Kaisa_2012_3_photo by Veikko Somerpuro
Mathematical logic
This is the core course of the mathematical logic specialization of the Master's programme in Mathematics and Statistics.
The main topics of the course are the completeness theorems of propositional and predicate logic and Gödel's incompleteness theorems. Methods and topics needed for these are formal deduction, definability, primitive recursive and recursive functions. During the course, the students learn about the aims, strengths and limitations of formal proof systems.
Gödel's incompleteness theorem is sometimes called the most misunderstood theorem of mathematics. This course gives you the prerequisites needed to thoroughly understand what the theorem is really about!
Viestit
Aikataulu
Kuvaus
Optional course.
Master's Programme in Mathematics and Statistics is responsible for the course.
The course belongs to the Mathematics and Applied mathematics module.
The course is available to students from other degree programmes.
Mathematical routine aquired during B.Sc. level mathematics courses. Introduction to logic I&II help, but are not strictly necessary.
Master studies
The course gives basic knowledge in the strengths and limitations of formal proofs
Recommended time/stage of studies for completion: 1. year
Term/teaching period when the course will be offered: varying
The main topics of the course are the completeness theorems of propositional and predicate logic and Gödel's incompleteness theorems. Methods and topics needed for these are formal deduction, definability, primitive recursive and recursive functions.
Jouko Väänänen ”Matemaattinen logiikka” (alternatively e.g. Herbert B. Enderton ”A Mathematical Introduction to Logic”)
Lectures and exercises
Exam and excercises, Course will be graded with grades 1-5
Exam and exercises or general exam