UE Scientific programming in Python

Using a scientific programming language (e.g., Python) as a tool for modelling and numerical analysis.

 Outline:

1. Number representation systems and their precision
2. Data in Python
   1. Basic data structures: scalars, strings, lists, dictionaries, sets, tuples
   2. Matrix representations of numbers: the numpy ndarray (vs matrix),pandas data tables
   3. Read and write data according to the data type (CSV, JSON, pickle,. . . )
3. Array operations:
   1. Unitary operators MX0 –> MX1
   2. N-ary operators (MX0, . . . , MXn-1) –> MXn
4. Solving equations
   1. Linear matrix equations with applications to interpolation and regression
   2. Differential equations with applications to interpolation and prediction
5. Probability and statistics in Python
   1. Probability laws: distribution families, random variables, realisations
   2. Statistical tests

Mathematical background on probability and statistics, linear algebra and differential equations

1. https://www.scipy.org/
2. Bashier, E.B.M. (2020). Practical Numerical and Scientific Computing with MATLAB and Python (1st ed.). CRC Press.
3. H. P. Langtangen, A Primer on Scientific Programming with Python. Springer Berlin Heidelberg, 2016