Maheen: “I dunno. Why?”
Asad: “Because they’re so easily ‘shatterable’!”
Such was the state of the students of CS611 (Topics in Discrete Geometry) on the eve of submission of their take-home final exams. Being the overconfident sophomore that I was, I decided to defy the odds and take a graduate-level course and see how I fared. However, the ride turned out to be something I had not expected at all. The workload was ten times that of all my other courses with all homeworks being left incomplete despite a two-week deadline PLUS extensions. Top that with three weeks of missed lectures due to a vacation in Turkey, and the stage was set for me to get an F in this course.
However, the experience I got by taking this course is something that I have never experienced before. The course, for starters, is meant for graduate students, which means the only undergraduates to take the course were the ones who had a keen interest in the subject and were willing to learn something during the course, and not simply get a good grade. The atmosphere in a graduate level course is worlds apart from that in a class of freshmen who are taking the course because they must, according to University requirements. The discussions in class were like talking about the weather over coffee, which it was most of the times. Combine this with an instructor like Nabil Mustafa, and you have not a lecture, but rather a weekly get-together of keen mathematicians willing to share their thoughts on topics pertaining to discrete and computational geometry. And due to the multitude of corporate and formal events that tend to happen in LUMS on a Friday morning, there was many a time when the class used to break simply so everyone could go to the central courtyard to grab some free food.
The environment in such a class is extremely conducive to the learning process. Learning is much, much more than rote-learning of bookish facts. Learning, at least in Computer Science, cultivates in students a certain way of thinking - one which involves abstract reasoning and algorithmic steps which are are very important tools both for mathematicians and computer scientists. It is the ability of good mathematicians to abstract out real-world problems to a simpler problem whose solutions are either known or easily obtained, that makes them the most sought-after employees in the world today. In a class where everyone has something to add to a discussion, something I have never witnessed in a Math lecture before, it is the positive attitude of your peers towards the course that makes you want to go with the flow as well. One may want to describe the attitude as contagious. At the end of the course, when everyone had to present an actual mathematical paper to the rest of the class, it was an excellent simulation of the kind of research that happens in the real world today. It was as if the class as a whole was part of a large research group working on different sections of one big mathematical enigma.
Another very good thing about such high-level courses is the lenient grading. At higher levels of education, actual learning takes precedence over your grade point average, so you are free to study without fretting over mundane issues such as your grade in the course. It was studying for the sake of studying as I had never seen before, and on top of all that, I came out with a shiny A!