| Unit name | Logic |
|---|---|
| Unit code | MATH30100 |
| Credit points | 20 |
| Level of study | H/6 |
| Teaching block(s) |
Teaching Block 1 (weeks 1 - 12) |
| Unit director | Dr. Fujimoto |
| Open unit status | Not open |
| Pre-requisites |
Normally: the 1st Year Pure Maths units (or an equivalent): MATH11511 Number Theory & Group Theory, MATH11006 Analysis 1 and MATH 11521 Further Topics in Analysis |
| Co-requisites |
None |
| School/department | School of Mathematics |
| Faculty | Faculty of Science |
Unit aims
To teach the fundamentals of mathematical logic.
General Description of the Unit
The course covers the basic model theory and proof theory of 1st order languages, the Gödel Completeness Theorem and the Godel Incompleteness Theorems characterising the non-provability of the consistency of a formal system within that system.
These theorems are the foundations of 20'th century logic.
Relation to Other Units
Logic is a prerequisite for the Level 7 unit Axiomatic Set Theory It is essential for an understanding of much of the foundations of mathematics but is not restricted to that. In particular it is essential for much of analytical philosophy.
It is of particular interest to students taking the joint Mathematics and Philosophy degrees, or the MA in Philosophy of Mathematics
Further information is available on the School of Mathematics website: http://www.maths.bris.ac.uk/study/undergrad/
Learning Objectives
After taking this unit, students should be familiar with the basic principles of first order logic and should understand the technique of arithmetisation of syntax which underlies the proofs of the Gödel Incompleteness Theorems.
Transferable Skills
Assimilation and use of novel and abstract ideas.
Lectures and problems classes.
100% Examination
Raw scores on the examinations will be determined according to the marking scheme written on the examination paper. The marking scheme, indicating the maximum score per question, is a guide to the relative weighting of the questions. Raw scores are moderated as described in the Undergraduate Handbook.
Course notes will be supplied.
