By the end of this unit you should be able to:
Section 1: Sets
use set notation;
determine whether two given sets are equal and whether one given set is a subset of another;
find the union, intersection and difference of two given sets.
Section 2: Functions
determine the image of a given function;
determine whether a given function is one-one and/or onto;
find the inverse of a given one-one function;
find the composite of two given functions.
Section 3: The language of proof
understand what is asserted by various types of mathematical statements, in particular implications and equivalences;
produce simple proofs of various types, including direct proof, proof by induction, proof by contradiction and proof by contraposition;
read and understand the logic of more complex proofs;
disprove a simple false implication by providing a counter-example.
Section 4: Two identities
understand and use the Binomial Theorem;
understand and use the Geometric Series Identity;
understand and use the Polynomial Factorisation Theorem.
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