Undergraduate Course: Naive and Axiomatic Set Theory (MATH10034)
Course Outline
School |
School of Mathematics |
College |
College of Science and Engineering |
Course type |
Standard |
Availability |
Available to all students |
Credit level (Normal year taken) |
SCQF Level 10 (Year 4 Undergraduate) |
Credits |
10 |
Home subject area |
Mathematics |
Other subject area |
Specialist Mathematics & Statistics (Honours) |
Course website |
http://student.maths.ed.ac.uk |
|
|
Course description |
Course for final year students in Honours programmes in Mathematics.
1. Development in naive set theory of Cantor's basic results on cardinals and ordinals.
2. The Schroder-Bernstein Theorem and cardinal arithmetic, including exponentiation.
3. Ordinal number theory, the Axiom of Choice and Zorn's Lemma.
4. The formal axiomatic ZFC set theory and the role of the axioms in mathematics, including Power set, Choice, and Replacement.
5. Non-standard models in set theory. Inaccessible cardinals.
6. Independence results.
7. Godel's model of constructible sets, with reference to Choice and Continuum Hypothesis. |
Entry Requirements
Pre-requisites |
|
Co-requisites |
|
Prohibited Combinations |
|
Other requirements |
None
|
Additional Costs |
None |
Course Delivery Information
|
Delivery period: 2010/11 Semester 1, Available to all students (SV1)
|
WebCT enabled: Yes |
Quota: None |
Location |
Activity |
Description |
Weeks |
Monday |
Tuesday |
Wednesday |
Thursday |
Friday |
King's Buildings | Lecture | | 1-11 | | | 09:00 - 09:50 | | | King's Buildings | Lecture | | 1-11 | | | | | 09:00 - 09:50 |
First Class |
First class information not currently available |
|
Delivery period: 2010/11 Semester 1, Part-year visiting students only (VV1)
|
WebCT enabled: Yes |
Quota: None |
Location |
Activity |
Description |
Weeks |
Monday |
Tuesday |
Wednesday |
Thursday |
Friday |
King's Buildings | Lecture | | 1-11 | | | | | 09:00 - 09:50 | King's Buildings | Lecture | | 1-11 | | | 09:00 - 09:50 | | |
First Class |
Week 1, Tuesday, 09:00 - 09:50, Zone: King's Buildings. JCMB, Lecture Theatre C |
Summary of Intended Learning Outcomes
1. To understand how to set up the language of set theory.
2. To understand and use the concepts of transfinite cardinal and ordinal arithmetic.
3. To understand an axiom system for set theory. |
Assessment Information
15% Coursework/85% Examination.
Visiting Student Variant Assessment
15% Coursework/85% Examination. |
Please see Visiting Student Prospectus website for Visiting Student Assessment information |
Special Arrangements
Not entered |
Contacts
Course organiser |
Dr Liam O'Carroll
Tel: (0131 6)50 5070
Email: L.O'Carroll@ed.ac.uk |
Course secretary |
Mrs Alison Fairgrieve
Tel: (0131 6)50 6427
Email: Alison.Fairgrieve@ed.ac.uk |
|
copyright 2010 The University of Edinburgh -
1 September 2010 6:18 am
|