Aims & Learning Objectives:
Aims: The aim is to explore pure mathematics from a problem-solving point of view. In addition to conventional lectures, we aim to encourage students to work on solving problems in small groups, and to give presentations of solutions in workshops.
At the end of the course, students should be proficient in formulating and testing conjectures, and will have a wide experience of different proof techniques.
The topics will be drawn from cardinality, combinatorial questions, the foundations of measure, proof techniques in algebra, analysis, geometry and topology.