From an undergrad school of Math to a grad school of Computing just to learn Computable Analysis — What are the consequences? I am Park Shinhwan (박신환) from Korea University. I am a senior undergraduate student.

First, I have to mention that the topic of the undergrad school I'm in is not exactly Mathematics. It was Mathematics (수학과) until 2017, but just after I entered the school, its name changed to Data Computational Science (데이터계산과학전공). Though I don't think there had been much of a difference. It was just some lectures that heavily relies on programming languages such as C, Python, SAS, MATLAB, and Java were added.

Second, I have to mention that I am on a double major curriculums. The secondary major is Electronic &amp; Informational Engineering (전자및정보공학과).

As the title suggests, I have been interested in Computable Analysis since some months ago. Though I had wanted to enter a grad school of Mathematics, I concerned that most grad schools of Mathematics wouldn't teach about Computable Analysis.

But there was a gleam. Apparantly KAIST's grad school of Computing has a lab about Complexity and Computation of real numbers, and their professor researches about Computable Analysis! That means I definitely should enter this grad school.

Still, I have a concern. It looks like the topic of the lab has a gap from the mainstream topics of the grad school itself, and a grad student of the lab agreed so.

So what would be the consequences after I enter the grad school? I definitely will be dedicated to the lab, but should I take the lectures about mainstream topics anyway?

You can see the lectures of the undergrad school I'm in here, the lectures of the secondary major here, and the lectures of the grad school here.
Computable Analysis as a subject sits on the border of mathematics and computer science, and correspondingly, you can find researchers from this area in either kind of department. There is not much correlation between whether a given researcher works on the more CS or on the more math aspects of computable analysis and what department they are found in. Either kind of grad school will have courses which are helpful in becoming an expert in computable analysis, and others that aren't. As such I would not put much weight on whether a department is CS or math in figuring out whether it is the right place for you to pursue computable analysis as a subject.

As computable analysis is a rather niche subject, you'll only find it in select places. In Korea, KAIST is indeed the place to go for it. If you do want to do computable analysis at a math department, you could eg go to Japan instead. A source for who is active in this area, you can consult 
http://cca-net.de/members.php
although this list is not that terribly up-to-date.