The notation used throughout the course is listed below. Notation in machine learning is not fully consistent, because the field overlaps with many others, but conventions have emerged and we follow them.
Across the course, a neural network is written $f_\theta$, with parameters $\theta$, so a prediction is $\hat y=f_\theta(x)$. $N$ is the number of training examples, and $n$ is kept for the size of a subset, such as one class or one test group. $C$ is the number of classes, indexed by $c$, and $B$ is the batch size. In Module 8, where an image is restored from measurements, $y$ is the measurement and $x$ the image to recover.