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School of Mathematics

# MATH63021 - 2012/2013

General Information
• Title: Set Theory
• Unit code: MATH63021
• Credits: 15
• Prerequisites: None
• Co-requisite units: None.
• School responsible: Mathematics
• Members of staff responsible: Dr H Simmons
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## Specification

### Aims

To introduce students to set theory and its role in mathematics.

### Brief Description of the unit

Set theory began to develop in the late 19th century, and now is important in several areas of mathematics. This is a first course on the ideas developed since then. Although Axiomatic Set Theory is mentioned in the course, the material is developed informally, not from a set of axioms.

### Learning Outcomes

On successful completion of the course unit students will be able to demonstrate facility with the notions of elementary set theory.

None.

### Syllabus

1. Basic material [4]
2. The cardinal comparison of sets [4]
3. The rationals and reals as linearly ordered sets [4]
4. Introduction to order types and ordinals [4]
5. The Axiom of Choice [3]
6. Zorn's lemma and maximizing principles [3]

### Textbooks

A full set of notes will be available from
http://www.cs.man.ac.uk/~hsimmons/SetTheory/settheory.html

There is no recommended textbook to cover the course. The following are some good books to consult.

• A. G. Hamilton, Numbers, Sets and Axioms, CUP Press (in paperback).
• Y. N. Moschovakis, Notes on Set Theory, Springer-Verlag Undergraduate Texts in Mathematics.
• H. B. Enderton, Elements of Set Theory, Academic Press.

### Teaching and learning methods

Three lectures a week plus one weekly office hour. In addition students should expect to do at least seven hours private study each week for this course unit.

### Assessment

Coursework: two take home tests; weighting 10% each,
End of semester examination: two and a half hours; weighting 80%