| Unit name | Logic |
|---|---|
| Unit code | MATH30100 |
| Credit points | 20 |
| Level of study | H/6 |
| Teaching block(s) |
Teaching Block 2 (weeks 13 - 24) |
| Unit director | Professor. Horsten |
| Open unit status | Not open |
| Pre-requisites |
Level 1 Pure Mathematics |
| Co-requisites |
None |
| School/department | School of Mathematics |
| Faculty | Faculty of Science |
We use mathematical techniques to analyse formal proposition and predicate languages together with the structures which they can describe. We study the notions of satisfiability, validity and logical consequence. We prove the completeness theorem (that the sentences provable from a set of axioms are precisely those true in all structures in which the axioms are true). We discuss the first Incompleteness Theorem of Godel, that not all true statements of arithmetic are provable from any effectively given set of axioms for number theory.
Aims
To teach the fundamentals of mathematical logic.
Syllabus
Relation to Other Units
Logic is a prerequisite for the Level 4 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.
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.
The final assessment mark for Logic is calculated from a 2 ½ -hour written examination in May/June consisting of FIVE questions. A candidate's best FOUR answers will be used for assessment. Calculators are NOT permitted be used in this examination.
Course notes will be supplied.
