Monday, June 22, 2009
Linear Algebra...
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.
Wednesday, June 17, 2009
Linear Algebra Workshop
I am attending a 11 day workshop (for faculty) on Application Oriented Linear Algebra at PESIT. 3 days over and so far sooooooooo good. If I mention one name here, no other testimonial is needed. Any current/past IIScian would know the quality of it quickly, and that big name is nothing but "Prof. R.Vittal Rao".
It is weird but true that during my 2 and half yrs stay at IISc I didn't attend a single class by this person. I had just watched a few videos. One has to sit in his class to get the complete feel of it. Every now and then he'd tell some real stories of the institute, and as we all know, any story associated with institute is very interesting.
He doesn't like the idea of coming late or going late. It seems he'd lock the door from inside as soon as he enters the class and tell the students that they are free to walk out and lock him from outside, if he exceeds time. He said, he was never locked in so far.
We asked him which book would be good for linear algebra and the guy says, "I should write a book". He doesn't support the idea of teaching from a book. He adds, "If one can't understand concepts at undergrad level, one can never get hold of them later. Hence it is important to focus on learning, rather than getting marks". If only every student realizes this!
I'll give just one example on how he teaches. There's this concept of Eigenvalues and Eigenvectors of a matrix A. Eigenvectors are those which resist the change in direction. They say, "Hit me with a strong A, I might get a dent (I might shrink or elongate), but I won't turn, I am strong". Someone long ago said, Maths is "study of invariants." So, we are interested in those which do not change.
He doesn't actually teach, he just talks. He talks Maths. He makes us feel we talk Maths too. People like him are difficult to get. I would love to be as appealing as him. I would definitely try. I always feel it is not sufficient to appreciate someone. The real appreciation should be shown in terms of actions.
It is weird but true that during my 2 and half yrs stay at IISc I didn't attend a single class by this person. I had just watched a few videos. One has to sit in his class to get the complete feel of it. Every now and then he'd tell some real stories of the institute, and as we all know, any story associated with institute is very interesting.
He doesn't like the idea of coming late or going late. It seems he'd lock the door from inside as soon as he enters the class and tell the students that they are free to walk out and lock him from outside, if he exceeds time. He said, he was never locked in so far.
We asked him which book would be good for linear algebra and the guy says, "I should write a book". He doesn't support the idea of teaching from a book. He adds, "If one can't understand concepts at undergrad level, one can never get hold of them later. Hence it is important to focus on learning, rather than getting marks". If only every student realizes this!
I'll give just one example on how he teaches. There's this concept of Eigenvalues and Eigenvectors of a matrix A. Eigenvectors are those which resist the change in direction. They say, "Hit me with a strong A, I might get a dent (I might shrink or elongate), but I won't turn, I am strong". Someone long ago said, Maths is "study of invariants." So, we are interested in those which do not change.
He doesn't actually teach, he just talks. He talks Maths. He makes us feel we talk Maths too. People like him are difficult to get. I would love to be as appealing as him. I would definitely try. I always feel it is not sufficient to appreciate someone. The real appreciation should be shown in terms of actions.
Wednesday, June 10, 2009
Writer? Yes?..No?..Not sure.
Some of my friends have been suggesting me to start writing something "great"- a book for example, instead of limiting myself to blogging. Respecting their suggestions I thought about it.
Here is an enumeration of essential qualities to be satisfied to be a good writer:
1. Creativity and the capacity to let the imaginations wander,
2. Ability to assemble the imaginations and give them a shape,
3. Good hold on the language, attention to the grammar/spelling,
4. Excellent vocabulary, which, according to the scholars is a result of knowledge and wisdom,
5. Ability to wear someone else's hats or shoes or shirts/sarees or whatever even if it is not of one's size,
6. Absence of the habit of projecting one's own personality on the characters. Every character has to think and behave in its own way. The writer should not write based on what he/she would do during that situation.
7. Variety in the making of characters: The writer should be able to create different sorts of personalities. Under no circumstances, the reader should be forced to think, "Hey, this character here is so inconsistent/erratic", unless that was intended,
8. Should have deep knowledge in at least one field. Must be capable and confident of doing thorough study in any other field and write about it. For this, decent breadth of knowledge is necessary,
9. Controlled redundancy in writing,
10. A work should entertain a large class of people. However good it may be, unless it appeals to the readers, it is not worth the effort. If one writes for one's own satisfaction, one can as well write in a diary.
11. Detachment from the work. Pretty soon, usually if the first work itself is successful, an author gets so attached to his concepts that he loses the ability to think along the other dimensions. In case of positive feedback, one is inclined to be overwhelmed and in case of negative feedback, one tends to be defensive,
11. Detachment from the work. Pretty soon, usually if the first work itself is successful, an author gets so attached to his concepts that he loses the ability to think along the other dimensions. In case of positive feedback, one is inclined to be overwhelmed and in case of negative feedback, one tends to be defensive,
12. A writer should be level headed, not judgmental and should not have self-righteous attitude.
Now, my dear friends, you are free to give your feedback openly or in private. You can add points to these. Rate me/my writings based on those. My objective analysis about myself tells me that there's a long way to go.
Monday, June 08, 2009
Why Do People Help Others?
Isn't the human psychology a bit [read-very] weird? When we see someone else or ourselves helping a fellow human or an animal, do we examine the psychology behind it? Here is an attempt towards thorough analysis:
There are several intentions behind "helping". Depending on the intentions, people are divided into the following categories.
First one: One belonging to this division is taught at home and school this mantra: "Help others". They may not even know why they are doing it, it has become their nature.
Second one: As a person grows up, he learns a lesson through his experiences-"If I help others, they help me in my need". With this understanding, when he helps someone, he makes sure that the person at the receiving end has the ability to reciprocate. This checking can often happen subconsciously. That is the reason behind such people getting angry upon hearing the statement, "You are selfish, when you help me also, you do it with selfish motives". No one wants to hear the truth about themselves, especially when one knows it.
Third one: One can help another not necessarily with selfish motives. Nevertheless, what happens is, when the other person does not reciprocate, this person can feel bad. This category is the milder version of the second category. At the time of helping, there won't be any calculation going on, but later, if the need arises, there will be some expectation.
Fourth one: Some people help others just to boost their self-respect. You will hear such people often say, "I am good. I have been kind to people. God(?) will do good to me". This is another form of helping with selfish motives. Only difference is that these people expect the unseen hands to help them during their tough times.
Fifth one: There is yet another set of people who derive joy by seeing a smile in others' faces. For this reason they help. If we observe them closely, we can make out that these people are very much into solving big problems of others, because, bigger the problem, the more the other person smiles, and the more happiness they get.
Sixth one: People from this category do it just as a duty. They are beyond all reasoning. If you thank them for what they did, "Anyone in my position would have done the same. If not me, you would have got someone else to do it for you. Your purpose is served and that is what matters here." Can't help but comment, "What a way to live!"
More inputs/references are welcome. Which one do you place yourself in, can tell you a lot about your own character and attitude.
Wednesday, June 03, 2009
Patenting the Suicide Idea
"A philosopher is the one who has solutions to all the problems but his/her own". - Aparna/Shreevathsa
One philosopher got fed up by so many problems that she decided to commit suicide. She told her friend about her decision.
He did not object, instead asked, "So, which one are you going to use? Jumping off the cliff? Taking the sleeping pills? cutting the blood vessels? Cyanide?..."
This lady thought for sometime and replied, "No, I am not going to use any of these. I am going to innovate even during my death."
He asked, "What is the use?"
"I am going to patent that particular suicide idea!".
"What is the use?"-the friend asked again.
"So that I'll be of some use to my relatives after my death too".
Her mother asked, "But, if they use your idea to commit suicide without paying us, whom can we sue?"
With that, the useless discussion came to an end.
By now, the dumbest reader would've easily guessed that the philosopher in the above paragraph is me! By the way, the word "dumb" does not mock the literally dumb people. It has a secondary meaning "dull", moronic. Just remembered: if you haven't watched "Dumb and Dumber"-a 1994 movie on the cross-country adventures of two good-hearted but incredibly stupid friends-you must watch it. Last time I watched it in 2003. Should watch once again.
OK, I know I am jumping from one topic to another in an ad hoc way; I know that. Many a times I talk like this only. The real culprit is my unusually strong associative memory. The moment I say "associative", I just remembered that artificial neural networks store the information in the same way as human brain does, i.e., in an "associative" way. This I learnt in my 7th sem B.E.. We had a subject called Fuzzy logic and Neural Networks. Really good. My B.E. project also involved neural networks. Funny topic. We had an excellent teacher by name Dr.P.Subbanna Bhat. He used to teach this one. He was my project guide too. You see, this is what happens if one uses "associative memory". One tends to jump from philosopher to Subbanna Bhat and back to philosopher too, just because this Subbanna Bhat Sir used to talk lot of good philosophy. I think I inherit a part of it and often use it in the classroom.
Remembered one more thing. This Subbanna Bhat Sir happens to be my students' grandteacher. We invented this idea of grandteacher-grandstudent relationship in IISc. We did it when we came to know that one of our professors, Dr.Utpal Mukherjee was a student of Prof.Gallager of MIT (not Manipal or Madras) who was the pioneer of LDPC codes. We used to take pride in telling, "We are the grandstudents of Prof.Gallager". We used to work out an entire lineage like this. In IISc, it did not lead to any complications. But in undergrad colleges, one can get into a whole lot of mess. For example, after some years, if my student joins as a teacher in RVCE EC Dept, and both of us take class for the same set of students, then I become a grandteacher of my own students. I might even become great grandteacher of my own students, if I wait for long enough.
Got bored? Do I sound a bit like J.D.Salinger in his controversial work, "The Catcher in the Rye"? This is a must read book for those who have crossed twenty. Reading before that age is a bit dangerous. A bit disturbing/ philosophical book actually.
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