Hey Gengruiliang, 

Obviously, this is a common mistake made by my students too. This is a very useful website which explains the Chinese grammar points in English. I got many of my teaching ideas there. https://resources.allsetlearning.com/chinese/grammar/

This is the summary of the differences between ‘不’ and '没'.

1. 不

* is used for negating in the present and future. 

* is used to negate habitual actions  

* is normally used with adjectives 

* is used to ask questions

* is used almost exclusively with some verbs ( Correct: 不是、不在、不知道、不认识 ;  Wrong: 没是、没在、没知道、没认识)

2. 没

* is used to negate past questions  

* only 没 is used to negate 有 ( Correct: 我没有（没）钱、他没（没有）车 ;  Wrong: 我不有钱、他不有车）

* is used to make comparisons  

You may refer to the website for detail description.

All the best, Gengruiliang.

@CK Leow: “没在” and "没认识“ are wrong? This is quite surprising to see, because I've definitely heard them used before! Here are just a few examples from jukuu.com

没有，现在她没在这里。”公证人答道。

我要找的人没在。

他们当中我们没认识几个人

他没认识到危险性。

Is this a kind of non-standard useage similar to "ain't" in English?

Of course, 没在 is seen all the time when 没 and 在 are part of different phrases (ie. the 没 negates a verb after the adverbial phrase). But that's not really the same thing.

你为什么没在糕点上撒点糖呢?

我从来没在外面待到这么晚。

不 is adv, 没is both adv and verb,

so you don`t add a noun behind 不 directly, but you can add a verb behind 不 directly，

you can add a noun behind 没 directly，you can add a verb behind 没 directly too。

however，there is a special case, 没有 is a fixed set, 没and 没有 have the same meaning, 没有 is also a verb;

不是 is a fixed set too,

you can`t speak 不有、没是，

不有、没是 is never correct
when we read 没 mo4, 没 means "to sink", or "to submerge"