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Module MAU11204: Introduction to Set Theory and General Topology
 Credit weighting (ECTS)

5 credits
 Semester/term taught

Hilary term 201920
 Contact Hours

11 weeks, 3 lectures including tutorials per week

 Lecturer

Prof Paschalis Karageorgis
 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
 MAU11202
 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. Reassessments if required will consist of 100% exam.