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2023/24 Undergraduate Module Catalogue

MATH2041 Logic

10 creditsClass Size: 120

Module manager: Dr Andrew Brooke-Taylor

Taught: Semester 1 (Sep to Jan) View Timetable

Year running 2023/24

Pre-requisite qualifications

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

This module is mutually exclusive with

MATH2042Logic with Computation
PHIL2122Formal 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.


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.


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 typeNumberLength hoursStudent hours
Private study hours68.00
Total Contact hours32.00
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

Assessment typeNotes% 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.

Exam typeExam duration% of formal assessment
Standard exam (closed essays, MCQs etc)2 hr 00 mins85.00
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: 28/04/2023 14:54:41


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