2024/25 Undergraduate Module Catalogue

MATH2041 Logic

10 creditsClass Size: 120

Module manager: Dr Andrew Brooke-Taylor
Email: a.d.brooke-taylor@leeds.ac.uk

Taught: Semester 1 (Sep to Jan) View Timetable

Year running 2024/25

Pre-requisite qualifications

Familiarity with proof by mathematical induction.
Interest in abstract, mathematical proof writing.

This module is mutually exclusive with

MATH2042	Logic with Computation
PHIL2122	Formal Logic

Module replaces

MATH2040 Mathematical Logic 1

This module is approved as a discovery module

Module summary

This 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

On completion of this module, students should be able...
1. To describe the fundamental notions of mathematical logic, including the distinction between syntax and semantics.
2. To present a proof of the completeness theorem in the propositional case and introduce a first order predicate calculus.

Learning outcomes
1. To express logical arguments in a formal language and thereby to analyse their correctness.
2. To distinguish between syntax and semantics, and give simple formal proofs in a natural deduction system.
3. To give a proof by induction on a finite tree.
4. To apply the soundness and completeness theorems to establish whether a formula is derivable from a set of axioms or not.

Syllabus

1. Propositional Logic. Syntax. Semantics. Satisfiability, tautologies, contradictions. Disjunctive and conjunctive normal forms. A formal proof system. Completeness and compactness.
2. Boolean algebras and partially ordered sets.
3. Predicate Logic. Language and syntax. First-order structures. Truth in a structure. Prenex normal form. A formal proof system.

Teaching methods

Delivery type	Number	Length hours	Student hours
Workshop	10	1.00	10.00
Lecture	22	1.00	22.00
Private study hours			68.00
Total Contact hours			32.00
Total hours (100hr per 10 credits)			100.00

Private study

Studying and revising of course material.
Completing of assignments and assessments.

Opportunities for Formative Feedback

Regular problem solving assignments.

Methods of assessment

Coursework

Assessment type	Notes	% of formal assessment
In-course Assessment	.	15.00
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.

Exams

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 list

The reading list is available from the Library website

Last updated: 29/04/2024 16:16:33

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