(in Polish) Przedmioty obieralne na studiach drugiego stopnia na kierunku bioinformatyka (course group defined by Faculty of Mathematics, Informatics, and Mechanics)

• Classes - 30 hours
• Lecture - 30 hours

• Classes - 30 hours
• Lecture - 30 hours

This is a fundamental course in functional analysis. The course gives a basic knowledge on Banach and Hilbert spaces and their geometric properties. The next topic of the course concerns linear functionals and operators in these spaces and their properties. The course gives also basic informations on spectra and spectral properties of linear operators. In particular, spectra of compact operators in Hilbert spaces are discussed.

• Lecture - 30 hours

(in Polish) Na wykładach zostaną przedstawione zagadnienia związane z procesem fotosyntezy, widzianym jako ciąg procesów umożliwiających, w oparciu o złożony, hierarchicznie zorganizowany układ strukturalny, wykorzystanie reakcji fotochemicznych. Zostaną omówione fizyczne podstawy procesów fotochemicznych, budowa strukturalna kompleksów białkowo-barwnikowych roślin i ich przestrzenna organizacja w błonach chloroplastów. Omówiona zostanie biogeneza i budowa chloroplastów oraz procesy związane z regulacją fotosyntezy. Szeroko zostaną przedstawione współczesne kierunki badań nad fotosyntezą, w tym modyfikacje tego procesu i zagadnienia sztucznej fotosyntezy.

• Classes - 30 hours
• Lecture - 30 hours

• Classes - 30 hours
• Lecture - 30 hours

(in Polish) Wykład jest kontynuacją wykładu Inżynieria Finansowa. Na wykładzie będą przedstawione wybrane metody wyceny instrumentów opcyjnych na stopę procentową oraz praktyki rynkowe wyceny opcji walutowych. Ćwiczenia będą się koncentrowały na przykładach numerycznych ilustrujących omawiane na wykładzie metody.

• Classes - 30 hours
• Lecture - 30 hours

• Classes - 30 hours
• Lecture - 30 hours

The course aims to introduce into the theory of quantized and

categorified invariants of knots. After explaining the classical Alexander,

Conway, Jones and HOMFLY-PT polynomials, we will quantize them

with the use of representations of quantum groups and the Reshetikhin-

Turaev functor and categorify to the Khovanov-Lee homology. All technicalities will be explained on the spot when needed. The course is based on selected fragments of the literature listed below. The suggestions for further reading will be provided.

• Classes - 60 hours
• Lecture - 30 hours

Contemporary evolutionary biology and ecology can hardly exist without molecular tools. These tools however differ from classic molecular applications. Studies in molecular ecology and evolution are focused on specific research topics, such as sources and mechanisms of the genetic differences between individuals or signatures of selection.

From technical point of view, studies of non-model species usually have to deal with difficult sources of DNA material, low material quantity or poor quality, problems with sample preservation and storage etc.

• Lecture - 30 hours

The number of tourists traveling steadily increases, especially in Europe, more and more people are going on holiday to tropical, subtropical and other countries. This subject is to introduce and deepen the knowledge about human and zoonotic parasites belonging to the "Neglected Tropical Diseases" group, less known exotic diseases that we can meet while going on vacation to various parts of the world. The presented knowledge about the routes of infection and diagnosis of these diseases will allow selection of the appropriate prevention methods and enable safe travels to the tropics.

• Classes - 30 hours
• Monographic lecture - 30 hours

Convex geometry deals mainly with convex sets in Euclidean spaces. During the lectures we shall focus on certain important inequalities in this field, including isoperimetric and concentration inequalities, Brunn-Minkowski type inequalities and Khinchine inequalities.

• Classes - 30 hours
• Lecture - 30 hours

• Classes - 30 hours
• Lecture - 30 hours

The lecture is an introduction to the supervised learning, in other words statistical prediction, focused on modern linear methods and largely (about 2/3) based on "The Elements of Statistical Learning" by Hastie, Tibshirani and Friedman.

• Classes - 20 hours
• Lecture - 70 hours

International Summer School is a 5-day course, providing students with the knowledge and practical skills about plant genome editing by CRISPR/Cas9.

Learning activities: lectures, laboratory exercises, in silico exercises, virtual labs, and the final conference with a discussion of the legislative, economic, and ethical aspects of genome editing by CRISPR/Cas9.

Research tasks:

1. Identification of target genes for the protection of plants of agricultural interest

2. Planning of experiments using genome editing, including molecular biology and bioinformatics

3. Application of genome editing tools to plant-pathogen interactions

4. Analysis of sequences derived from genomic editing events

5. Plant in vitro cultures

6. Phenotyping of plant disease

Students are required to prepare a final report around 2 months after completing the course. The report should be prepared by international groups (around 4 persons). The results of the work will be presented during a remote meeting

• Classes - 30 hours
• Lecture - 30 hours

• Classes - 30 hours
• Lecture - 30 hours

This course presents a survey of more advanced methods of PDE theory: smoothness of solutions of elliptic equations, method of difference quotients, Fredholm theory, elements of Schauder theory and semigroup theory, variational methods.

• Lab - 30 hours
• Lecture - 30 hours

• Lab - 30 hours
• Lecture - 30 hours

The lecture aims to present central issues in modern functional programming in languages such as Haskell, Coq, Idris, especially focusing on usung types for program specification and verification.

• Lab - 70 hours
• Lecture - 20 hours

• Lab - 70 hours
• Lecture - 20 hours

The course focuses on new methods in molecular biology with potential applications in biotechnology. The lecture will introduce the students to the experimental part. The classes are divided into thematic blocks:

1. CRISPR

2. Protein as products

3. Intellectual Property in Biotechnology

The course covers the following list of tasks and topics:

- preparation of constructs for heterologous expression, alternative cloning methods (SLIC, GATEWAY), computer analysis of genes and genomes,

expression and purification of proteins with biotechnological applications,

- The CRISPR genome editing method, the construction of mutants using this method, and discussion of its applicative variants

- Elements of patent law with particular emphasis on biotechnology patents (so-called 'case study').

During the course, special attention will be paid to the student's work (or work in pairs), both in terms of practical and in silico experiments and terms of theoretical knowledge

• Classes - 30 hours
• Lecture - 30 hours

• Classes - 30 hours
• Lecture - 30 hours

This is an introductory course in algebraic geometry. The aim is to introduce students to algebraic varieties and their basic geometric properties. At the end of the course examples of applications of algebraic geometry will be shown.

• Classes - 30 hours
• Lecture - 30 hours

• Classes - 30 hours
• Lecture - 30 hours

Fundamental notions of the category theory, additive and abelian categories. Tensor product in the category of modules. Projective and injective modules, resolvents. Graded groups, chain complexes and their homologies.

Derived functors of Hom and of the tensor product. Presheaves, sheaves and their cohomologies.

Simplicial cohomologies and Cech cohomologies. Coverings and principal bundles; cohomological interpretation.

• Classes - 30 hours
• Lecture - 30 hours

• Classes - 30 hours
• Lecture - 30 hours

Game theory was initiated by von Neumann and Morgenstern as a mathematical theory of rational behaviour. A game comprises description of possible moves and payoffs for each of the players. Typically, each player searches for a strategy maximizing her payoff. The rational behaviour of players is well described by the concept of Nash equilibrium.