2016/17 Undergraduate Module Catalogue
MATH2040 Mathematical Logic 1
10 creditsClass Size: 110
Module manager: Dr Richard Elwes
Taught: Semester 2 (Jan to Jun) View Timetable
Year running 2016/17
Pre-requisite qualificationsFamiliarity with proof by mathematical induction.
Interest in abstract, mathematical proof writing.
This module is mutually exclusive with
This module is approved as a discovery module
Module summaryThis module is an introduction to mathematical logic introducing formal languages that can be used to express mathematical ideas and arguments. It throws light on mathematics itself, because it can be applied to problems in philosophy, linguistics, computer science and other areas.
Objectives- To describe the fundamental notions of mathematical logic, including the distinction between syntax and semantics.
- To present a proof of the completeness theorem in the propositional case and introduce a first order predicate calculus.
On completion of this module, students should be able to:
(a) express logical arguments in a formal language, and thereby to analyse their correctness;
(b) find disjunctive normal form for a propositional formula and prenex normal form for a first order formula
(c) distinguish between syntax and semantics, and give simple formal proofs in a natural deduction system.
1. Some basic set theory (possibly including functions, relations, possibly orderings, Countable/uncountable sets, possibly Boolean algebras)
2. Propositional Logic. Syntax. Semantics. Satisfiability, tautologies, contradictions, tautologies. Disjunctive and conjunctive normal forms. A formal proof system. Completeness and (possibly) compactness.
3. Predicate Logic. Language and syntax. First-order structures. Truth in a structure. Possibly prenex normal form. A formal proof system.
|Delivery type||Number||Length hours||Student hours|
|Private study hours||68.00|
|Total Contact hours||32.00|
|Total hours (100hr per 10 credits)||100.00|
Private studyStudying and revising of course material.
Completing of assignments and assessments.
Opportunities for Formative FeedbackRegular problem solving assignments
Methods of assessment
|Assessment type||Notes||% of formal assessment|
|Total percentage (Assessment Coursework)||15.00|
There is no resit available for the coursework component of this module. If the module is failed, the coursework mark will be carried forward and added to the resit exam mark with the same weighting as listed above.
|Exam type||Exam duration||% of formal assessment|
|Standard exam (closed essays, MCQs etc)||2 hr 00 mins||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 listThe reading list is available from the Library website
Last updated: 08/04/2016
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