browsing and surfing

[Ju]

1. I am browsing the internet.
2. I am surfing around internet.

3. I am browsing the web.
4. I am surfing the web.

Are the above sentences correct?

Thank you,

[SirGod]

* Not a teacher

Only 1, 3 and 4. I would also write Internet (with a capital i). The same thing for Web (with capital w).

[5jj]

Only 1, 3 and 4.
I would also write Internet (with a capital i). The same thing for Web (with capital w).

I see no need for capital letters there.