asymptotes

I began my graduate studies in computer science in 2003. After 3 years of part time study, I started groping for a thesis topic in Artificial Intelligence (AI). The experience was fun (and torturing- I had to change topics 3 times, but it was still fun… and torturing). I learned a couple of things along the way. I outline these things in this article. 1.Error feedback leads to perfection Neural Networks (NN) is an AI technique that mimics how a brain learns through billions of neurons and their interactions with each other. One of the most popular training (or learning) method for Neural Networks rely on informing other (digital) neurons about the error levels of the current output of the network. This is called the Back Propagation Algorithm. Lesson Many times we dread facing our faults, whether we discover them ourselves or others inform us about them. But come to think of it, knowing about our faults is one of the best ways to improve. I...

People tend to think that exams would be much easier if they're in multiple-choice format. But does having more choices really make them easier? Consider the test item below: Who among the following scientists contributed to the atomic theory? A.) John Dalton B.) Charles Darwin C.) J.J.Thompson D.) Albert Einstein ... ... ... S.) All of the above T.) All letters above that are valid Roman Numerals U.) All letters above that correspond to a Fibonacci number V.) All letters above which are valid symbols of an element in the periodic table W.) All letters above which are elements of the union of the sets in U and V X.) All letters above which are elements of the intersect of the sets in V and W Y.) None of the above Z.) Sirit (Filipino word for ¨I give up¨)   Post Script A few lessons we can gather from the above post: * Having a lot of choices may not be good all the time. * No matter how many choices you have, you always have to choose the right one. * ...

Note: You need to know Tagalog/Filipino to appreciate this proof.  Problem: Prove the following: log 2   = z   n Proof Expanding the Left Hand Side of the equation: log two = z n Substituting phonetically log tu = z n Expanding the Right Hand Side of the equation... log tu = zzzzzzz.... Using the commutative property: tu log = zzzzzzz.... Q.E.D.

It's been more than ten years since I took up differential and integral calculus (more familiarly known as Math 54) during my college days in UP Diliman. I've long forgotten most of the formulas and techniques I learned then, but the memory of the person who taught them to me remains vivid. She was Ma’am K. The first thing that struck me about Ma'am K was her mastery of the subject she was teaching. She would explain things with conviction and authority, even reciting long theorems from memory. She also remained focused on the exposition of the lesson. Once, while teaching, the chalk fell off her hand, but she continued with the discussion even as she was picking it up from the floor. Later on, it became obvious to me that she possessed an extraordinary intelligence. But Ma’am K was not just an intelligent instructor, she was also a competent one. I've met some very intelligent professors in U.P., but many of them, sad to say, do not know how to teach. They s...