MAU11204 Analysis on the real line
| Module Code | MAU11204 |
|---|---|
| Module Title | Analysis on the real line |
| Semester taught | Semester 2 |
| ECTS Credits | 5 |
| Module Lecturer | Prof. Florian Naef |
| Module Prerequisites | MAU11201 Single-variable calculus |
Assessment Details
- This module is examined in a 2-hour examination at the end of Semester 2.
- Continuous assessment contributes 10% towards the overall mark.
- Any failed components are reassessed, if necessary, by an exam in the reassessment session.
Contact Hours
11 weeks of teaching with 3 lectures and 1 tutorial per week.
Learning Outcomes
On successful completion of this module, students will be able to
- Prove or disprove logical equivalences.
- Use the predicate calculus.
- Prove or disprove set equivalences.
- Test the properties of relations.
- Prove and apply the theorems that are covered in class.
Module Content
- Propositional calculus and predicate calculus.
- Set theory and cardinal numbers.
- Open, closed, complete, connected and compact subsets of the real line.
- Heine-Borel theorem, Bolzano-Weierstrass theorem, uniform continuity.
- Proofs of the fundamental theorem of calculus, the intermediate value theorem and the extreme value theorem.