intro to complex numbers
This course exists to level the playing field. Like most of the cohort (as far as I could tell), I had covered the content at school before, but a small proportion hadn't studied A-level Further Maths, or came from a country whose school curriculum didn't cover complex numbers. It runs as just two lectures in the very first academic week.
Lectured by Balliol's very own tutor Luci, the course introduces complex numbers more rigorously than at school, but doesn't go far beyond this. Complex numbers pop up in many other Prelims courses, so an understanding of the fundamentals is necessary. The Part A Complex Analysis course goes into much more detail.
The one problem sheet was fairly simple, although I do remember being marked down for not explaining my solutions rigorously enough.
syllabus
Complex numbers and their arithmetic. The Argand diagram (complex plane). Modulus and argument of a complex number. Simple transformations of the complex plane. De Moivre's Theorem; roots of unity. Euler's theorem; polar form of a complex number. Polynomials and a statement of the Fundamental Theorem of Algebra.