Computer Science

ECMM415 - Logic and Philosophy of Mathematics (2012)

MODULE TITLE CREDIT VALUE Logic and Philosophy of Mathematics 15 ECMM415 Dr Antony Galton (Coordinator)
DURATION: TERM 1 2 3
DURATION: WEEKS 0 11 weeks 0
 Number of Students Taking Module (anticipated) 18
DESCRIPTION - summary of the module content

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.
Pre-requisite module: ECM1707

AIMS - intentions of the module

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

INTENDED LEARNING OUTCOMES (ILOs) (see assessment section below for how ILOs will be assessed)

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 apply the logical and analytical skills acquired in the module to improving your reasoning abilities in more general contexts.

SYLLABUS PLAN - summary of the structure and academic content of the module

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.

LEARNING AND TEACHING
LEARNING ACTIVITIES AND TEACHING METHODS (given in hours of study time)
 Scheduled Learning & Teaching Activities Guided Independent Study 62 88
DETAILS OF LEARNING ACTIVITIES AND TEACHING METHODS
 Category Hours of study time Description Scheduled Learning & Teaching activities 20 Lectures Scheduled Learning & Teaching activities 10 Tutorials Scheduled Learning & Teaching activities 2 Class tests Scheduled Learning & Teaching activities 30 Individual assignments Guided independent study 88 Lecture & assessment preparation; wider reading

ASSESSMENT
FORMATIVE ASSESSMENT - for feedback and development purposes; does not count towards module grade
Form of Assessment Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
Two class tests 1 hour each 1,2 In-class

SUMMATIVE ASSESSMENT (% of credit)
 Coursework Written Exams 20 80
DETAILS OF SUMMATIVE ASSESSMENT
Form of Assessment % of Credit Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
Written exam – closed book 80 2 hours 1,4 None
Coursework – CA1 10 10 hours 1,2,5 Feedback sheet
Coursework – CA2 10 10 hours 1,2,6 Feedback sheet

DETAILS OF RE-ASSESSMENT (where required by referral or deferral)
Original Form of Assessment Form of Re-assessment ILOs Re-assessed Time Scale for Re-reassessment
All above Written exam (100%) All Last week of August

RE-ASSESSMENT NOTES

If a module is normally assessed entirely by coursework, all referred/deferred assessments will normally be by assignment.
If a module is normally assessed by examination or examination plus coursework, 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.

RESOURCES
INDICATIVE LEARNING RESOURCES - The following list is offered as an indication of the type & level of
information that you are expected to consult. Further guidance will be provided by the Module Convener

ELE – http://vle.exeter.ac.uk

Type Author Title Edition Publisher Year ISBN Search
Set Chiswell I and Hodges W Mathematical Logic, Oxford Texts in Logic 3 Oxford University Press 2006 [Library]
Set Smith P Introduction to Goedel's Theorems Cambridge University Press 2008 [Library]
Set Brown JR Philosophy of Mathematics: A contemporary Introduction to the World of Proofs and Pictures Routledge 2008 [Library]
CREDIT VALUE ECTS VALUE 15 7.5
PRE-REQUISITE MODULES ECM1707
NQF LEVEL (FHEQ) AVAILABLE AS DISTANCE LEARNING M (NQF level 7) No Monday 12 March 2012 Wednesday 17 October 2012
KEY WORDS SEARCH None Defined