Single-Course Engelsk 5 ECTS

Computer-based Introduction to Data Analysis for Physics, Nano-, and Health Technology

Overall Course Objectives

At the end of this course, participants should be able to: identify which elementary kinds of random behavior are likely to be encountered in a given situation and know how to decide if it is the case and to use it in data analysis and modeling of stochastic processes; perform basic estimation and curve-fitting when data is subject to different types of stochastic influences; and validate their results by performing Monte Carlo simulations of elementary stochastic behavior of various kinds.

See course description in Danish

explain properties of binomial-, Poisson-, Gauss-, exponential-, Erlang-, Gamma-, and Cauchy-distribution.
explain the principle of and apply maximum likelihood estimation as well as maximum likelihood-estimate parameter values for said distributions from given data.
explain the contents of the Central Limit Theorem.
computer-simulate random walks and simple Brownian motion, explain their mathematical nature, and model mathematically Brownian motion in simple force fields.
perform a power spectrum analysis of trapped and persistent Brownian motion and relate it to optical tweezers.
explain and apply Fick’s theorems, the diffusion equation, and the convection-diffusion equation.
analyze data-analytic and modeling situations to identify stochastic elements and recognize where said probability distributions occur.
evaluate whether a probability distribution or model is in statistical accordance with given data.
fit curves to uncorrelated data with maximum likelihood estimation and its special case of weighted least squares method. Identify situations where these methods apply or not.
identify simple correlations in a time series, explain their consequences for its analysis, incl. how to then obtain correct errors on averages over a stationary time series.
identify data-analytical and/or modeling situations which falls outside the scope of this course.
communicate problems and solutions to peers.

This course caters to students in nano-science, physics, biophysics, health tech, chemistry, and well beyond. Its substance is core knowledge on which the understanding of all stochastic phenomena is based, including all experimental data analysis. Examples used for illustrations are important cases chosen from physics, bio-physics, and nano-science, e.g., optical tweezers and diffusion in nanochannels. But even the examples are universal, as far as their math is concerned, and occur with just a change of units in other contexts. It is a hands-on course. Math is introduced when students in computer simulations observe phenomena that can be described mathematically and to develop data-analytic tools. The data-analytical methods will be applied to real and/or synthetic data in mini-projects throughout the course. The programming language used is MatLab but Python may be used by the student with a little extra effort. Assistance with MatLab/Python programming is offered, but some routine with such programming languages and mathematics is required.

Mathematics and ability to calculate with pencil, paper, and computer corresponding to the level of DTU’s MSc programme in Engineering Physics.
Skills in basic MATLAB/Python programming.

Weekly lectures, theoretical exercises, independent study, computer exercises, small projects.