## MATH2040 Mathematical Logic 1

### 10 creditsClass Size: 200

Module manager: Professor H D MacPherson
Email: H.D.Macpherson@leeds.ac.uk

Taught: Semester 1 (Sep to Jan) View Timetable

Year running 2008/09

This module is approved as an Elective

### 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

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.

### Syllabus

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.

### Teaching methods

Due to COVID-19, teaching and assessment activities are being kept under review - see module enrolment pages for information

 Delivery type Number Length hours Student hours Example Class 11 1.00 11.00 Lecture 22 1.00 22.00 Private study hours 67.00 Total Contact hours 33.00 Total hours (100hr per 10 credits) 100.00

### Methods of assessment

Due to COVID-19, teaching and assessment activities are being kept under review - see module enrolment pages for information

Coursework
 Assessment type Notes % of formal assessment In-course Assessment . 15.00 Total percentage (Assessment Coursework) 15.00

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated

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