This course is designed to introduce and develop the fundamental skills needed for advanced study in Pure Mathematics. The precise language of professional mathematicians is introduced and the skills needed to read, interpret and use it are developed.

The 'Axiomatic Method' will be developed along with its principal ingredients of 'Definition' (a statement of what a term is to mean), 'Theorem' (something that inevitably follows from the definitions) and 'Proof' (a logical argument that establishes the truth of a theorem).

Constructing proofs, and much other mathematical practice relies on the difficult art of 'Problem Solving' which is the other main theme of the course. Facility comes only with practice, and students will be expected to engage with many problems during the course.

The principal areas of study which are both essential foundations to Mathematics and which serve to develop the skills mentioned above are sets and functions, and number systems and their fundamental properties.