Taught: Semester 1 (Sep to Jan) View Timetable
Year running 2025/26
MATH2041
This module is not approved as a discovery module
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.
This module will introduce students to the area of mathematical logic. Through lectures and problems, students will learn how to express ideas and arguments in a system of formal logic. This will enable them to analyse the structure of such arguments, as well as make arguments and observations about what is and isn’t possible to express in these systems.
On successful completion of the module students will have demonstrated the following learning outcomes relevant to the subject:
1. Express logical arguments in a formal language and thereby analyse their correctness.
2. Distinguish between syntax and semantics, and give simple formal proofs in a natural deduction system.
3. Apply the soundness and completeness theorems to establish whether a formula is derivable from a set of axioms or not.
Skills Learning Outcomes
On successful completion of the module students will have demonstrated the following skills learning outcomes:
a. Communicate through written work technical information and reasoning.
b. Apply analytical thinking and technical knowledge to solve problems.
c. Write in a clear, concise, and focused way.
d. Manage workloads, deadlines, and workplace pressure through prioritisation and productivity skills.
1. Propositional Logic, syntax and semantics.
2. Satisfiability, tautologies, contradictions, truth tables.
3. Disjunctive and conjunctive normal forms.
4. A formal proof system for propositional logic.
5. Completeness and compactness for propositional logic.
Additional topics that build on these may be covered as time allows. Such topics may be drawn from the following, or similar:
6. Boolean algebras and partially ordered sets.
7. Predicate logic, language and syntax. First-order structures. Truth in a structure. Prenex normal form. A formal proof system.
8. Introduction to set theory.
Methods of assessment
The assessment details for this module will be provided at the start of the academic year
| Delivery type | Number | Length hours | Student hours |
|---|---|---|---|
| Lecture | 22 | 1 | 22 |
| Seminar | 5 | 1 | 5 |
| Private study hours | 73 | ||
| Total Contact hours | 27 | ||
| Total hours (100hr per 10 credits) | 100 | ||
The reading list is available from the Library website
Last updated: 30/04/2025
Errors, omissions, failed links etc should be notified to the Catalogue Team