Finally, I & my mentor has decided to narrow my research area for my thesis in Scientific Computing/Computational Mathematics and not into the Theoretical Computer Science. The two are actually at the different ends of the spectrum of the blending of Math & Comp Sci.
Scientific Computing/Computational Mathematics is the use of computing to solve Mathematical problems (or science/engineering problems that can be modeled mathematically). So, here, computing is the tool, while math is the main idea.
Theoretical Computer Science is the use of Mathematics to solve Computing problems. So, here, math is the tool, while computing is the main idea.
We decided to do the former for various reasons:
- My mentor specialty is on Scientific Computing/Computational Mathematics and not on Theoretical Computer Science. This is the major reason. Besides, no one in IPB (perhaps in Indonesia) has the specialty in Theoretical Comp Sci, while in IPB there are a number of lecturers that master scientific computing. So, I can get a second mentor to consult to more easily.
- Scientific Computing has more practical use, which lead to make it easier to get research funding, get jobs (research and industrial), etc compared to Theoretical Comp Sci.
- The field is more related to my background in Engineering Physics, and my plan to pursue Ph.D in Mathematics (Applied Math). Mathematical modeling and computing of physical phenomena and system dynamics is at the heart of what I learned in my old days in Engineering Physics. So, it is more like I build up things on top of that foundations and it will be the base for my next studies. Isn't cool that you can be a Mathematician, Computer Scientist, Physicist, Software Engineer, all at once? 
Btw, I am not that lucky ones who already has thesis idea before coming into grad school. So, I must find ways to find problems worthy to be solved as thesis. One way is to become Teaching Assistant or Research Assistant. Luckily, I was very honored when my mentor accept me to become her TA, and it will be in Numerical Analysis class in the Department of Mathematics. Yes, Math Dept. Not Comp Sci Dept. . You will find open problems in one area only if you immerse yourself into it. Being a TA is one way to immerse yourself into something. More than TA, I hope I can join research too. So that I can publish as well.
So, my next days will be filled with a lot of reading of Numerical Analysis stuff and Scientific Computing/Computational Math in general. That includes refreshing and brushing up my MATLAB skill, which the last time I used it was about ten years ago. You know, I've been using C# A LOT lately, and some Mathematica for the fun of it. . I hope I can already find a title for my thesis by the end of this semester. So that next semester I can already start the writing and the research. I hope I can finish my master study on time.
But then, it all doesn't mean I don't dig Theoretical Comp Sci anymore. It's just for the thesis for my master degree. I don't know, if God allows me, I may have 30+ years ahead to be active in research/work, which some outputs may fall into the Theoretical Comp Sci category. Who knows...
In the time being, I will start to fuse all my energy and effort in mastering Scientific Computing/Computational Mathematics... and it will start with Numerical Analysis.
So, my loved ones (you know who you are!), I am sorry in advance if I may be a bit distracted in the days to come... (distracted, as I've always been (?)).
Dr. Sri, thanks!