Life as a tutor#2

It's been more than a month since my previous (and the only other) blog entry on my experiences as a tutor at IIT Kanpur. It's less than my anticipated periodicity of making the entries but not entirely unexpected. During this gap I sometimes did feel like penning some my thoughts but couldn't gather enough motivation or didn't have the peace of mind to do it. Moreover, from my past experiences I have observed that one often has sudden intellectual discoveries or abstract realizations in such  strange situations or unexpected places that unless one has sufficient time and resources (or perhaps some kind of skill/practice) to preserve those thoughts in their pristine form, it becomes very difficult to recollect them later on in their entirety or for them to have the same effect as they did originally. Probably that has also been the case with me. 

I am currently at my home in Chandigarh - there's a week long mid-semester recess at my institute - after nearly 3 months since my last visit and with no particular agenda (except one, which I will mention later) on my mind. I have had a decent start today by normal standards (e.g. not waking up at noon time which has usually been the case on previous such visits) and feel quite at ease to make this entry.

... I spent a few minutes just now thinking of some interesting experiences worth mentioning but couldn't find any despite having taken 4 more tutorials.. I mean, of course, from an academic point of view I have had the opportunity to solve and discuss some interesting problems in the class which also allowed me to (1) gain more insights and (2) treat them in a way which is less mathematical and more intuitive, but I don't think the readers would be interested in knowing those technicalities (in case you do, feel free to get in touch with me!) and it will take a considerable time to explain them here. However, let me go ahead and illustrate an example of one such problem that I discussed in the previous tutorial class (#8):

Try to image a long wooden plank of dimensions, say 2 m length, 30 cm width  and 5 mm height (phatta, as they call it in Hindi/Punjabi).... Wait, I just found the exact problem on the internet! Just take a look at the below picture. Its caption is the problem statement. And don't worry, I won't go solving the problem here. I just want to highlight a few interesting features of this problem.

1. Okay.. but what does it mean??: Those who are not familiar with the concept of 'bending moment' won't be able to make out what the problem statement actually means. Here's what it means:

Where should the two bricks be placed so that the risk that the plank will collapse under the weight of the books is minimum?

And my guess is that even those who know the concept of 'bending moment' won't be able to make this interpretation without putting in a little extra mental effort. I think the above translated problem statement is likely to be understood by a layman - as a thought exercise imagine two extreme cases: (1) the bricks are placed at the ends of the plank (2) the bricks are placed very close to the plank's center. Can you intuitively feel these two cases presenting a high risk for the plank to collapse? Thus, there might be a case, somewhere in the middle of (1) and (2) (i.e., when 'a' is nearly half of the plank's length) when that risk is minimum. In fact, this is how I presented the problem to the students. Only afterwards I described the problem in terms of the 'bending moment' concept. If you are curious, the answer is: a=0.586L, obtained under certain idealizations (a jargon employed whenever engineers wish to acknowledge that their mathematical model adopted for solving the problem, despite their best efforts, does not exactly match the real one!), which is interestingly not very far from what one might expect intuitively.


2. Other possibilities: Another interesting thing about this problem is that once the logic behind the solution method is understood, one can solve for other interesting variations of the problems (e.g. given some finite number of books of different weights, what is/are (1) the best way(s) to arrange them on the plank and (2) best way(s) to place the two brick supports, such that the risk that the plank will collapse is minimum). I was able to illustrate these possibilities in the class.


3. Optimization technique: A further interesting feature of the problem was regarding the approach to be adopted for optimization (a term associated with any problem which involves estimating values of certain parameters which maximize/minimize some quanti(ty/es) of interest, e.g. length 'a' in this case). I won't explain the details here but I would like to mention that the approach that I discussed in the class was less mathematical and more intuitive (mathematical, nevertheless) which I thought the students will be able to geometrically visualize. At one stage, I asked the students to come forth and mark the answer on a graph that I had drawn on the blackboard and one student did volunteer and marked it correctly, to which I gave my commendations generously!

I hope the above brief discussion will lend some concreteness to (a)-(e) exercises that I mentioned in the previous blog entry under 'New discoveries' sub-heading. 

So, I have had the opportunity to solve such interesting problems in the class. I think I will end this entry here since its now lunch time here and I am feeling hungry. Also I believe the readers would probably want it to end. Hopefully, I will share the rest of the things tomorrow. Oh, and I will also probably mention the agenda that I have on my mind these days!