Please note that Patrick recaps the last lecture near the start and you may want to pause those slides. You can find that lecture here: https://www.youtube.com/watch?v=aRx9yTxpJOE
In this lecture, the fourth in the first year undergraduate 'Constructive Mathematics' course, we state and prove the Banach contraction mapping theorem (in one dimension) for guaranteeing the convergence of a fixed point iteration.
You can watch many other student lectures via our main Student Lectures playlist (also check out specific student lectures playlists): https://www.youtube.com/playlist?list=PL4d5ZtfQonW0A4VHeiY0gSkX1QEraaacE
All first and second year lectures are followed by tutorials where students meet their tutor in pairs to go through the lecture and associated problem sheet and to talk and think more about the maths. Third and fourth year lectures are followed by classes.