Is it possible to convince a group of people that they master something, when they in fact don't? Is it possible to prove that a bunch of individuals were (or could be) convinced to be good at something (even really difficult), but it was in fact their illusion of knowledge?

Here's a bit more detail: let's take an average class at school. Let's give them a math teacher, whose way of teaching math is extremely mnemonic, still facing hard subjects. They'll be asked exactly what they were told at lesson, without any reworking demanded. The teacher will assign the highest marks to those students who are able to repeat the better. Will some of them eventually get to believe they are good at math, when in fact they can scarcely ever apply what they're studying or explain the ideas behind?

I did not find what I was looking for in the Wikipedia persuasion though.
Your question relates a bit to the self-efficacy literature.

Underlying ability is one cause of self-efficacy. And presumably, there are many mechanisms by which people can form an accurate opinion of their ability.

That said, there are various known ways of increasing or decreasing self-efficacy without changing actual efficacy.

For example, there is the big-fish-little-pond effect. Basically, you can increase self-efficacy by putting people in an environment with others who are less capable. 

Similarly, giving people feedback that they are good or giving people tasks suited to their ability will increase a sense of self-efficacy.
Some of these strategies are considered effective teaching especially if it helps overcome obstacles related to students even trying. But it can also be problematic if people allocate resources based on an inaccurate belief about their strengths and weaknesses.