PMVPPM Selected topics in advanced mathematics

Faculty of Economics and Administration
Autumn 2008
Extent and Intensity
2/1. 4 credit(s). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Vítězslav Veselý, CSc. (lecturer)
doc. RNDr. Vítězslav Veselý, CSc. (seminar tutor)
Guaranteed by
doc. RNDr. Vítězslav Veselý, CSc.
Department of Applied Mathematics and Computer Science – Faculty of Economics and Administration
Contact Person: Lenka Hráčková
Timetable
Fri 9:20–11:00 S310
  • Timetable of Seminar Groups:
PMVPPM/1: Fri 11:05–11:50 S310, V. Veselý
Prerequisites
The course is intended for the 1-st year MSc students enrolled in the study program "Mathematical and statistical methods in economy".
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course offers selected topics of higher mathematics not being commonly lectured on BSc level but required in subsequent MSc courses of this study program. It follows the three-term BSc course "Introduction to Matematics I-III". After having passed the course the students get basic theroetical knowledge and practical computational skills in the fields of linear regression, abstract Lebesgue integration, basics of probability theory, functional analysis and summation of power and Laurent series in the domain of complex numbers with special emphasis on Fourier series expansions. The contents may be modified and/or updated according to current needs.
Syllabus
  • The course is divided into seven parts with six of them comprising standard topics and one involving optional specific topics.
  • 1. Linear regression analysis
  • 2. Abstract Lebesgue integration: measurable sets, measure, measurable functions, construction of abstract Lebesgue integral and its basic properties confronted with the Riemann integral
  • 3. Introduction to probability theory: probability space, conditional probability, random variables and random vectors, their distribution, cumulative distribution function (CDF), probability density function (PDF) for both unconditional and conditional distribution, stochastic independence
  • 4. Basics of functional analysis: common functional spaces, orthogonal projection operator and its applications
  • 5. Summation of power and Laurent series in the complex domain: region of convergence, classification of singularities by the specific form of the expansion, linear convolution in relation to products of series
  • 6. Fourier analysis of periodic functions: Fourier series expansions, conditions of convergence, Parseval identity, discrete Fourier transform, applications
  • 7. Additional and optional specific topics selected by the lecturer to comply with current needs of subsequent courses.
Literature
  • ANDĚL, J. Základy matematické statistiky. Praha: MFF UK, 2005. info
  • KOLMOGOROV, Andrej Nikolajevič and Sergej Vasil‘jevič FOMIN. Základy teorie funkcí a funkcionální analýzy. Translated by Vladimír Doležal - Zdeněk Tichý. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1975, 581 s. info
  • RUDIN, Walter. Analýza v reálném a komplexním oboru. 1. vyd. Praha: Academia, 1977, 463 s. URL info
  • DEBNATH, Lokenath and Piotr MIKUSIŃSKI. Introduction to Hilbert spaces with applications. 2nd ed. San Diego: Academic Press, 1998, xviii, 551. ISBN 0122084365. info
  • KUFNER, Alois and Jan KADLEC. Fourierovy řady (Fourier series). Praha: Academia, 1969. info
  • ČÍŽEK, Václav. Diskretní Fourierova transformace a její použití. 1. vyd. Praha: SNTL - Nakladatelství technické literatury, 1981, 160 s. URL info
Assessment methods
The course has a form of a lecture (2 lessons) and a seminar (1 lesson). The course is concluded by the oral exam. In the seminar the students treat and present selected problems from the lecture in more detail. Students' performance at the seminar is incorporated into the final grading.
Language of instruction
Czech
Follow-Up Courses
Further Comments
Study Materials
The course is taught annually.
The course is also listed under the following terms Autumn 2007.
  • Enrolment Statistics (recent)
  • Permalink: https://is.muni.cz/course/econ/autumn2008/PMVPPM