The
main goal of the course given by **prof. UAM dr hab. Tomasz Górecki, dr Paweł Mleczko** and **dr Bartosz Naskręcki** is to teach the students a few programming tools which
will allow them to symbolically solve mathematical problems and to enhance
their presentation of the mathematical concepts. We will with the free software
based on Python such as SageMath or SymPy. During sessions we will focus on
practical implementation of the problems and on the presentation of solutions
in the human-friendly form. See below.

Scientific research methodology

*(45
hours course for Ph.D. students from Doctoral School)*

**Course
teachers:**

- prof. UAM dr hab. Tomasz Górecki (Statistical methods)
- dr Paweł Mleczko (LaTeX)
- dr Bartosz Naskręcki (SageMath)

**Time
and place:**
Thursdays, 10:00 – 11:30 and 11:45 –
13:15, room D-2

**Evaluation:** To pass
the course students will prepare a project that combines the knowledge of all
modules included in the course.

**Statistical methods**

Prof. UAM dr hab. Tomasz Górecki:

E-mail: tomasz.gorecki@amu.edu.pl

Office hours:Wednesday 10.00 – 11.00, Thursday 9.00 – 10.00

**Topics:**

- Introduction to R language (dplyr library)
- Simple data plots: scatterplot, boxplot and (ggplot2 library)
- Descriptive statistics: mean, median, mode, variance, standard deviation, standard error
- Statistical tests – introduction
- Goodness of fit tests: exact test, test chi2 and test G
- Comparison of two populations: – t test for independent and dependent samples. Wilcoxon test
- Assumptions in statistical tests: normality, homoscedasticity of variance – Box-Cox method
- Comparison of multiple samples – one-way and multiway analysis of variance (ANOVA). Kruskal-Wallis test and Friedman test. Post-hoc comparison
- Independence tests.
- Pearson and Spearman coefficient of correlation.
- Simple regression. Multiple regression

**Literature:**

- Biecek, P. (2016). Odkrywać! Ujawniać! Objaśniać!, Wydawnictwo UW.
- Biecek, P. (2017). Przewodnik po pakiecie R, GiS.
- Crawley, M.J. (2012), The R Book, Wiley.
- Gągolewski, M. (2014). Programowanie w języku R, PWN.
- Górecki, T. (2011). Podstawy statystyki z przykładami w R, BTC.
- James, G., Witten, D., Hastie, T., Tibshirani, R. (2017). An Introduction to Statistical Learning with Applications in R. Springer.
- Koronacki, J., Mielniczuk, J. (2009). Statystyka dla studentów kierunków technicznych i przyrodniczych, WNT.
- Zieliński, R. (1990). Siedem wykładów wprowadzających do statystyki matematycznej, PWN.

**Gains:**

Ph. D. student is supposed to gain knowledge in selected statistical methods. In particular, the following topics will be elaborated:

- R language – basics of programming and visualization.
- Main descriptive statistics.
- Basics of statistical tests and estimation.
- Main assumptions in parametric tests.
- Tests to compare two or more means.
- Measuring and testing dependency
- Analysis of correlation and regression.

**LaTeX**

Dr Paweł Mleczko:

E-mail: pml@amu.edu.pl

Office hours: Tuesday 12.00 – 13.00

The part connected to LaTeX will contain the advanced course with the special aim on mathematical packages and all kind of drawings, plots etc.

**The
preliminary schedule contains workshops on**

- Mathematical packages (mathtools package),
- Tabular kind environments (booktabs and siunitx packages),
- Advanced fonts management (fontspec and mathspec packages),
- Drawings, diagrams, and graphs (tikz and pgfplots packages),
- Importing/exporting data from/to external files.

**SageMath**

dr Bartosz Naskręcki

E-mail: bartnas@amu.edu.pl

Office hours:

**Topics:**

- Introduction to Python programming language
- Jupyter notebooks and introduction to SageMath
- Implementation of basic loop structures, function declarations
- Time analysis and auxiliary functions
- Plotting: 2D, 3D plots and other types of plots
- Interactive modules
- Symbolic systems of equations
- Applications to linear algebra
- Applications to number theory
- Applications to analysis
- Graph theory and combinatorics

**Literature:**

- Python manual (www.python.org)
- SageMath manual (www.sagemath.org)
- SymPy manual (www.sympy.org)
- Donald Knuth, The art of programming
- Martin H. Weissman, An illustrated theory of numbers

**Gains:**

The main goal of the course is to teach the students a few programming tools which will allow them to symbolically solve mathematical problems and to enhance their presentation of the mathematical concepts. We will with the free software based on Python such as SageMath or SymPy. During sessions we will focus on practical implementation of the problems and on the presentation of solutions in the human-friendly form.

Informację wprowadził/a: **Marek Nowak**

© Faculty of Physics UAM, ul. Uniwersytetu Poznańskiego 2, 61-614 Poznań, phone +48 61 829-5202 lub 5152, 5150, 5154, fax +48 61 829-5155, e-mail: fizyka@amu.edu.pl