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.

Proofs of the fundamental theorem of calculus, the intermediate
value theorem, and the extreme value theorem.

Module Prerequisite

MA1125 Single variable clacuus and Introduction Analysis

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.