Basic Category Theory
Informacje ogólne
Kod przedmiotu: | 360-MS2-1BCTa |
Kod Erasmus / ISCED: | (brak danych) / (brak danych) |
Nazwa przedmiotu: | Basic Category Theory |
Jednostka: | Wydział Matematyki |
Grupy: | |
Punkty ECTS i inne: |
5.00
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Język prowadzenia: | angielski |
Rodzaj przedmiotu: | fakultatywne |
Założenia (opisowo): | (tylko po angielsku) To follow this course students only need to know the basics of sets and functions. We will use examples from abstract algebra (groups and rings), so knowledge of these topics will be an advantage. |
Tryb prowadzenia przedmiotu: | mieszany: w sali i zdalnie |
Skrócony opis: |
(tylko po angielsku) Field of science: natural science; discipline: mathematics Category theory takes a very general and abstract view of mathematics, which allows us to spot patterns and connections which are not obvious at first glance. These connections deepen our understanding of many familiar mathematical objects and constructions. In this course we will develop the basics of category theory --- categories, functors and natural transformations --- and build up a library of examples to help us understand these concepts. These examples can be chosen based on the background of the students. In the second part of the course we will study other aspects of category, such as universal properties, adjoints and limits, where we see that many familiar ideas in mathematics are actually special cases of these very general notions. |
Pełny opis: |
(tylko po angielsku) Course profile: academic Field of science: natural science; discipline: mathematics Second cycle Year of study 1; semester 1 Lecture: 30 hours; Problem class: 30 hours ECTS credits: 5 Verification methods: lectures, homework exercises, group discussion, presentations, self-studying literature Student workload: attending lectures 30 hours attending problem classes 30 hours homework exercises 15x 2hours = 30 hours class preparation and notes 15x 0.5hours = 7.5 hours consultations ~5x 0.5hours = 2.5 hours examination preparation 7hours |
Literatura: |
(tylko po angielsku) Steve Awodey, Category Theory. Oxford University Press, 2010. Available online at https://arxiv.org/abs/1612.09375. Saunders Mac Lane, Categories for the working mathematician (second edition). Graduate Texts in Mathematics, volume 5. Springer, 1998. Emily Riehl, Category theory in context. Dover, 2017. |
Efekty uczenia się: |
(tylko po angielsku) KA7_UW02 abstract mathematical reasoning ability KA7_UW10 can use algebraic methods to solve problems KA7_UW13 can prove mathematical statements using diverse tools KA7_UK05 English proficiency KA7_UU02 can search mathematical literature for information, including in English |
Metody i kryteria oceniania: |
(tylko po angielsku) Grading |
Zajęcia w cyklu "Rok akademicki 2023/24" (w trakcie)
Okres: | 2023-10-01 - 2024-06-30 |
Przejdź do planu
PN WT ŚR CZ PT |
Typ zajęć: |
Ćwiczenia, 30 godzin
Wykład, 30 godzin
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Koordynatorzy: | Andrew McKee | |
Prowadzący grup: | Andrew McKee | |
Lista studentów: | (nie masz dostępu) | |
Zaliczenie: |
Przedmiot -
Zaliczenie na ocenę
Ćwiczenia - Zaliczenie na ocenę |
Właścicielem praw autorskich jest Uniwersytet w Białymstoku.