Cogito Ergo Sum

Last week, we had Prof. C. R. Pradeep with us, apart from Vittal Rao. He is also a wondrous guy. All these teachers are excellent story-tellers. They'll have ample number of them from their own life or from the life of famous Mathematicians. Nice thing about C.R.Pradeep is that he thinks aloud in the class. He pretends to have got confused and hence resolves students' confusions. He said, "Maths is not about learning definitions, but rather learning why they are defined that way."

Today's lectures were by Prof. Ashok Rao. I found Ashok Rao's approach very ad hoc! Don't think I mean it in a negative sense. It helps in a way to look at concepts in a holistic way. He has a very unconventional method of teaching. One should listen to the bold statements he makes in the class! No one and no system of education is spared. One should have real confidence to make such remarks, seriously!

One thing common among these teachers is that they are from the same institute, and that's the only thing common. Each one has his own method of teaching, his own way of visualizing. Vittal Rao taught Pradeep and Ashok Rao, but he has not prepared his copies. He brings out the latent talent of the students. Students explore themselves under his guidance. Ashok Rao says, "Vittal Rao doesn't know how great he is, he has produced 100 great teachers and 100 great students in India. That's an achievement beyond words".

Nowadays the meaning of good teaching is not well understood. If someone can make a student "comprehend" what the book says, that's supposed to be good teaching. In my view, good teaching is a lot more than that. I am sure I don't know what a great teaching means. Good teaching means generating the interest to learn. It means teaching something that the books can not convey. It means making a student think, make him realize that he can be much more than what he is today.

I know, I would've missed so much had I not attended this workshop. Thanks to my HOD, I got a chance. Like a fool, when I was at IISc, I had never attended any of the classes by any of these 3 resourceful persons. One can never know what one has missed, unless and until one gets a chance to have it. This is true in any aspect of life. For example, unless you attempt to read a novel, you'll never know, whether you'll like it. You might or might not like it, but it is wrong to assume that you'll not like a novel, when you have poor reading habits. Same is the case with movies. Similar is the case with enjoying any other art form. Finally, extending the theory further, just think of how wrong it is to assume that you'll not like somebody, when you've hardly known that person, or when you have just a biased view! Trust me there are people who make such assumptions.

Life is congruent to Mathematics in general and Linear Algebra in particular. Sounds like a far-fetched statement? I am not saying "Jeevanave ondu lekkachaara" i.e. "Life is an account-book". While studying Linear Algebra, I could find a few analogies with life. For example, just like how a linear transformation transforms a vector from one vector space to another, many incidents transform us. They induce some attributes, they take away some, they modify. Sometimes for the better, sometimes for the worse. An incident can be "annihilating transform" on some people, just analogous to Ax = 0. It can make us better like, multiplication of a matrix with its eigenvector. An eigenvector does not change its direction and if the corresponding eigenvalue is greater than one, it gets amplified in magnitude. Analogously, some people and situations can strengthen our character.

Actually, everyone uses Linear Algebra in either professional or personal life; only subconsciously. {For example, the primeminister has to deal with some 1000 cross 1000 matrix (grossly underestimated). All his calculations are about how several factors ultimately affect GDP.} This workshop is helping us to be more and more conscious of it. It is such a beautiful thing. In fact, these professors say, a well focused highschool kid can understand it. It has to be learnt in a proper way, the first time one learns it. If a student chooses opts this subject for scoring, I am sure he'll end up neither learning, nor scoring. Choose it to learn it; enjoy while learning. You'll ultimately get good marks.