This week I’ve been wrapping up Unit I1: Real functions and graphs, and making a start on I2: Mathematical language. The last few sections of I1 introduce some really interesting-looking graphs – I particularly like cycloids and cardoids. Partly because the graphs remind me of Spirograph pictures, and partly because the names sound like monster robots from a classic sci-fi film!

Cycloid

Cardoid

I’m really enjoying I2 so far, much more than I1. The first section is about sets, and it introduces a bit of new notation for the binomial coefficient – instead of writing $^nC_k$ to indicate choosing k items from a set of n elements, we now have to write it like this:

It looks a bit weird to me, like it’s supposed to be a vector. I wonder if it’s actually anything to do with vectors, or if it’s just a coincidence?

Anyway, the second section of I2 is about functions, which isn’t quite as exciting as the sets stuff, but it seems fairly straightforward, with a lot of material repeated from MS221. It does introduce a new way of representing an onto function, though:

I remember having a bit of trouble getting the definition of an onto function to stick in my head during MS221, so it’s nice to have a good, clear diagram to illustrate the idea. Hopefully it will stick this time!