MM808: Logic and set theory (5 ECTS)
STADS: 13004001Level
Master's level course
Teaching period
According to needs.
Teacher responsible
Email: jessica@imada.sdu.dkTimetable
| Group | Type | Day | Time | Classroom | Weeks | Comment |
|---|---|---|---|---|---|---|
| Common | I | Tuesday | 14-16 | Spørg underviseren | 15-22 | |
| Common | I | Tuesday | 16-18 | Spørg underviseren | 15-22 | |
| Common | I | Friday | 14-16 | IMADA Seminarrum | 15-22 | |
| Common | I | Friday | 16-18 | IMADA Seminarrum | 15-22 |
Show personal time table for this course.
Comment:
Ubegrænset deltagerantal. 4. kvartal.
Prerequisites:
None
Academic preconditions:
MM509 and MM519
Course introduction
Primarily to give an introduction to fundamental concepts in logic so as to make it possible to understand and prove the incompleteness theorem of Gödel. The course also covers the foundation of mathematics: set theory.
Expected learning outcome
After having followed the course the student should be able to:
• account for basic concepts in logic and set theory.
• go through and explain the steps in proofs from the course syllabus.
• pinpoint the overall structure in proofs of central theorems from the course syllabus. The student should also be able to pinpoint which assumptions the proof relies on.
• Use methods and results from the course to solve problems.
• Solve simple theoretical exercises within the syllabus.
• Formulate the written assignment in a correct mathematical language.
Subject overview
Logic: Proposition calculus (informal and formal). 0th and 1st order languages and systems. Recursive functions and relations. Gödels theorem. Turing machines and computability. Set theory: Discussion of axioms (how to define a set?). Cardinal and ordinal numbers. The axiom of choice, the principle of well ordering, and Zorns Lemma.
Literature
There isn't any litterature for the course at the moment.
Website
This course uses e-learn (blackboard).
Prerequisites for participating in the exam
None
Assessment and marking:
A 3 day "take home exam". Pass/fail. Internal examiner.
Reexamination according to the rules approved by the Study Board.
Expected working hours
The teaching method is based on three phase model.
Forelæsninger: 24 timer
Eksaminatorietimer/opgaveregning: 12 timer
Educational activities
Language
This course is taught in Danish.
Course enrollment
See deadline of enrolment.
Tuition fees for single courses
See fees for single courses.
