed in more detail.

Lecture syllabus:
1. Complex numbers, complex function of complex variable, exponential function.
2. Fourier series.
3. Hilbert spaces of finite dimension, unitary matrices.
4. Discrete Fourier transformation (DFT) and Fast Fourier transform (FFT).
5. Basic objects from theory of multivariate functions.
6. (Constrained) extrema of multivariate functions.
7. General optimization problem.
8. Weak and strong duality.
9. Linear programming (introduction, formulation).
10. Linear programming (problem in standard form).
11. SIMPLEX algorithm.
12. Examples and applications of Linear programming.

Seminar syllabus:
1. Complex numbers, complex function of complex variable, exponential function.
2. Fourier series.
3. Hilbert spaces of finite dimension, unitary matrices.
4. Discrete Fourier transformation (DFT) and Fast Fourier transform (FFT).
5. Basic objects from theory of multivariate functions.
6. (Constrained) extrema of multivariate functions.
7. General optimization problem.
8. Weak and strong duality.
9. Linear programming (introduction, formulation).
10. Linear programming (problem in standard form).
11. SIMPLEX algorithm.
12. Examples and applications of Linear programming.

Literature:
Howard Karloff: Linear Programming.
O. Julius Smith: Mathematics of the Discrete Fourier Transform with Audio Applications.
J. Kopáček: Matematika nejen pro fyziky II (lecture notes in czech).

Requirements:
The fundamental knowledge of mathematical analysis and linear algerbra is required as they are given in BI-ZMA and BI-LIN.

Informace o předmětu a výukové materiály naleznete na https://courses.fit.cvut.cz/BI-VMM/

The course is also part of the following Study plans:
Study Plan Study Branch/Specialization Role Recommended semester
NI-PB.2020 Computer Security V Není
NI-ZI.2020 Knowledge Engineering V Není
NI-SPOL.2020 Unspecified Branch/Specialisation of Study V Není
NI-TI.2020 Computer Science V Není
NI-TI.2023 Computer Science V Není
NI-NPVS.2020 Design and Programming of Embedded Systems V Není
NI-PSS.2020 Computer Systems and Networks V Není
NI-MI.2020 Managerial Informatics V Není
NI-SI.2020 Software Engineering (in Czech) V Není
NI-SP.2020 System Programming V Není
NI-WI.2020 Web Engineering V Není
NI-SP.2023 System Programming V Není
BI-SPOL.2015 Unspecified Branch/Specialisation of Study V Není
BI-WSI-PG.2015 Web and Software Engineering V Není
BI-WSI-WI.2015 Web and Software Engineering V Není
BI-WSI-SI.2015 Web and Software Engineering V Není
BI-ISM.2015 Information Systems and Management V Není
BI-ZI.2018 Knowledge Engineering V Není
BI-PI.2015 Computer engineering V Není
BI-TI.2015 Computer Science V Není
BI-BIT.2015 Computer Security and Information technology V Není
BI-SPOL.21 Unspecified Branch/Specialisation of Study V Není
BI-PI.21 Computer Engineering 2021 (in Czech) V Není
BI-PG.21 Computer Graphics 2021 (in Czech) V Není
BI-MI.21 Business Informatics 2021 (In Czech) V Není
BI-IB.21 Information Security 2021 (in Czech) V Není
BI-PS.21 Computer Networks and Internet 2021 (in Czech) V Není
BI-PV.21 Computer Systems and Virtualization 2021 (in Czech) V Není
BI-SI.21 Software Engineering 2021 (in Czech) V Není
BI-TI.21 Computer Science 2021 (in Czech) V Není
BI-UI.21 Artificial Intelligence 2021 (in Czech) V Není
BI-WI.21 Web Engineering 2021 (in Czech) V Není
NI-TI.2018 Computer Science V Není
BI-BIT.2015 Computer Security and Information technology V 4


Page updated 28. 3. 2024, semester: Z/2023-4, L/2019-20, L/2022-3, Z/2019-20, Z/2022-3, L/2020-1, L/2023-4, Z/2020-1, Z,L/2021-2, Send comments to the content presented here to Administrator of study plans Design and implementation: J. Novák, I. Halaška