## Module and Programme Catalogue

#### Find information on

This module is discontinued in the selected year. The information shown below is for the academic year that the module was last running in, prior to the year selected.

## MATH2040 Mathematical Logic 1

### 10 creditsClass Size: 115

Module manager: Dr Andrew Brooke-Taylor
Email: A.D.Brooke-Taylor@leeds.ac.uk

Taught: Semester 1 View Timetable

Year running 2018/19

### Pre-requisite qualifications

Familiarity with proof by mathematical induction.

Interest in abstract, mathematical proof writing.

### This module is mutually exclusive with

 PHIL2122 Formal Logic

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

- 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) distinguish between syntax and semantics, and give simple formal proofs in a natural deduction system;
(c) give a proof by induction on a finite tree.

### Syllabus

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