Unit information: Logic in 2020/21

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

Description including Unit Aims

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.

Intended Learning Outcomes

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.

Teaching Information

The unit will be taught through a combination of

• synchronous online and, if subsequently possible, face-to-face lectures
• asynchronous online materials, including narrated presentations and worked examples
• guided asynchronous independent activities such as problem sheets and/or other exercises
• synchronous weekly group problem/example classes, workshops and/or tutorials
• synchronous weekly group tutorials
• synchronous weekly office hours

Assessment Information

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.

Reading and References

Recommended

• Heinz-Dieter Ebbinghaus, Jörg Flum, and Wolfgang Thomas, Mathematical Logic, Springer, 1994
• Herbert Enderton, A Mathematical Introduction to Logic, Academic Press, 2001