## I Wrote for You, You Wrote for Me

When you know it is your last year in your undergraduate endeavor, one thing you have to prepare is your yearbook write-up. It is not easy (again at least to me) because you have to find someone who can do it for you. Luckily, I have friends and one of them happened to be my best bud – RC Mancenido.

It was October 2010 when I had written a write-up for him and after some short three months, he did one for me. Apparently, they had an earlier deadline.

**Here’s mine for him:**

Reserved and shy – he is mistaken to be so;

but knowing him more proves anyone who thinks of this wrong.

Academic person is his best description of all,

a clever man who never misses the honor roll

Lover of wisdom, of books and the Bible,

such passions make him exceptionally knowledgeable.

Principled in good terms, so don’t get him wrong;

for he is a Christian, in heart and in soul

Hats off for this one of a kind man,

everyone who knows him couldn’t stop giving him a hand.

Aside from his popular and shallow “GC, tongue-tied and quiet” descriptions, Ralph Christian Mancenido is a writer, an award-winning essayist, a man of history, a Facebook addict, a penny-wise, a music lover, a balladeer, a frustrated math enthusiast, an unprofitable servant, a Christian, and a Bible reader.

Known to only a few is his being overly neat and spick-and-span as proved by an average of 45 minutes of taking a bath, 30 minutes being the minimum, and twice a day. Another undisclosed fact is his ambition of being a diplomatic official – an ambassador of he-only-knows-what.

Most striking is this: Ralph has dreamt of being the FIRST summa cum laude graduate of the NCPAG but “unfortunately” the dream turned to just being the SECOND…

**Here’s his for me:**

I met a budding mathematician three years ago (whether in the body, I do not know; or outside of the body, I do not know; God knows) such a one was to become my best friend, a comrade who sticks closer and more thoughtful than a brother does.

As the careful ears decipher the code of notes and unleash the harmony in music, the same is the eyes of his mind in appreciating the exactness of the universe through numbers and logic. Profoundly fascinated in finding meanings out of abstractions, he effectively imparted to me a deeper perspective in viewing the reality while maintaining a sense of contentment amidst simplicity.

He is hard to define, I know. A highly sociable person and yet still has a pinch of shyness within himself. He is a student that frequently spends a whole night without sleep just to finish a math problem set and yet still has an unswerving energy to perform his tasks as a Bible advocate in the University.

I could see him in the future as a brilliant actuary just like what he wants to be. That budding mathematician I met three years ago undeniably has a great potential to mark his name in the history. Yet, with God’s help and mercy, he will stay as humble as he is.

In his write up for me, I have to mention that there’s no chance for me to be a brilliant actuary now. Also, RC Mancenido did graduate as a summa cum laude.

Yours Truly,

Random Choice

## Goodbyes to an Old Self

I used to be an achiever, a know-it-all, a challenger. But short six years ago, I wished for mediocrity. My reason – I was tired of expectations.

That is how UP came. I chose the university as my foreseen refuge from my past world of glories. I wanted to be an average student.

The hope did not fail me. I was a typical UP student. I have met friends who are far better than I was, and it felt home. Just like the others, I was a late-night crammer, a perennial absentee, and an org buddy. But I was conscious. My simple goal then was to learn more and not to not make the grades. In most of my college days, I was never a nerd nor a grade conscious.

There were few times though when I grieved for the feeling of being one of the top scorers. And to end such a nostalgic sense, I remember myself resorting to my ‘*I can if I want’ *delusion. It has been a really long delusion. I still got the ego back then.

Come my last semester, I faced a near no-graduation experience. One of my math electives has almost plunked; I needed to hit a high target grade just to pass. Passing back then meant my graduation. I cried but I made myself for my friends helped me. The last and final exam of my undergraduate years was a make-it or break-it. With God’s mercy, I graduated… with no Latin honors. And I still can recall my proud self saying “*I should have been, if I wanted to*”. Ego, still.

Today, I am writing this to distinguish the past from the present. Reliving my past glories is a dangerous narcotic to me. I thank God I noticed it. I must admit, it is only now that I am realizing the delusion and the ego I had.

In every time I start barking up my hypothetical *what if*’s, I steer myself to seeing the real past – that I did not make it. And I can say that it is not by choice, but it’s what I am. I note to self that I must have no regrets. I know what I did, I had my priorities. I did it God’s way, and with His help.

Yours Truly,

Random Choice

## All I’ve Got Is Twenty-One

When asked if I want to be a teacher or a researcher, I positively came back with ‘I want to be both’. YES, I wanted to be mathematician who can also teach. And I got the job.

But the first semester of academic year 2012-2013 has got me thinking, do I really want what I am doing?

At the moment, I still don’t know the answer to such an unexpected follow-up. I’m already 21 and I still don’t have a picture of who I am really gonna be.

All I know is that since I started teaching, I am 21 things richer now.

- The first day of school is the biggest day. Break the barrier.
- Ice-breakers are my good conversation starters.
- Some students did not really learn maths in high school, they learned to memorize.
- The least I could do is to make a student not a math-hater.
- There are motivations in defining a thing. Make them think why things are the way they are.
- Teach them how to play by teaching them the basics first. Encourage self-discovery.
- Mortal sins in maths will always be committed, correct them anyway.
- Some students do nod even if they don’t understand a thing.
- That attendance is not important is a case-to-case basis.
- Never underestimate determination.
- That sleeping in class is okay is a case-to-case basis.
- Give good rewards and incentives. After all, grades don’t matter.
- There will always be classes that you will love and classes that you will each time hate, but always wear a smile.
- Encourage them to consult, they won’t do it anyway.
- There are students who are better than the teacher. Most of them think they are, rarely some of them are really are.
- Failing your students is emotionally challenging but harder is to pass them with you knowing that they learned nothing.
- Studying while teaching makes you understand your students better.
- There is such a thing as mathematical maturity.
- What is easy for you can be the hardest thing for students
- The teacher is not always the teacher. He also learns from his students and from his discussions.
- It is difficult to end a semester.

It’s not really bad after all. I learned new things, I made new friends, and hopefully I touched new lives. But then again, do I belong to the academe? 😦

Yours Truly,

Random Choice

## With Tears, The One I Wrote Some Years Ago

It was March 2011 when I finished writing my manuscript – my undergraduate research paper. It felt happy and accomplished. Till I found out that I haven’t written my Acknowledgements.

Then I became nostalgic and happier and lonely. And for the next 15 minutes of that moment, I wrote:

My sincerest gratitude is to You Lord for this paper could have not been possible to accomplish without You in my life.

I thank God for giving me a family who has never stopped believing in me. To my grandmothers and grandfather who shared my dreams and aspirations by always morally and financially supporting me, I know it wasn’t always easy but for loving me, I owe you my best thanks. I will never forget.

I thank God for giving me the chance to work with Dr. Agnes Paras. For your patience, guidance and understanding, I have no word but thanks.

I thank God for sending me my best of friends in the Institute of Mathematics: Kaye Sangalang, Abbey Otilano, Hermie Monterde, and Freda Pueblos. For the concern and sympathy through all the good and bad times we had in our endeavors, thank you.

I thank God for lending me a short but sweet moment with my fellow Bible readers. For making my stay in UP memorable and worth it; for taking care of me during my saddest days; for the help of making me who I am now; for the glimpse of eternal friendship, thank you BREAD Society.

I thank God for the best Kuya and the lovable Ingkong who crossed my life out of the blue.

From the humblest to the greatest things I have, for the things I know and for the things I do not know, and for the unspeakable gift, to God be the glory.

Sincerely Yours,

Random Choice

Q.E.D.

## My Axiom of Choice

Too many options give us too many choices. But what gives us no choice? Is it the absence of options? When we have no choice, do we really have ‘no choice’, at all?

I chose to tickle your mind with my elementary questions and assumptions on ‘choice’, thinking that the word is good to play around and with other words. But this piece is not about the usual ‘choice’ that you know; not on the typical ‘choice’ that you can take for granted.

Would you believe that choice is a mathematical term? There is actually a *choice function*, an *Axiom of Choice*. Let me be me for a while.

If C is a family of nonempty sets, then we can choose a member from each set in that family. In other words, there exists a function f defined on C with the property that for each set S in the family, f(S) is a member of S.

If you find this hard to understand, don’t worry, this is not my main point. But such a function is called a *choice function*. Very roughly speaking, it is a function on a family of nonempty sets which “chooses” a member from each set in the family. And the *Axiom of Choice* says that we almost always have a *choice function*.

It is indeed like saying that we almost always have a choice. Isn’t it counterintuitive? Well that is Zermelo’s *Axiom of Choice*. But this piece is not about the ‘choice’ that a person of my shoes will impliedly know; not on a mathematical version of having a choice.

This piece is about My Axiom of Choice – the one I had so few years ago. The Axiom of Choice I learned and heard from a mentor; and that same axiom taught me how to do well.

That Axiom of Choice I always use when in doubt and lost; the one that makes me see a choice when I feel I have no choice. And in troubled times, it is one that gives me no choice but to keep dreaming and to keep the fight.

I have chosen to embrace my Axiom of Choice. And when I picked it, I was in full grasp that it is a once and for all choice; and so that Axiom of Choice gives me no real choice but to stay firm and dedicated and strong.

My Axiom of Choice, sometimes I call it, faith.

I might be so down at times; but all I have to do is to invoke My Axiom of Choice.

With tears,

Random Choice

Q.E.D.

## Corollary to a Theorem

We often hear the words *conjecture*, *theorem*, *postulate*, *axiom*, *corollary*, and *lemma* in the field of Mathematics. And not one of them is synonymous to the other – at least to me.

Mathematicians are usually keen to patterns. Mathematical results, just like in any other hard science, are derived from observations. If, for example, you have spotted a pattern that is seemingly present in all the things you are observing, you will CONJECTURE its being true. Through a rigorous logical and mathematical argumentation from your set of AXIOMS (propositions regarded as self-evidently true), you will prove that your conjecture is true. And when proven so, it will be a THEOREM. When another idea is an immediate consequence of your theorem, then it is COROLLARY. A corollary, hence, is also a theorem which is a result of some other theorems.

Let us have a very simple and relevant illustration.

Consider on one hand Jose Luis Miranda claiming that June 30, 2012 is the end of the world. On the other hand, Eliseo Soriano saying that June 30 is not yet the end of the world. Also take as an axiom the biblical words:

“*When a prophet speaks in the name of the LORD, if the word does not come to pass or come true, that is a word that the LORD has not spoken; the prophet has spoken it presumptuously. You need not be afraid of him*” (Deut. 18:22)

Both Miranda and Soriano made their claims sufficient days before the 30th of June. So we may really view the situation as a prophet’s versus another prophet’s pronouncement. (Click this for more background on the issue.)

But TODAY is July 10, 2012 and my world is still mathematical! Just to say, Miranda is wrong and from our axiom, WE SHOULD NOT BE AFRAID OF HIM.

Our theorem could now be stated as:* “June 30, 2012 is not end of the world and Miranda has just spoken presumptuously and that he is false!”*

Corollary to our theorem is that SORIANO IS RIGHT IN HIS CLAIMS.

To GOD be the glory!

Yours Argumentatively,

Random Choice

Q.E.D.

## Eureka! I’m Blogging

*“We all use math every day; to predict weather, to tell time, to handle money. Math is more than formulas or equations; it’s logic, it’s rationality, it’s using your mind to solve the biggest mysteries we know. **“*

Thanks to the traditional opening line of the series *Numb3rs*, I’ve got perfect words to start with.

In my case, I need to use Math every day. This is not actually a necessity but a preference. I could be someone else than a typical college instructor of Mathematics who would often bore students with his discussions of often-regarded-as impractical matters of life. But at the moment, I want to be an educator.

*“But wait, impractical? Ouch! Challenge accepted! I will prove you wrong!”*

That’s the inside me, arguing. Although I know that it is hard to prove something, I know that at the very least, I can substantiate it’s not being impractical.

So today I claim:

*Through Mathematics, I can see things.*

Eureka! I’m blogging and promising to share in simplest words the perks of being a math enthusiast.

To GOD be the glory!

Yours Truly,

Random Choice

Q.E.D