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2009/10 Taught Postgraduate Module Catalogue
MATH5102M Advanced Logic
15 creditsClass Size: 30
Module manager: Dr C Harris
Email: charlie@maths.leeds.ac.uk
Taught: Semester 2 (Jan to Jun) View Timetable
Year running 2009/10
Pre-requisites
MATH2040 | Mathematical Logic 1 |
This module is mutually exclusive with
MATH3102 | Mathematical Logic 2 |
This module is not approved as an Elective
Module summary
Metamathematics and proof theory try to answer fundamental questions about axiomatic theories (e.g. number theory) like: - Are they consistent (free from contradiction)? - How do we know? - Could they be developed by computers without human assistance? (answer: no) - Are mathematicians necessary? (answer: yes). The main goal is to prove Godel's Incompleteness Theorems (1931) which show that if a formal theory has strong enough axioms then there are statements which it can neither prove nor refute.Objectives
On completion of this module, students should be able to:a) carry out elementary proofs in first-order formal logic and Peano Arithmetic;
b) prove representability and recursiveness of basic number-theoretic functions and relations;
c) understand and reproduce proofs of Godel's Completeness Theorem for predicate logic, Godel's Incompleteness Theorems for Peano Arithmetic, Lob's Theorem and related results;
d) describe connections between incompleteness, consistency, computability and undecidability;
e) show a capacity for independent study, including further development of the theory via a range of more challenging homework problems, and through an oral presentation.
Syllabus
- Revision of first-order logic including Godel's Completeness Theorem;
- the axiomatic method and formal Peano Arithmetic;
- recursive functions and representability;
- the arithmetization of syntax and Godel's First Incompleteness Theorems;
- Lob's Theorem and the Second Incompleteness Theorem;
- consistency, undecidability and computability;
- non-standard models of arithmetic.
Additional topics chosen from: decidable fragments of arithmetic, Rosser's theorem, and reflection principles.
Teaching methods
Delivery type | Number | Length hours | Student hours |
Example Class | 7 | 1.00 | 7.00 |
Lecture | 26 | 1.00 | 26.00 |
Private study hours | 117.00 | ||
Total Contact hours | 33.00 | ||
Total hours (100hr per 10 credits) | 150.00 |
Private study
- Reading lecture notes: 72 hours- Solving coursework problems: 25 hours
- Preparing for examination and oral presentation: 20 hours.
Opportunities for Formative Feedback
Regular problems sheets.Methods of assessment
Coursework
Assessment type | Notes | % of formal assessment |
Presentation | 10 minute oral presentation | 15.00 |
Total percentage (Assessment Coursework) | 15.00 |
Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated
Exams
Exam type | Exam duration | % of formal assessment |
Standard exam (closed essays, MCQs etc) | 3 hr | 85.00 |
Total percentage (Assessment Exams) | 85.00 |
Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated
Reading list
The reading list is available from the Library websiteLast updated: 24/03/2010
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- Undergraduate module catalogue
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