# 2015/16 Undergraduate Module Catalogue

## MATH2040 Mathematical Logic 1

### 10 creditsClass Size: 110

**Module manager:** Dr R Elwes**Email:** R.H.Elwes@leeds.ac.uk

**Taught:** Semester 2 (Jan to Jun) View Timetable

**Year running** 2015/16

### 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) 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 |

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

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

### Reading list

The reading list is available from the Library websiteLast updated: 29/07/2015

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