How good are Lasallians? (part 1)

Let me open this column with mathematical questions. If you are a technical course student or professor, answer these:

1. Given a regular pyramid with a triangular base set in a two-dimensional plane, select any edge of the three sides of the face touching the plane and use the edge as an axis to turn over the pyramid. Find the probability that, after repeating the action n times, the original face is again touching the plane.

2. Let a, b, c be positive real numbers. In the xyz-space, consider the plane R consisting of points (x,y,z) satisfying the conditions
x <= a, y <= b, z = c
Let P be the source of light on the plane z = c + 1 moving along the ellipse
(x2 / a2 ) + (y2 / b2 ) = 1, z = c + 1
once around. Sketch and calculate the area of the shadow projected by the plane R on the xy-plane.

For the humanities counterpart, answer these:

1. Find the maximum and minimum values of f(x) = x3 − 2x2 − 3x + 4 over the interval from -7/4 to 3 inclusive.

2. Consider the point P (2, 0, 1) in xyz-space and the curve z = y2 in the yz-plane. As point Q moves along this curve, let R be the point of intersection of the line PQ (extended) and the xy-plane. Letting F be the graph of the set of points R, draw F in the xy-plane.

These are entrance examination questions to a Japanese university, to be answered in 25 minutes each. I obtained these from maa.org. The prominent detail is the degree of difficulty of the problems. Even second year engineering students will find the humanities problems obstinately difficult; so much more will humanities students.

If DLSU would follow this format for application exams, I guesstimate that 95 percent of the Lasallian population would be whittled. DLSU would earn lots of money from charging students fees for reconsideration. Spurt out some of the great names in DLSU, chances are they won’t be able to solve any.

Though it may not be applicable to DLSU, one should consider why even humanities students are required to have good mathematical knowledge. Even abstract matters like politics could be made systematic with mathematics, for mathematics is not tied to numbers alone. Rather, it is the thinking and problem-solving capacity that mathematics molds in a person. It is a thinking skill that no other subject can teach. There are no math-hating persons; there are only math-fearing persons.

Sidestepping from the issue, I find it weird that mathematics in DLSU, especially in engineering, is strictly mechanical in nature. It robs students the possibility of getting the most out of math. As Paul Zeitz said in the title of his book, math problem solving is an art.

Going back, one root of the problem may be the prevalent culture in the Philippine educational system. But that will not be discussed here. In DLSU, things should be considered differently, I hope.

How good are Lasallians?


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Star Scholars are normally considered the best of the best in the country of that particular batch. Some have made it a game to obtain the other prestigious scholarships: the Oblation and the Merit scholarships.

But in this setting, greatness is not absolute; it depends only on the criteria used to gauge greatness. Hence, a great boxer would tend to become mincemeat in the mixed martial arts ring because he does not know how to wrestle. He gains worldwide fame in the boxing ring because boxing does not place importance on wrestling, in fact, wrestling moves are barred. It is the same with scholarships, say the star scholarship: the way the selection process is structured favors some students to become star scholars, although they may not necessarily be the greatest.

Why would the champion of the Philippine Mathematical Olympiad of my batch be studying in DLSU and not have scholarship of any kind? Why would my friend become a Nanyang exchange scholar and yet not become a star scholar?

It depends only on the criteria. If the criteria places importance on holistic development, then not even Albert Einstein or Stephen Hawking would have become a star scholar had they studied here. However, they would far outshine any star scholar of their time – this will be their only merit.

It can be seen from another aspect: The Star Scholars – or awarded people in general – are such only because the people who can beat them are not given the same opportunity. I remember this crisply said by a professor. For instance, provincial students are not given the same opportunities to get into DLSU, since the Marketing Communications Office focuses more on the cities.