A level Mathematics, or equivalent. We look at the main number systems, integers, rational numbers, real numbers and complex numbers, and the mathematical ideas drawn from set theory needed to make the concepts involved clear.
Numbers are abstract objects.
How can we be sure that they have the properties we ascribe to them. We look at the main methods of proof used by mathematicians to establish mathematical facts. Why do we need proofs. The main number systems. Complex numbers, modulus and argument, triangle inequality, De Moivre's Theorem, n-th roots of complex numbers.