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Module MAU11204: Analysis on the real line

Credit weighting (ECTS)
5 credits
Semester/term taught
Semester 2
Contact Hours
11 weeks, 3 lectures including tutorials per week
Lecturer
Prof. Florian Naef
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
MAU11201 Single-variable calculus
Assessment Detail
This module will be examined in a 2 hour examination. Continuous assessment will contribute 20% to the final grade for the module at the annual examination session. Re-assessments, if required, will consist of 100% exam.