| 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 |
| Units you must take before you take this one (pre-requisite units) |
MATH10010 Introduction to Proofs and Group Theory and MATH10011 Analysis |
| Units you must take alongside this one (co-requisite units) |
None |
| Units you may not take alongside this one | |
| 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.
The unit will be taught through a combination of
90% Timed, open-book examination 10% Coursework
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.
If you fail this unit and are required to resit, reassessment is by a written examination in the August/September Resit and Supplementary exam period.
If this unit has a Resource List, you will normally find a link to it in the Blackboard area for the unit. Sometimes there will be a separate link for each weekly topic.
If you are unable to access a list through Blackboard, you can also find it via the Resource Lists homepage. Search for the list by the unit name or code (e.g. MATH30100).
How much time the unit requires
Each credit equates to 10 hours of total student input. For example a 20 credit unit will take you 200 hours
of study to complete. Your total learning time is made up of contact time, directed learning tasks,
independent learning and assessment activity.
See the Faculty workload statement relating to this unit for more information.
Assessment
The Board of Examiners will consider all cases where students have failed or not completed the assessments required for credit.
The Board considers each student's outcomes across all the units which contribute to each year's programme of study. If you have self-certificated your absence from an
assessment, you will normally be required to complete it the next time it runs (this is usually in the next assessment period).
The Board of Examiners will take into account any extenuating circumstances and operates
within the Regulations and Code of Practice for Taught Programmes.
