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2012/13 Undergraduate Module Catalogue
MATH3102 Mathematical Logic 2
15 creditsClass Size: 50
Module manager: Dr Andy Lewis
Email: andyl@maths.leeds.ac.uk
Taught: Semester 1 (Sep to Jan) View Timetable
Year running 2012/13
Pre-requisites
MATH2040 | Mathematical Logic 1 |
This module is mutually exclusive with
MATH5102M | Advanced Logic |
MATH5103M | Advanced Logic |
This module is approved as an Elective
Module summary
Metamathematics and proof theory try to answer fundamental questions about axiomatic theories (eg 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
- To develop fundamental concepts and techniques of Mathematical Logic sufficient to prove Godel's Incompleteness Theorems, and to relate them to notions of computability, decidability and undecidability.- To enable students to understand and write formal proofs in logical style.
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 Incompleteness 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.
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.
Teaching methods
Delivery type | Number | Length hours | Student hours |
Lecture | 33 | 1.00 | 33.00 |
Private study hours | 117.00 | ||
Total Contact hours | 33.00 | ||
Total hours (100hr per 10 credits) | 150.00 |
Private study
Studying and revising of course material.Completing of assignments and assessments.
Opportunities for Formative Feedback
Regular problem sheets.Methods of assessment
Exams
Exam type | Exam duration | % of formal assessment |
Standard exam (closed essays, MCQs etc) | 2 hr 30 mins | 100.00 |
Total percentage (Assessment Exams) | 100.00 |
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: 08/01/2013
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