Computer Science

Most mathematics modules aim for the sky, exploring ever more advanced and complex structures that build upon previously learnt material to extend your knowledge towards ever higher levels in the vast edifice that is modern mathematics. This module is different: it digs down into the very foundations, and looks closely at the nuts and bolts of mathematical reasoning and and the basic logic that underpins it. You will learn that all is not what it seems: it can be proved, mathematically, that there is a clear sense in which mathematics cannot be reduced to pure logic or formal reasoning. This calls into question the whole nature of the enterprise, leading to philosophical questions about the nature of mathematics and the status of the abstract entities, which form its subject matter.

The aim of this module is to introduce you to formal logic in the form of classical first-order predicate calculus. This module also explores the logical underpinnings of mathematical thought and examines a range of philosophical viewpoints concerning the nature of mathematics.

On successful completion of this module, you should be able to:

Module Specific Skills and Knowledge:
1 express propositions in logical notation and test the validity of inferences formally;
2 understand the logical basis for mathematical proof and the nature of axiomatisation;
3 appreciate the role of logic in the development of mathematics;
4 critically evaluate different points of view regarding the nature of mathematics.
Discipline Specific Skills and Knowledge:
5 apply the logical skills acquired in the module to improving the quality of mathematical proofs you produce.
Personal and Key Transferable/ Employment Skills and  Knowledge:
6 use the logical and analytical skills acquired in the module to improve your reasoning abilities in more general contexts.

- logic: propositional calculus, predicate calculus, proof theory, model theory, soundness, completeness and semi-decidability;
- foundations of mathematics: axiomatic set theory, Peano arithmetic, Gödel's incompleteness theorems;
- philosophy of mathematics: platonism, formalism and constructivism.

Referred and deferred assessment will normally be by examination. For referrals, only the examination will count, a mark of 40% being awarded if the examination is passed. For deferrals, candidates will be awarded the higher of the deferred examination mark or the deferred examination mark combined with the original coursework mark.

ELE – http://vle.exeter.ac.uk

Reading list for this module: