One thousand and one yellow daffodils

A long day of staring at my notes, feeling stupid, tired, coldy and demotivated. Things finally started to go click about an hour ago. Assignment 4 deals with implicit functions over the space of n × (k+l) matrices - not something I've ever worked with before. I have that strange, half-numb, groping feeling that comes from working with formulae which describe something I don't yet understand.

Question 1 of the assignment asks us to prove that there is a unique z for every x in the relation z⁷ +x⁴z = x⁵ + 1. I did this using what Chris has called the Implicit Function Theorem, second version [seems to be similar to the Wolfram MathWorld version]. This is probably an example of what, in first year, we used to call "using a steam roller to crush a walnut", but I don't really know how else to go about it. I don't like this practice of having to start the assignment before the first tutorial.

Correction: I didn't get 1.5/2 for question 3 of assignment 2 - it was actually 0.5/2. Today I forced myself to go through the model answers for the assignment, a somewhat informative exercise.