MM565: Introduction to category theory
Study Board of Science
Teaching language: Danish or English depending on the teacher, but English if international students are enrolled
EKA: N300052102
Assessment: Second examiner: Internal
Grading: 7-point grading scale
Offered in: Odense
Offered in: Spring
Level: Bachelor
STADS ID (UVA): N300052101
ECTS value: 5
Date of Approval: 28-09-2020
Duration: 1 semester
Version: Archive
Comment
Entry requirements
Academic preconditions
Students taking the course are expected to have a basic knowledge of algebra, corresponding to the contents of the courses MM505 and MM551.
Course introduction
The aim of the course is to introduce to category theory, which is a formalization of mathematical structure. Category theory has, a part from its mathematical relevance, applications in computer science (programming language theory).
The course primarily builds on the knowledge acquired in the courses MM505 (Linear algebra) and MM551 (Algebra 1). The course gives the student a deeper insight into the similarities between different mathematical structures.
In relation to the competence profile of the degree it is the explicit focus of the course to:
The course primarily builds on the knowledge acquired in the courses MM505 (Linear algebra) and MM551 (Algebra 1). The course gives the student a deeper insight into the similarities between different mathematical structures.
In relation to the competence profile of the degree it is the explicit focus of the course to:
- Give the competence to take responsibility for the academic development and specialization.
- Give the competence to develop an overview of the interplay between different mathematical disciplines.
- Give skills to work concretely with new mathematical tools and objects.
- Give skills to learn and understand advanced mathematical theories at a more independent level.
- Give knowledge and understanding of category theory as exemplified by different parts of mathematical theory (primarily algebra).
- Bring perspective into the student’s mathematical knowledge.
Expected learning outcome
The learning objective of the course is that the student demonstrates the ability to:
- Reproduce definitions and results, including their proofs, covered in the course.
- Be able to use these results to analyse concrete examples.
- Formulate and present definitions, proofs and calculations in a mathematically rigorous way.
Content
The following main topics are contained in the course: A selection of the 5 main concepts in category theory:
- categories
- functors
- natural transformations
- universality
- adjunction
Literature
Examination regulations
Exam element a)
Timing
June
Tests
Oral examination
EKA
N300052102
Assessment
Second examiner: Internal
Grading
7-point grading scale
Identification
Student Identification Card
Language
Normally, the same as teaching language
Duration
30 minutes
Examination aids
Allowed, a closer description of the exam rules will be posted in itslearning.
ECTS value
5
Additional information
The examination form for re-examination may be different from the exam form at the regular exam.
Indicative number of lessons
Teaching Method
The teaching method is based on three phase model.
- Intro phase: 28 hours
- Skills training phase: 28 hours, hereof tutorials: 28 hours
Activities during the study phase:
- Solution of weekly assignments in order to discuss these in the exercise sections
- The students are expected to familiarize themselves with the material covered in the lectures
- Self study of various parts of the course material
- Reflection upon the intro and training sections
Teacher responsible
| Name | Department | |
|---|---|---|
| Henning Haahr-Andersen | haah@imada.sdu.dk | Institut for Matematik og Datalogi |
| Jens Kaad | kaad@imada.sdu.dk | Analysis |