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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.