You are here
Courses > Undergraduate > Courses & Modules
Module MA1124: Analysis on the Real Line II
- Credit weighting (ECTS)
-
5 credits
- Semester/term taught
-
Hilary term 2015-16
- Contact Hours
-
11 weeks, 3 lectures including tutorials per week
-
- Lecturer
-
Prof. Donal O'Donovan
- 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.
- Module Content
- The purpose of this module is to rigorously prove the theorems that
have been used in Analysis I, to introduce the students to set theory
and logic, and to introduce the students to the topology of the real
line. Topics will include
- The propositional calculus and the 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.
- Module Prerequisite
- MA1123 Analysis I
- Assessment Detail
- This module will be examined in a 2 hour examination in Trinity term. Continuous assessment will contribute 15% to the final grade for the module at the annual
examination session. Supplemental grade will consist of 100% examination.