MM565: Introduction to category theory

The Study Board for 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: 05-10-2022


Duration: 1 semester

Version: Approved - active

Comment

The course is co-read with MM857.

Entry requirements

None

Academic preconditions

Students taking the course are expected to have a basic knowledge of algebra, corresponding to the contents of the courses MM505/MM568 and MM551/MM567.

Course introduction

The aim of the course is to introduce the student 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:

  • 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:

  1. categories
  2. functors
  3. natural transformations
  4. universality
  5. adjunction

Literature

See itslearning for syllabus lists and additional literature references.

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 - Name

Language

Normally, the same as teaching language

Duration

30 minutes

Examination aids

To be announced during the course

ECTS value

5

Indicative number of lessons

42 hours per semester

Teaching Method

The teaching method is based on three phase model.

  • Intro phase: 28 hours
  • Skills training phase: 14 hours, hereof tutorials: 14 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 E-mail Department
Nadia Ott nmott@imada.sdu.dk Institut for Matematik og Datalogi

Timetable

Administrative Unit

Institut for Matematik og Datalogi (matematik)

Team at Registration

NAT

Offered in

Odense

Recommended course of study

Profile Education Semester Offer period

Transition rules

Transitional arrangements describe how a course replaces another course when changes are made to the course of study. 
If a transitional arrangement has been made for a course, it will be stated in the list. 
See transitional arrangements for all courses at the Faculty of Science.