Proseminars for Mathematics (course group defined by Faculty of Mathematics, Informatics, and Mechanics)
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2023 - Academic year 2023/24 2024 - Academic year 2024/25 (there could be semester, trimester or one-year classes) |
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| 2023 | 2024 | |||||||
| 1000-1L22AMUD |
 
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Classes
Academic year 2023/24
Groups
Brief description
(in Polish) Celem proseminarium jest: 1) wprowadzenie w wybrane zagadnienia analizy matematycznej, które nie były omawiane podczas kursowego wykładu, 2) wprowadzenie w podstawowe zagadnienia układów dynamicznych i teorii ergodycznej. |
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| 1000-1L23MFU |
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Classes
Academic year 2023/24
Groups
Brief description
No brief description found, go to course home page to get more information.
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| 1000-1L20PTG |
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Classes
Academic year 2023/24
Groups
Brief description
(in Polish) Celem proseminarium jest zapoznanie studentów z nowoczesnymi dziedzinami szeroko rozumianej topologii i geometrii. Seminarium będzie podzielone na dwa nurty: pierwszy dotyczący geometrycznej teorii grup, drugi dotyczący różnych aspektów topologii rozmaitości. |
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| 1000-1L24UM | n/a |
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Classes
Academic year 2024/25
Groups
Brief description
(in Polish) Proseminarium będzie poświęcone głębokim sieciom neuronowym. Głównymi obiektami badań w tej dziedzinie są: sieć, funkcja straty oraz metoda optymalizacji. Sieć to funkcja wektorowa będąca złożeniem wielu prostszych przekształceń, czyli warstw – liczba warstw to głębokość sieci. Wartość sieci zależy od wektora argumentów oraz dodatkowo od wektora parametrów. Nieujemna funkcja straty określa błąd dopasowania parametrów sieci do danych uczących. Argumentami funkcji straty są parametry sieci, a parametrami dane uczące. Z kolei metoda optymalizacji to algorytm służący do poszukiwania lokalnego minimum funkcji straty uśrednionej na danych. Minimalizację średniej funkcji straty nazywa się “uczeniem” lub “trenowaniem” sieci. |
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| 1000-1L12BTG |
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Classes
Academic year 2023/24
Groups
Brief description
Mathematical modelling of various pehnomena originating from biology or social sciences. |
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| 1000-1L00SD |
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Classes
Academic year 2023/24
Groups
Brief description
An introduction to the topic of automatic decision support, related to various domains in mathematics as well as to advanced methods of computer-based approximative solutions of complex problems. |
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| 1000-1L00RR |
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Classes
Academic year 2023/24
Groups
Brief description
This seminar is addressed to students interested in applications of mathematical methods to describe a wide diversity of phenomena in physics, biology, chemistry, and medicine. |
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| 1000-1L03GP |
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Classes
Academic year 2023/24
Groups
Brief description
This seminar extends the standard course in Algebra I. Discussion of various classes of groups and rings, their constructions and structural theorems. Applications of groups and rings to number theory (diofantine equations), to geometry (e.g., isometry groups of polyhedra) and to combinatorics (group actions vs. double counting). |
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| 1000-1L09MN |
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Classes
Academic year 2023/24
Groups
Brief description
Numerical methods for solving certain problems in applied sciences. |
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| 1000-1L00RP |
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Classes
Academic year 2023/24
Groups
Brief description
Extensions of the standard courses in probability. Topics usually include the Laplace transform, generating functions, and applications of probability theory to real-life problems and to other branches of mathematics. |
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| 1000-1L13MSB |
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Classes
Academic year 2023/24
Groups
Brief description
The subject of the seminar will be: (a) modeling of information processing in biological neural networks, (b) modeling the formation of clusters (swarms) in the systems of interacting individuals (birds, fish, players in evolution games with migration). It will be done using the basic tools of stochastic analysis and the elements of information theory, such as: Markov chains, Birth and Death processes, Fokker-Planck equation, the concepts of entropy and mutual information, elements of statistical physics and machine learning. We will discuss some examples from neuroscience and biology both in micro scale (dynamics and plasticity of synapses), as well as in macro scale (learning and information storing in neural networks, formation of swarms, elements of evolutionary games). |
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