Mathematical Methods and Modelling

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Code Completion Credits Range
16MMM Z 2 0+2
Jaroslav Klusoň (guarantor), Tomáš Urban (guarantor)
Department of Dosimetry and Application of Ionizing Radiation

Application of mathematical methods, modelling and data processing in dosimetry, radiological physics, medicine and experimental physics. Processing, analysis and evaluation of spectra (peak search and fitting, deconvolution), data analysis, statistical processing and visualization (smoothing, numerical differentiation, creation of histograms), modelling (Monte Carlo method) and examples of applications (calculation of the response of detection systems, efficiency and resolution, calculations of the angular energy distributions of dosimetric quantities in radiation fields/beams, measuring methods simulation/design). Demonstration/training of applications of selected codes (Gnuplot, ROOT, MCNP, Vised, Sabrina, Body Builder,SRIM/TRIM, Geant).


Basic courses of matematics and statistics

Basic knovledge of programming and computer literacy

Syllabus of lectures:

1. Introduction (selected concepts from probability theory and mathematical statistics)

2. Application of numerical methods in dosimetry (implementation of computational methods on computer)

3. Monte Carlo method, computational codes for radiation transport simulation

4. Transport of the indirectly ionizing radiation through matter, SRIM code

5. Detection of ionizing radiation (determination of responses and detector response matrices, convolution with resolution function)

6. Spectra evaluation, methods of identification/determination of peak areas and unfolding/deconvolution spectra

7. Application of numerical methods for shielding analysis/design

8. Data Visualization

Syllabus of tutorials:

1. Fundamentals of Unix, filtering and sorting of data, AWK program

2. Computer code ROOT, smoothing, derivation and fitting of data

3. Response of detectors and deconvolution of data, spectrometric data analysis, peak search methods

4. SRIM, Geant and Fluka programs (features, fields of application, demonstrations)

5. Data visualization methods (Root, Gnuplot)

6. Fundamentals of radiation transport simulation

Study Objective:


Gain overview and practical skills in application of the selected mathematical methods for calculations and processing and analysis of data in the fields of dosimetry, spectrometry particle and radiation physics, radiation protection and medicine.


Practical use of mathematical and numerical methods for spectrometric data analysis, deconvolution of spectra, and basis of model calculations using selected SW tools.

Study materials:

Key references:

[1] Lux, I., Koblinger, L.: Monte Carlo Particle Transport Methods- Neutron and Proton Calculations, ISBN 0-8493-6074-9, CRC Press, 1991.

[2] Use of MCNP in Radiation Protection and Dosimetry, Edited by Gualdrini, G., Casalini, L., ENEA, ISBN 88-8286-000-1, Bologna - Italy, May 13-16 1996.

[3] Computer code ROOT, http://root.cern.ch

Recommended references:

[4] Computer code SRIM/TRIM, http://www.srim.org/

Media and tools:

computer lab

computer codes and SW/tools

Further information:
Time-table for winter semester 2020/2021:
Time-table is not available yet
Time-table for summer semester 2020/2021:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2021-03-02
For updated information see http://bilakniha.cvut.cz/en/predmet24361805.html