University of Warsaw - Central Authentication System

QUICK START
STUDENTS AND STAFF
FACULTIES
COURSES
- Category theory in foundations of computer science
STUDIES
DORMITORIES
HELP

Category theory in foundations of computer science

General data

Course ID:	1000-2M10TKI
Erasmus code / ISCED:	11.3 Kod klasyfikacyjny przedmiotu składa się z trzech do pięciu cyfr, przy czym trzy pierwsze oznaczają klasyfikację dziedziny wg. Listy kodów dziedzin obowiązującej w programie Socrates/Erasmus, czwarta (dotąd na ogół 0) – ewentualne uszczegółowienie informacji o dyscyplinie, piąta – stopień zaawansowania przedmiotu ustalony na podstawie roku studiów, dla którego przedmiot jest przeznaczony. / (0612) Database and network design and administration The ISCED (International Standard Classification of Education) code has been designed by UNESCO.
Course title:	Category theory in foundations of computer science
Name in Polish:	Teoria kategorii w podstawach informatyki
Organizational unit:	Faculty of Mathematics, Informatics, and Mechanics
Course groups:	(in Polish) Przedmioty obieralne na studiach drugiego stopnia na kierunku bioinformatyka Elective courses for Computer Science
Course homepage:	http://www.mimuw.edu.pl/~tarlecki/teaching/ct/
ECTS credit allocation (and other scores):	6.00 Basic information on ECTS credits allocation principles: the annual hourly workload of the student’s work required to achieve the expected learning outcomes for a given stage is 1500-1800h, corresponding to 60 ECTS; the student’s weekly hourly workload is 45 h; 1 ECTS point corresponds to 25-30 hours of student work needed to achieve the assumed learning outcomes; weekly student workload necessary to achieve the assumed learning outcomes allows to obtain 1.5 ECTS; work required to pass the course, which has been assigned 3 ECTS, constitutes 10% of the semester student load. view allocation of credits
Language:	English
Type of course:	elective monographs
Mode:	Classroom
Short description:	Universal algebra and category theory are by now two classical areas of mathematics that offer abstract concepts, methods and results which have been widely adopted in foundations of computer science and by now form the standard language to deal with, among others, modelling, design, and systematic construction of complex software systems. The course recalls basic concepts of universal algebra and introduces the language of category theory, limited to the most elementary and important notions and related results. We hint at least at the possible appliocations of the categorical language in various areas of computer science, for instance in type theory and in foundations of algebraic specifications. The course will consists of lectures and tutorials, in practice without a strict separation between them. It will be offered in English, but it may be carried out in Polish in case only Polish-speaking studants register.
Full description:	Plan:  Many-sorted sets, basic notions and notationf of set theory.  Many-sorted algebras, basic algebraic concepts.  Terms, equations, equational varieties; equational calculus.  Initial algebras, algebraic specifications with initial semantics.  Related algebraic frameworks.  Categories and basic catoegorical concepts.  Limits and colimits.  Functors and natural transformations.  Adjunctions.  Monads and algebras.  Cartesian-closed categories and semantics of typed lambda calculus.
Bibliography:	 G. Graetzer, Universla Algebra, Springer, 1979.  S. MacLane, Categories for the Working Mathematician, Springer, 1971  D.T. Sannella, A. Tarlecki, Foundations of Algebraic Specificiations and Formal Program Development, Springer, 2012.
Learning outcomes:	(in Polish) Wiedza:  Zna podstawowe pojęcia oraz najważniejsze klasyczne wyniki algebry ogólnej (K_W01, K_W02).  Zna podstawowe pojęcia oraz proste wyniki teorii kategorii (K_W01, K_W02).  Zna i rozumie niektóre zastosowania algebry ogólnej i teorii kategorii w podstawach informatyki (K_W01, K_W02). Umiejętności:  Potrafi potrafi udowodnić niektóre klasyczne wyniki algebry ogólnej i proste wyniki teorii kategorii (K_U01).  Potrafi znależć interpretację abstrakcyjnych pojęć algebry ogólnej i teorii kategorii w konkretnych środowiskach logicznych (K_U01, K_U09, K_U10).  Potrafi znależć uogólnienie pojęć i własności konkretnych środowisk logicznych w terminach algebry ogólnej i teorii kategorii (K_U01, K_U09, K_U10).  Potrafi uzasadnić metody budowania modularnych programów funkcyjnych w terminach algebry ogólnej i teorii kategorii (K_U01, K_U02, K_U10). Kompetencje:  Zna ograniczenia własnej wiedzy i rozumie potrzebę dalszego kształcenia, w tym zdobywania wiedzy pozadziedzinowej (K_K01).  Potrafi precyzyjnie formułować pytania, służące pogłębieniu własnego zrozumienia danego tematu lub odnalezieniu brakujących elementów rozumowania (K_K02).
Assessment methods and assessment criteria:	Written take-home exam, marked by the lecturer, likely to take the form of a larger assignment with multiple subtasks. If the exam is needed earlier, please contact the lecturer. There will be a special subtask or a separate assignment at a more advanced level for PhD students taking the exam.

Classes in period "Winter semester 2023/24" (past)

Time span:	2023-10-01 - 2024-01-28	Selected timetable range: weekly course term Navigate to timetable MO TU W TH FR WYK CW
Type of class:	Classes, 30 hours more information Lecture, 30 hours more information
Coordinators:	Andrzej Tarlecki
Group instructors:	Andrzej Tarlecki
Students list:	(inaccessible to you)
Examination:	Examination

Classes in period "Winter semester 2024/25" (future)

Time span:	2024-10-01 - 2025-01-26	Selected timetable range: weekly course term Navigate to timetable
Type of class:	Classes, 30 hours more information Lecture, 30 hours more information
Coordinators:	Andrzej Tarlecki
Group instructors:	Andrzej Tarlecki
Students list:	(inaccessible to you)
Examination:	Examination

Course descriptions are protected by copyright.
Copyright by University of Warsaw.