| 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 | Dr. Fujimoto |
| Open unit status | Not open |
| Pre-requisites |
MATH10004 Foundations and Proof and MATH10005 Introduction to Group Theory (or MATH10010 Introduction to Proofs and Group Theory) MATH10003 Analysis 1A and MATH10006 Analysis 1B (or MATH10011 Analysis) |
| Co-requisites |
None |
| School/department | School of Mathematics |
| Faculty | Faculty of Science |
Unit Aims
To teach the fundamentals of mathematical logic.
Unit Description
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 20th century logic.
Relation to Other Units
Logic is a prerequisite for 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.
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.
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