Here is the link to my personal course notes for this class. They are created based on Ross's, Rudin's textbooks and Professor Zhou's lectures. https://kelvinlee200113.github.io/notes/104.pdf (They might contain typos or logical errors.)

1. What's the difference between uniform continuity and continuity?
2. What's the difference between pointwise convergence and uniform convergence?
3. Is a series of continuous functions necessarily continuous?

• No, consider $f_n(x)=x^{n}-x^{n-1}$ and $\sum_n f_n(x)$ is not continuous.