| Unit name | Set Theory |
|---|---|
| Unit code | MATH32000 |
| Credit points | 20 |
| Level of study | H/6 |
| Teaching block(s) |
Teaching Block 1 (weeks 1 - 12) |
| Unit director | Professor. Welch |
| Open unit status | Not open |
| Pre-requisites | |
| Co-requisites |
None |
| School/department | School of Mathematics |
| Faculty | Faculty of Science |
The theory of sets provides a foundation for all of mathematics. We shall discuss, informally, axioms for sets and develop the theory of infinite ordinal and cardinal numbers and their 'arithmetic'. This refines the idea of 'uncountable'. We shall discuss various undecidable statements in Set Theory, such as the continuum hypothesis: is every set of real numbers either countable or in a 1-1 correspondence with all of R?
Aims
To introduce the students to the general theory of sets, as a foundational and as an axiomatic theory.
Syllabus
Relation to Other Units
Set Theory may be regarded as the foundation for all mathematics. This course is a prerequisite, is a for the level M Axiomatic Set Theory M1300.
For students interested in the philosophy of mathematics,: this course is related to a number of units in the philosophy department in philosophy of mathematics. It should thus be of interest to any joint Maths/Philosoohy degree students.
The student should come away from this course with a basic understanding of such topics as the theory of partial orderings and well orderings, cardinality, ordinal numbers, and the role of the Axiom of Choice. He or she should also have become aware of the role of set theory as a foundation for mathematics, and of the part that axiomatic set theory has to play.
Lectures and Exercise Sheets.
The assessment mark for Set Theory is calculated from a 2 ½-hour written examination in April, consisting of FIVE questions. A candidate's best FOUR answers will be used for assessment. Calculators are NOT permitted be used in this examination.
Full Lecture notes will be provided.
There are 3 copies of both [1] and [3] in the Queen's Building library (one of each on restricted Short Loan as is a copy of [2]).
[1] Elements of Set Theory, by H.Enderton, Academic Press.
[2] Classic Set Theory, D. Goldrei, Chapman & Hall.
[3] The theory of sets and transfinite ordinal numbers, by B. Rotman & G.T. Kneebone, Oldbourne Mathematical Series. QA248 ROT.
The following cover more than we need (they are also in the library):
[4] The Joy of Sets K. Devlin, Springer (at least two library copies)
In [5] (Chapters 1-5, 10,11 are sufficient) but is couched in more sophisticated language.
[5] Discovering Modern Set Theory I by W.Just and M. Weese, AMS Graduate Studies in Mathematics, Vol. 8.
If you are intending to do the 4'th Year Axiomatic Set Theory, the following is paperback and is a worthwhile purchase; for the M32000 course Chapters 1-7 cover what we need.
[6]Intermediate Set Theory, by F.R.Drake and D. Singh, J.Wiley & Co.
