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PhD 2023 #004: We are DOST scholars. Finally!

So today we are officially DOST-ASTHRDP scholars. Just received word from one of my classmates. Finally! It's been a long time coming. I would say the news has less impact than I expected. Maybe I grew tired of waiting. But I was relieved. Relieved that it's actually happening. At last! Relieved that there's gonna be support from DOST. To be honest, I was ecstatic for a while. Yay! But it only lasted a second? Three seconds, max. Because I remembered that I have so much to do - exams to take, weekends to study. I am way behind on my coursework. I also have job responsibilities to fulfill before I officially resign. It's funny how my mind works. It's like it doesn't want me to celebrate. But I'm gonna freaking celebrate. Shut up, mind! I deserve this. Live life one day at a time. Do things one at a time. Ciao, for now. Remember, life is beautiful.

PhD 2023 #003: Why pursue a PhD in Math?

So some students have been asking me what's the point of doing a PhD? What are the advantages? And I answer that usually a PhD is needed to be a school principal. I gave that answer because that's the context that they can relate to. But that's not really my answer. I don't plan on being a school principal or have a management role anytime soon. So, why pursue a PhD? The main reason is because I wanna do something that I'm naturally good at. I'm good at math so I want to lean more into that. Because that's where my advantage lies. Which is funny because I wasn't always a natural at math. Yes, I was good at math in my elementary and high school years. I was even an MTAP participant at one point. But I didn't think of doing math as a career. Until I had no other choice. But that's a story for another time. High school and college math might have come easy to me. But proper math was a different beast. Rigorous thinking did not ...

PhD 2023 #002: What is PhD 2023?

PhD 2023 is a series of blog posts that I'm planning to write regarding my experiences as a PhD Math student at MSU-IIT . Photo by  Pixabay  from  Pexels As you may or may not know, I was a board exam topnotcher in the September 2016 LET . And I regret that I haven't documented the whole journey. That would have been epic.  So now that I'm starting this new journey, it would be a waste not to document it all - the highs and lows, the sighs and the woahs.  I even suspect that I enrolled in this program simply because I want to document it. I may be joking but there's some truth to this. Anyway, this PhD series is going to be non-linear.  So is life. So is research. It's going to mirror the process of doing research. If all goes well, I'll graduate by 2023. Hence the name. But that's a long way to go. There's no rush. I wanna enjoy the process. 

PhD 2023 #001: Baptism by fire (How I failed my first exam as a PhD student)

According to investopedia.com , "b aptism by fire is a phrase originating from Europe that describes an employee that is learning something the hard way through a challenge or difficulty." I regret to start this series with this post. But this experience prompted me to document it all. Something to look back to when all is said and done. So here’s what happened. I just took my first exam as a PhD Math student. And I did poorly. Not zero, but pretty bad. Photo by  Andrea Piacquadio  from  Pexels   Our first long exam on Abstract Algebra was on the 20 th  . I asked to take the test the day after because I didn’t have enough time to finish the exam that day. I had other obligations. Also, I haven’t studied anything. No notes nor printed copies of the reference book which is Algebra by Hungerford. How could I? I haven’t attended a single lecture. But that’s not an excuse not to prepare beforehand. More on that later. So the exam day came. And ...

Inertia is a double-edged sword

You know that feeling when you're stuck doing the same thing again and again with no change in sight? It's annoying, right? It's very hard to get out of it when you've been stagnant for so long. It's so hard to make a change. You're stuck in the same position as you were before. That's why it's so hard to start a new habit. Or stop a bad one. Unless, something will trigger you to move. Internally or externally. That's the downside of inertia. The good side of inertia is when you're moving, you're really moving. Right? Once you get started, momentum is on your side. In physics speak, momentum is mass times velocity. The greater the velocity, the greater the momentum. When you're moving, when you're constantly doing action, it just keeps you going. You get energized so you keep going then you see results so you keep going and so on and so forth. It's a self-sustaining loop. But what is inertia? According to Wikipedia, "iner...

Proving is like connecting the dots

I want to talk about this. I know that YouTube has auto-generated captions if the uploaded video is in English. It would be so much more useful if they can also generate captions for other languages, for example, Filipino. Like that would be awesome. This post is actually generated from an audio file that I uploaded on youtube which I edited afterwards. Anyway, this is the plan. It's really... I'm having a hard time just being spontaneous. I have a huge filter and I just can't spit things out. One other option is to write on the phone. But that's actually hard because the tactile feedback from typing with a physical keyboard is not there. It's hard. Talking is much more spontaneous. I overthink less when talking. I've been wanting to post a tutorial video about proving. I missed proving so much. Say you know what you're trying to prove so you start with the given, right? You start with what you know based on the definitions. Then you come up with implica...

Special Numbers: 0 and 1

Genesis 1:3-1:4 Among the integers, I believe 0 and 1 are the most interesting. Adding 0 to any number does not change that number. More precisely, a  + 0 =  a   and 0 + a = a for all integers  a . In group theory terminology, 0 is the identity element under addition or the additive identity. You may ask, is there also such a thing as multiplicative identity? Yes, there is! In fact, by the title of this post you probably know what it is. One is the multiplicative identity. That is,  a  x 1 =  a  and 1 x  a  =  a  for all integers  a . Does 0 play an important role in multiplication? Yep! Multiplying by 0 always yields 0. More precisely,  a  x 0 = 0 and 0 x  a  = 0 for all integers  a. We may also say that 0 the absorbing element under multiplication. A field has at least 2 elements A field is a set together with two operations satisfying certain conditions . An example of...