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CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2024/2025
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Welcome page > Faculty of Information Technology > Department of Applied Mathematics > Selected Mathematical Methods

Selected Mathematical Methods

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Code Completion Credits Range Language
BI-VMM Z,ZK 4 2P+2C Czech
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-MA1/2, BI-DML and BI-LA1/2.

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.

J.Kopáček: Matematika nejen pro fyziky II (lecture notes in czech).

Note:
Further information:
https://courses.fit.cvut.cz/BI-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:
Data valid to 2024-11-21
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