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### Course Overview

Set theory was introduced by Cantor in 1872, who was attempting to understand the concept of "infinity" which defied the mathematical world since the Greeks. Set Theory is fundamental to modern mathematics - any mathematical theory must be formulated within the framework of set theory, or else it is deemed invalid. It is the alphabet of mathematics.

In this course we will study naive set theory. Fundamental object such as the natural numbers and the real numbers will be constructed. Structures such as partial orders and functions will be studied. And of course, we will explore infinite sets.

### Course Details

Study Type Level Undergraduate 1 Second Sub Session 15 credits (7.5 ECTS credits) None. No Dr William Turner

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### What courses & programmes must have been taken before this course?

• Either MA1005 Calculus 1 (Studied) or MA1006 Algebra (Studied)

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### Course Description

Syllabus

• The algebra of sets.
• Relations and functions.
• Construction of the natural numbers.
• Induction and strong induction.
• Finite sets.
• Construction of the integers.
• Construction of the rational numbers.
• Dedekind cuts and the real numbers.
• Countability and uncountability.
• Zorn's lemma.

Course Aims

### Degree Programmes for which this Course is Prescribed

• BSc Applied Mathematics
• BSc Mathematics
• BSc Mathematics with Gaelic
• BSc Mathematics-Physics
• MA Applied Mathematics
• MA Mathematics
• Master of Engineering in Computing Science
• Mathematics Joint
• Mathematics Major
• Mathematics Minor

### Contact Teaching Time

55 hours

This is the total time spent in lectures, tutorials and other class teaching.

### Assessment

1st Attempt: 1 two hour written examination (70%) in course assessment (30%)

Resit: 1 two-hour written examination paper (maximum of 100% resit and 70% resit with 30% in-course assessment).

### Formative Assessment

Informal assessment of weekly homework through discussions in tutorials.

### Feedback

In-course assignments will normally be marked within one week and feedback provided to students in tutorials.

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