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PřF:F7270 Math. methods for data anal. - Course Information

## F7270 Mathematical methods for numerical data analysis

**Faculty of Science**

Spring 2020

**Extent and Intensity**- 2/1/0. 3 credit(s) (plus extra credits for completion). Type of Completion: k (colloquium).
**Teacher(s)**- Mgr. Filip Münz, PhD. (lecturer)

prof. Mgr. Dominik Munzar, Dr. (lecturer)

Mgr. Filip Münz, PhD. (seminar tutor) **Guaranteed by**- prof. Mgr. Dominik Munzar, Dr.

Department of Condensed Matter Physics - Physics Section - Faculty of Science

Contact Person: Mgr. Filip Münz, PhD.

Supplier department: Department of Condensed Matter Physics - Physics Section - Faculty of Science **Timetable of Seminar Groups**- F7270/01: No timetable has been entered into IS.
**Prerequisites**- Knowledge of mathematics, physics and experimental physics on the bachelor curriculum level.
**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**- Physics (programme PřF, B-FY)

**Course objectives**- The goal of this course is to explain basic procedures in the probability theory and mathematical statistics, especially in application to experimental data treatment and stating and testing of the hypotheses.
**Learning outcomes**- Student are able upon finishing this course to:

- describe a random variable (RV) with several characteristics;

- give properties of a combination of RVs (average, maximum);

- name several discrete and continuous distributions of RVs, roughly characterize them and bring them into the context of experimental practice;

- specify basic properties of a good statistic estimate;

- use a maximum likelihood method for an estimate of a specific parameter;

- apply a linear model to a chosen problem;

- conduct a hypothesis test of a match between experimental and theoretical distribution **Syllabus**- Probability, random variables. Random vector, statistical dependence. Central limit theorem. Multidimensional normal distribution. Standard probability distributions and their relationships. Statistical estimates, maximum likelihood, least squares. Position of an unknown symmetrical distribution. Linear model for multiple unknowns. Nonlinear model, numerical minimization. Statistical tests, Pearson and Kolmogorov method.

**Literature***Statistical methods in experimental physics*. Edited by Frederick E. James. 2nd ed. Hackensack, N.J.: World Scientific, 2006. xviii, 345. ISBN 9789812705273. info- MARTIN, B. R.
*Statistics for physical sciences : an introduction*. 1st ed. Boston: Academic Press, 2012. x, 302. ISBN 9780123877604. info - HUMLÍČEK, Josef.
*Statistické zpracování výsledků měření*. 1. vyd. Brno: Rektorát UJEP, 1984. 101 s. info - EADIE, W. T.
*Statističeskije metody v eksperimental'noj fizike : Statistical methods in experimental physics (Orig.) : Statistical methods in experimental physics (Orig.)*. Moskva: Atomizdat, 1976. 334 s. info - BARLOW, Roger.
*Statistics : a guide to the use of statistical methods in the physical sciences*. Chichester: John Wiley & Sons, 1989. xv, 204. ISBN 0471922943. info - COWAN, Glen.
*Statistical data analysis*. Oxford: Clarendon Press, 1998. xi, 197 s. ISBN 0-19-850155-2. info - ANDĚL, Jiří.
*Základy matematické statistiky*. 2., opr. vyd. Praha: Matfyzpress, 2007. 358 s. ISBN 9788073780012. info

*recommended literature*- BRANDT, Siegmund.
*Data analysis : statistical and computational methods for scientists and engineers*. Translated by Glen Cowan. 3rd ed. New York: Springer-Verlag, 1998. xxxiv, 652. ISBN 0387984984. info

*not specified***Teaching methods**- lectures, seminars, data analysis as a homework
**Assessment methods**- Final project evaluating computer-generated data: estimates, identification of outliers, testing data distribution, evaluation of indirect measurements, statistical dependence of retrieved parameters.
**Language of instruction**- Czech
**Follow-Up Courses****Further Comments**- Study Materials

The course can also be completed outside the examination period.

The course is taught annually. **Listed among pre-requisites of other courses****Teacher's information**- https://is.muni.cz/auth/el/sci/jaro2020/F7270/index.qwarp

- Enrolment Statistics (recent)

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