Selected Mathematical Methods
| Code | Completion | Credits | Range | Language |
|---|---|---|---|---|
| BIE-VMM | Z,ZK | 4 | 2P+2C | English |
- Course guarantor:
- Tomáš Kalvoda
- Lecturer:
- Marzieh Forough
- Tutor:
- Marzieh Forough
- Supervisor:
- Department of Applied Mathematics
- Synopsis:
-
The lecture begins with an introduction to the analysis of complex functions of a complex variable. Next, we present the Lebesgue integral. We then address Fourier series and their properties. Further, we introduce and study the properties of the Discrete Fourier Transform (DFT) and its fast implementation (FFT). We discuss the wavelet transform. We examine the linear programming problem in more detail and its solution using the Simplex algorithm. Each topic is demonstrated with interesting examples.
- Requirements:
-
The fundamental knowledge of mathematical analysis and linear algerbra is required as they are given in BI-MA1, BI-MA2 and BI-LA1.
- Syllabus of lectures:
-
1. Complex numbers, complex functions of a complex variable, exponential function.
2. Properties of holomorphic functions.
3. The Lebesgue integral.
4. Fourier series.
5. Finite-dimensional Hilbert spaces, unitary matrices.
6. Discrete Fourier Transform (DFT) and Fast Fourier Transform (FFT).
7. Wavelet transform.
8. Linear programming (introduction, formulation).
9. Linear programming (standard problem).
10. The SIMPLEX algorithm.
11. Examples and applications of linear programming.
12. Reserve
- Syllabus of tutorials:
-
1. Complex numbers, complex functions of a complex variable, exponential function.
2. Properties of holomorphic functions.
3. The Lebesgue integral.
4. Fourier series.
5. Finite-dimensional Hilbert spaces, unitary matrices.
6. Discrete Fourier Transform (DFT) and Fast Fourier Transform (FFT).
7. Wavelet transform.
8. Linear programming (introduction, formulation).
9. Linear programming (standard problem).
10. The SIMPLEX algorithm.
11. Examples and applications of linear programming.
12. Reserve
- Study Objective:
-
The goal of the course is to improve student's mathematical skills and to present classical mathematical methods with applications in IT.
- Study materials:
-
Howard Karloff: Linear Programming.
O. Julius Smith: Mathematics of the Discrete Fourier Transform with Audio Applications.
- Note:
- Further information:
- https://courses.fit.cvut.cz/BIE-VMM/
- Time-table for winter semester 2024/2025:
- Time-table is not available yet
- Time-table for summer semester 2024/2025:
- Time-table is not available yet
- The course is a part of the following study plans:
-
- Bachelor Specialization Computer Engineering, 2021 (elective course)
- Bachelor Specialization, Information Security, 2021 (elective course)
- Bachelor Specialization, Software Engineering, 2021 (elective course)
- Bachelor Specialization, Computer Science, 2021 (elective course)
- Bachelor Specialization, Computer Networks and Internet, 2021 (elective course)
- Bachelor Specialization Computer Systems and Virtualization, 2021 (elective course)
- Study plan for Ukrainian refugees (elective course)
- Bachelor Specialization, Computer Engineering, Version 2024 (elective course)