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Elective courses for 2nd stage studies in Mathematics (course group defined by Faculty of Mathematics, Informatics, and Mechanics)

Faculty: Faculty of Mathematics, Informatics, and Mechanics Courses displayed below are part of group defined by this faculty, but this faculty is not necessarily the one that organizes these courses. Read Help for more information on this subject.
Course group: Elective courses for 2nd stage studies in Mathematics
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2023Z - Winter semester 2023/24
2023L - Summer semester 2023/24
(there could be semester, trimester or one-year classes)
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2023Z 2023L
1000-1M23TMW
n/a
Classes
Summer semester 2023/24
  • Classes - 30 hours
  • Lecture - 30 hours
Groups

Brief description

Geometric measure theory is the study of geometric objects using the methods of measure theory. A manifold embedded in Rn can be associated a Hausdorff measure restricted to a given manifold or to a tangent bundle of that manifold. Considering a sequence of such measures and passing to the weak limit we get more general objects, e.g., varifolds or currents. We study functionals defined on such objects and their critical points, i.e. stationary varifolds (generalization of minimal surfaces). The lecture aims to present the current knowledge in this field to the extent that allows independent research. We will start with the classic area and coareavformulas and introduce the concept of rectifiability. Next, we shall discuss the basic theory of varifolds. Finally, we will focus on the pivotal concept of ellipticity of functionals, which has not been sufficiently explored so far.

Course page
1000-1M23GK
n/a
Classes
Winter semester 2023/24
  • Classes - 30 hours
  • Monographic lecture - 30 hours
Groups

Brief description

The course is dedicated to students interested in functional analysis in a broad sense, mathematical formalism of quantum mechanics or modern, yet elementary, mathematics.

Quantum graphs arise in quantum information and are natural counterparts of graphs. We will start with a quick introduction to quantum information theory, necessary to motivate the notion of a quantum graph. Afterwards we will introduce three equivalent definitions of quantum graphs, we will explain how to translate between them and will illustrate how each of them is useful in its own way. We will show how to construct plenty of examples of quantum graphs. In the last part of the course we will study properties of random quantum graphs: we will prove that a typical quantum graph does not admit any nontrivial symmetries.

Course page
1000-1M23ITM
n/a
Classes
Summer semester 2023/24
  • Classes - 30 hours
  • Lecture - 30 hours
Groups

Brief description

The lecture will be devoted to set-theoretic properties of ideals of Lebesgue measure zero sets and Baire first category sets, as well as other related classes of small subsets of the real line.

Course page
1000-1M22IF2
n/a
Classes
Summer semester 2023/24
  • Classes - 30 hours
  • Lecture - 30 hours
Groups

Brief description

(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.

Course page
1000-1M20KNW
n/a
Classes
Summer semester 2023/24
  • Classes - 30 hours
  • Lecture - 30 hours
Groups

Brief description

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.

Course page
1000-1M23LNT
n/a
Classes
Summer semester 2023/24
  • Classes - 30 hours
  • Lecture - 30 hours
Groups

Brief description
No brief description found, go to course home page to get more information.
Course page
1000-1M22NUM
n/a
Classes
Summer semester 2023/24
  • Lab - 30 hours
  • Lecture - 30 hours
Groups

Brief description

(in Polish) Przyjrzymy się specyfice wybranych zadań obliczeniowych spotykanych w zagadnieniach analizy danych oraz uczenia maszynowego oraz własnościom algorytmów używanych do ich rozwiązywania.

Course page
1000-1M17NGW
n/a
Classes
Summer semester 2023/24
  • Classes - 30 hours
  • Monographic lecture - 30 hours
Groups

Brief description

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.

Course page
1000-1M18SUM
n/a
Classes
Winter semester 2023/24
  • Classes - 30 hours
  • Lecture - 30 hours
Groups

Brief description

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.

Course page
1000-1M15TR2
n/a
Classes
Summer semester 2023/24
  • Classes - 30 hours
  • Lecture - 30 hours
Groups

Brief description
No brief description found, go to course home page to get more information.
Course page
1000-1M21WZU
n/a
Classes
Winter semester 2023/24
  • Classes - 30 hours
  • Monographic lecture - 30 hours
Groups

Brief description
No brief description found, go to course home page to get more information.
Course page
1000-2M23STI n/a
Classes
Summer semester 2023/24
  • Lecture - 30 hours
Groups

Brief description
No brief description found, go to course home page to get more information.
Course page
1000-1M18ZRR n/a
Classes
Summer semester 2023/24
  • Classes - 30 hours
  • Lecture - 30 hours
Groups

Brief description

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.

Course page
1000-1M00WA n/a
Classes
Winter semester 2023/24
  • Classes - 30 hours
  • Lecture - 30 hours
Groups

Brief description

The lecture is addressed to students of mathematics as well as to students of computer science interested in theoretical or applied aspects of approximate reasoning. Issues and problems discussed in the lecture are considered by many famous mathematicians and computer scientists to be among central problems of the current century, as important as deciphering the genetic code was for the second half of the 20th century. We will discuss problems important for making progress in many projects, in particular, interdisciplinary projects, in which mathematicians and computer scientists work together with specialists from other areas such as neuroscience, bioinformatics, psychology, economy, or complex adaptive systems. Different theoretical and applied aspects of methods of concept approximation from experimental data and domain knowledge will be covered.

Course page
1000-719DAV n/a
Classes
Summer semester 2023/24
  • Lab - 30 hours
  • Lecture - 30 hours
Groups

Brief description

The aim of the course is to introduce the techniques of data analysis and visualization to the students.

Course page
1000-2M23ZWL n/a
Classes
Summer semester 2023/24
  • Classes - 30 hours
  • Lecture - 30 hours
Groups

Brief description

The lecture presents the state-of-the art knowledge concerning the way a dictionary of symbols one can construct statements from (i.e. quantifiers, connectives, relations and function symbols) impacts the complexity of the satisfiability and provability problems.

Course page
1000-1M15DM n/a
Classes
Summer semester 2023/24
  • Classes - 30 hours
  • Lecture - 30 hours
Groups

Brief description

(in Polish) Celem zajęć jest zapoznanie przyszłych nauczycieli matematyki z uwarunkowaniami zawodu nauczyciela.

Course page
1000-1M07ET n/a
Classes
Winter semester 2023/24
  • Classes - 30 hours
  • Monographic lecture - 30 hours
Groups

Brief description

Basic notions and theorems of Category Theory will be discussed. Some specific applications will be covered in the last part of the course. I intend to discuss various aspects of Grothendieck topoi.

Course page
1000-1M23EK n/a
Classes
Winter semester 2023/24
  • Classes - 30 hours
  • Monographic lecture - 30 hours
Groups

Brief description

"Equivariant Cohomology in Algebraic Geometry"

Borel equivariant cohomology theory is introduced topologically and through differential methods. The theory is applied to classical objects of algebraic geometry, such as flag varieties and Grassmannians. Properties of projective manifolds are presented. Applications are based on equivariant formality and localization theorem for torus action. Equivariant Schubert calculus is discussed.

Course page
1000-1M10AF n/a
Classes
Winter semester 2023/24
  • Classes - 30 hours
  • Lecture - 30 hours
Groups

Brief description

I would like to present a part of the Fourier analysis appearing currently in the applied mathematics.

The main point will be the Paley-Littlewood decomposition, defining structure of functions. This point of view in a natural way introduces us Besov B^s_{p,q} and Triebel F^s_{p,q} function spaces -- being a fractional generalization of the classical Sobolev spaces. To understand the properties of this approach we recall the theory of Fourier multipliers -- the Marcinkiewicz theorem, which extends the elementary features of the L_2- on L_p-spaces. This part of the theory can be relatively easily extended on the nonlinear problems. We introduce the paraproducts to control the multiplication beyond the classical point of view. We plan to consider applications to concrete problems from PDEs, too.

Course page
1000-1M08MG n/a
Classes
Summer semester 2023/24
  • Classes - 30 hours
  • Lecture - 30 hours
Groups

Brief description

The lecture of geometric modelling is devoted to curves and surfaces in Bezier and B-spline representations (including NURBS), commonly used in computer graphics and in CAD software packages.

The course will be given in Polish, if no non-polish speaking students register for it.

Course page
1000-1M14GM3 n/a
Classes
Winter semester 2023/24
  • Classes - 30 hours
  • Lecture - 30 hours
Groups

Brief description

(in Polish) Geometria rzutowa: ujęcie od strony geometrycznej. Płaszczyzna rzutowa (rzeczywista), przekształcenia rzutowe prostych, pęków, stożkowych, pęków stycznych do stożkowych. Twierdzenia Desarguesa, Pappusa, Pascala, Brianchona. Dualność: biegun i biegunowa względem okręgu i stożkowych. Sprzężenie biegunowe. Inwolucje rzutowe, twierdzenia inwolucyjne. Pęki okręgów i stożkowych jako generatory inwolucji. Twierdzenie Ponceleta. Stożkowe w ujęciu rzutowym, twierdzenia Steinera i Braikenridge'a-Maclaurina. Rzutowe określenie ogniska i kierownicy stożkowych. Punkty urojone przecięcia prostej ze stożkową w ujęciu czysto geometrycznym.

Course page
1000-1M10AH2 n/a
Classes
Winter semester 2023/24
  • Classes - 30 hours
  • Lecture - 30 hours
Groups

Brief description

The lecture 'Harmonic Analysis 2' is planned as the continuation of 'Harmonic analysis', but passing the aforementioned course is not necessary.

Course page
1000-1M19RHG n/a
Classes
Winter semester 2023/24
  • Classes - 30 hours
  • Lecture - 30 hours
Groups

Brief description

We shall consider hydrodynamics equations – equations of Navier-Stokes, Boussinesq and magnetohydrodynamics. We are interested in the analysis of solutions of these equations in the context of problems appearing in geophysics. Lectures are accessible for students of mathematics and physics.

Course page
1000-1M19WDK n/a
Classes
Winter semester 2023/24
  • Classes - 30 hours
  • Monographic lecture - 30 hours
Groups

Brief description

The course will cover several basic topics studied in combinatorics. This includes classical counting techniques and combinatorial structures, combinatorics of points and convex sets in R^n, extremal combinatorics, the probabilistic method and its applications to graph theory and number theory, elements of graph theory, algebraic method, and analysis on the discrete cube. We shall focus on interactions between different fields of mathematics. In particular, we shall show how various probabilistic, analytic and algebraic methods can be used to study combinatorial objects.

Course page
1000-1M09WNN n/a
Classes
Winter semester 2023/24
  • Classes - 30 hours
  • Lecture - 30 hours
Groups

Brief description

The lecture is an introduction to a relatively new interdisciplinary field called "Computational Neuroscience" or "Neuroinformatics". The purpose of this field is to formulate realistic mathematical models or algorithms describing the ways in which the nervous system (brain) process information and

generally how it operates. This field is dynamically developing in USA and in some European centers (German, France), and it attracts people with backgrounds in physics, mathematics, and computer science. The lecture will be accessible to 3rd year students, because it does not require the knowledge of advanced mathematical theories. Information gathered during the lecture will essentially suffice to read original scientific papers, and maybe even to start your own investigations (e.g. under my direction).

Course page
1000-1M23MAM n/a
Classes
Summer semester 2023/24
  • Monographic lecture - 30 hours
Groups

Brief description

The lecture introduces participants to the theory of agent models based on ordinary differential equations and their discretization. These systems naturally arise in the theory of collective behavior, such as the formation of animal herds, schools of fish, or opinions in various groups. During the analysis, we will introduce concepts from machine learning in order to obtain desired models. The lecture will be held in cooperation with Dr. Jacek Cyranka from the Institute of Computer Science and Dr. Janek Peszek from the Institute of Applied Mathematics and Mechanics.

Course page
1000-1M22MIK n/a
Classes
Summer semester 2023/24
  • Classes - 30 hours
  • Lecture - 30 hours
Groups

Brief description
No brief description found, go to course home page to get more information.
Course page
1000-1M23KMO n/a
Classes
Summer semester 2023/24
  • Classes - 30 hours
  • Lecture - 30 hours
Groups

Brief description

This course is an introduction to abstract homotopy theory within the framework of model categories. The central concepts are weak factorization systems, model categories, Quillen functors and Quillen equivalences. The purpose of the lecture is to develop the theory of homotopy invariance inside model categories and methods of comparison between various homotopy theories and to discuss applications in algebraic topology and homological algebra.

Course page
1000-1M23OTE n/a
Classes
Winter semester 2023/24
  • Classes - 30 hours
  • Lecture - 30 hours
Groups

Brief description

The lecture aims to familiarize participants with the theory of optimal transport, in particular by deriving Wasserstein metrics. Finally, we will introduce the notion of a gradient flow in with respect to the Wasserstein metric and notice how many physical phenomena can be treated as gradient flows. If time permits, we'll finally talk about the mean-field limit for the Vlasov equation.

Course page
Krakowskie Przedmieście 26/28
00-927 Warszawa
tel: +48 22 55 20 000 https://uw.edu.pl/
contact accessibility statement USOSweb 7.0.1.0-2 (2024-02-19)