My Days Are Numbered
I don’t know when I started being fascinated with Mathematics. I can still recall a quiz in kindergarten wherein we were asked to do three addition items, and three subtraction items. Addition was easy, with the help of fingers. However, I was stumped with the second part. Since I honestly do not recognize the operation, I just made the subtrahend as the answer. I got the first one: 6 – 3 = 3, but the two others are wrong (like 9 – 4 = 4).
As a grade schooler in Lourdes School of Quezon City, I treated Math just like any other subject. Apparently, it was my teachers who took notice of what I can do. Starting Grade 3, I became one of Lourdes QC’s MTAP contestants. It was always tough, every school year, battling with the Chinese schools, who end up being champs almost always (trivia: Math majors will recognize the phrase “almost always” since it is used in higher Math). I think the effect of being selected as a school representative for Math prompted me to elevate it as my favorite subject; the converse (I like Math, therefore I will try to make it as a contestant) wasn’t the case.
As a high schooler in PSHS, knowing that the generation’s best will be my classmates, I had low expectations for myself in terms of being a contestant for the school. Somehow, my Math 1 teacher, Ma’am Helen Salac, took notice of what I can do (but what her “basis” is, I wouldn’t know) , so (I think) she recommended me to Ms. Banjo Bautista, then Pisay’s Math coach, and it snowballed from there on. (Coming back to Pisay to coach the new set of marks a full circle) In my last two years in Pisay, Sir Petri took over as our Math coach.
I was exposed to different topics in my Math subjects in Pisay, and that was when I realized that Mathematics is vast, and what I have learned so far is just a small (and to a certain extent, trivial) portion of it. Computations and arithmetic does not define Math at all, though they are very essential. Knowing the possible values of x is not as important as the solution accompanying the final answer. Math, then, is not just about speed, but also about elegance. Every statement in a proof should be side by side a fitting reason. It is no wonder eventually that I had BS Math as my course of choice.
As a college student in the Ateneo, the elegance part of Math took over, though this wasn’t always apparent to me and my blockmates, especially during hell weeks. Diversity came full blast too: Algebra, suddenly, became a mere tool, so that we will be equipped with the next courses to be served. There’s of course Calculus, taught in Math 5 in Pisay. We also had Abstract Algebra, where we learned that not commutativity is not always true in a given field. Linear Algebra focuses on matrices, its use in systems, and how they represent transformations. Real Analysis (no, there’s no “Fake Analysis”), summons calculus powers and analytic thinking. Ordinary Differential Equations was altogether different, but fascinating nonetheless, with its many visualizations. Actuarial and Financial Mathematics were offered as electives, and I took them both with excitement. Complex Analysis is about the algebra and calculus of complex numbers (a + bi), and many similar and contrasting results were discussed (we also had an oral exam in this subject). My favorite would have to be Discrete Mathematics, where counting techniques, combinatorics, recurrence relations, generating functions, Math logic, and graph theory arose. My interest in the subject made me excel too in my Probability class, and later on, Statistics. Of course I had a Geometry class in college, but we weren’t limited to Euclidean Geometry; we also discussed the hyperbolic, spherical, and affine kind. Another favorite is the Problem Solving Techniques class under Fr. Nebres. The aforementioned subjects, by the way, were scattered in my four-year stay, if you should ask.
I think I learned in high school how Math works, and I learned in college why Math works.
Still, the wonders on Math is evident in both the computational and conceptual perspectives. Recently, I shared to Thy Kingdom Camia one of my more nerdy Math games. When in traffic, I have the habit of looking at the plate numbers of passing vehicles. Standard plates contain three letters and three numbers. With the letters, I try to think of words (in English or Filipino) wherein the three letters appear in sequence. Given WRT, one cane think of write, warts, warranty, swerte, and so on. The numbers part is more exciting. I try to express the three-digit number as a sum of squares, and each square should only be used once. Thus, if the plate reads WRT 791, 791 should be expressed as 729 + 36 + 25 + 1 (the squares of 27, 6, 5, and 1, respectively). 467 can be expressed as 289 + 144 + 25 + 9 (the squares of 17, 12, 5, and 3, respectively). It is possible that a three-digit number can be expressed as a sum of unique squares in more than one way. Well, some of Camia became interested, but most were at best shocked and/or surprised, all the more when I said that the game should be played mentally, since you should try your best to find the sum before the vehicle leaves and another plate number is waiting to be decoded. More strange looks. Haha.
Number Theory (in which the little game above is categorized), to some, is useless and is relegated as just a series of exercises, but a certain field of Math can be around for centuries without apparent use, only to be very essential in the next. A fine example is cryptography, used by banks in security, and even the Internet. Two extremely large prime numbers are multiplied, and it (the product, an even larger number, but composite) serves as the code of protection. Only the makers of the code know the encoding key (big prime number 1) and the decoding key (big prime number 2). Before, the search for prime numbers is not considered important at all.
It took me very long to post a Math article just because I don’t know where to start. This entry isn’t even coherent. I have to admit Math figured prominently in my life (I deal with numbers on a daily basis), and I think it still will in the years to come. I hope too that it will, in yours.
As a grade schooler in Lourdes School of Quezon City, I treated Math just like any other subject. Apparently, it was my teachers who took notice of what I can do. Starting Grade 3, I became one of Lourdes QC’s MTAP contestants. It was always tough, every school year, battling with the Chinese schools, who end up being champs almost always (trivia: Math majors will recognize the phrase “almost always” since it is used in higher Math). I think the effect of being selected as a school representative for Math prompted me to elevate it as my favorite subject; the converse (I like Math, therefore I will try to make it as a contestant) wasn’t the case.
As a high schooler in PSHS, knowing that the generation’s best will be my classmates, I had low expectations for myself in terms of being a contestant for the school. Somehow, my Math 1 teacher, Ma’am Helen Salac, took notice of what I can do (but what her “basis” is, I wouldn’t know) , so (I think) she recommended me to Ms. Banjo Bautista, then Pisay’s Math coach, and it snowballed from there on. (Coming back to Pisay to coach the new set of marks a full circle) In my last two years in Pisay, Sir Petri took over as our Math coach.
I was exposed to different topics in my Math subjects in Pisay, and that was when I realized that Mathematics is vast, and what I have learned so far is just a small (and to a certain extent, trivial) portion of it. Computations and arithmetic does not define Math at all, though they are very essential. Knowing the possible values of x is not as important as the solution accompanying the final answer. Math, then, is not just about speed, but also about elegance. Every statement in a proof should be side by side a fitting reason. It is no wonder eventually that I had BS Math as my course of choice.
As a college student in the Ateneo, the elegance part of Math took over, though this wasn’t always apparent to me and my blockmates, especially during hell weeks. Diversity came full blast too: Algebra, suddenly, became a mere tool, so that we will be equipped with the next courses to be served. There’s of course Calculus, taught in Math 5 in Pisay. We also had Abstract Algebra, where we learned that not commutativity is not always true in a given field. Linear Algebra focuses on matrices, its use in systems, and how they represent transformations. Real Analysis (no, there’s no “Fake Analysis”), summons calculus powers and analytic thinking. Ordinary Differential Equations was altogether different, but fascinating nonetheless, with its many visualizations. Actuarial and Financial Mathematics were offered as electives, and I took them both with excitement. Complex Analysis is about the algebra and calculus of complex numbers (a + bi), and many similar and contrasting results were discussed (we also had an oral exam in this subject). My favorite would have to be Discrete Mathematics, where counting techniques, combinatorics, recurrence relations, generating functions, Math logic, and graph theory arose. My interest in the subject made me excel too in my Probability class, and later on, Statistics. Of course I had a Geometry class in college, but we weren’t limited to Euclidean Geometry; we also discussed the hyperbolic, spherical, and affine kind. Another favorite is the Problem Solving Techniques class under Fr. Nebres. The aforementioned subjects, by the way, were scattered in my four-year stay, if you should ask.
I think I learned in high school how Math works, and I learned in college why Math works.
Still, the wonders on Math is evident in both the computational and conceptual perspectives. Recently, I shared to Thy Kingdom Camia one of my more nerdy Math games. When in traffic, I have the habit of looking at the plate numbers of passing vehicles. Standard plates contain three letters and three numbers. With the letters, I try to think of words (in English or Filipino) wherein the three letters appear in sequence. Given WRT, one cane think of write, warts, warranty, swerte, and so on. The numbers part is more exciting. I try to express the three-digit number as a sum of squares, and each square should only be used once. Thus, if the plate reads WRT 791, 791 should be expressed as 729 + 36 + 25 + 1 (the squares of 27, 6, 5, and 1, respectively). 467 can be expressed as 289 + 144 + 25 + 9 (the squares of 17, 12, 5, and 3, respectively). It is possible that a three-digit number can be expressed as a sum of unique squares in more than one way. Well, some of Camia became interested, but most were at best shocked and/or surprised, all the more when I said that the game should be played mentally, since you should try your best to find the sum before the vehicle leaves and another plate number is waiting to be decoded. More strange looks. Haha.
Number Theory (in which the little game above is categorized), to some, is useless and is relegated as just a series of exercises, but a certain field of Math can be around for centuries without apparent use, only to be very essential in the next. A fine example is cryptography, used by banks in security, and even the Internet. Two extremely large prime numbers are multiplied, and it (the product, an even larger number, but composite) serves as the code of protection. Only the makers of the code know the encoding key (big prime number 1) and the decoding key (big prime number 2). Before, the search for prime numbers is not considered important at all.
It took me very long to post a Math article just because I don’t know where to start. This entry isn’t even coherent. I have to admit Math figured prominently in my life (I deal with numbers on a daily basis), and I think it still will in the years to come. I hope too that it will, in yours.
Labels: Math, plate number game
posted by mardan at 10:30 PM
2 Comments:
pax et bonum!
ma'am salac is gifted that way. :) she and ma'am banjo are two of the best teachers i've had.
your little brother,
JoEd, OFMCap.
I know I'm uber-late in reading this entry, but I just had to say: I *heart* this entry. I don't have the same ardent relationship with Math that you do, but I can totally relate to the nerdy fascination with one's field of study.:)
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