In: Math
When choosing a topic, I would prefer to already know about it. This is because if you already know about the topic, then you are choosing that topic out of pure interest. You are fascinated by the topic and want to do a deeper study in that topic. On the other hand, if you are choosing a topic that you a know a little about, then you are choosing it only on the basis of an idea of what it would be or on the basis of other's opinions without actually knowing about the topic.
However, there are pros and cons for each of these choices. First let us discuss choosing a topic that we already know about. The pros of this choice is that you would be interested in the topic and would be able to do a deeper study with passion. Since you already know about the topic, you can also provide suggestions to others. You would also have to spend less time in understanding the key concepts. But the cons of this choice is that you can sometimes get carried away, without understanding the actual logic involved in the topic. It is also possible that the topic that you choose is not the right topic in the direction of your future endeavors.
Next let us discuss choosing a topic that we know a little about. The pros of this choice is that you would be able to gain a lot of knowledge and you may also develop a keen understanding of this topic. Also, if you know a little about this topic but still you are choosing it, it must be beneficial for your future endeavors. The cons of this choice is that you may not actually like the topic or may have difficulty in understanding it . It is also possible that this topic may lead you to a place different than you thought it would.