How to survive with these kinds of curriculum?

[Adesh]

The institute where I'm studying consists of books, problems and exams which seems to me completely senseless. I have been a self-study guy ( actually this was a compulsion, not a desire) so I read some well renowned books like The Feynman Lectures on Physics, Spivak Calculus , Morrison and Boyd's Organic chemistry and others. I took video lectures too from the internet like those of Sir Herbert Gross' , Leonard Susskind and some others. This site helped me a lot and is still helping me. So, due to all this I got indulged in Science and Maths the way our ancestors (early Mathematicians and Physicists) wanted us ( I apologize if I'm committing an offense by imagining just anything but due to etiquette I have used the plural form of first person instead of singular form, that is using 'us' instead of 'me').

The institutes in which I'm right now have something which I hate and I try to depict the reason of my hatred. Consider this problem from my book :-

Let $$ a_1 , a_2 , a_3 ... $$ be an A.P. (Arithmetic Progression) . Prove that $$ \sum _{n=1} ^ {2m} (-1)^{n-1} a_n ^2 = \frac {m} {2m-1} ~ (a_1 ^2 - a_{2m} ^2) $$

Now, the problem is not that this question is hard or time consuming but to me it seems senseless. Let me give you some more taste of this
Evaluate :-
$$ sin (\pi/2) ~ sin (\pi/2^2) ~ sin (\pi/2^3)~~... ~sin(\pi/2^{11}) ~ cos(\pi/2^{12})$$

My educators over there could solve these problems easily and every quickly. I'm sharing a link, please see it Calculus.

But I know and I believe that people here are far better, more experienced and more generous than these educators. So, I must state my problems explicitly and which is quite hard to do :-

What is the difference between these problems and the problems we find in renowned books which are written by mathematicians? Problems in renowned books are hard too ( like SL Loney's , Irodov's , G.H. Hardy's ) but they are quite different from these and my mind finds it pleasant to do those problems.

Is there some problem with me only? Am I creating a non-existing dichotomy ? Are those question which I have stated not senseless?

How should I survive ? They will conduct exams with these types of question? I know I can't leave things if I don't like them, I must have to adapt myself at least for sometime .

I request all the senior members to please help me over here.

Thank you.

 

[fresh_42]

There is a basic difference between problems in a textbook and those being posed independently. The former are usually related to a certain chapter and their purpose is to tighten the theorems and techniques of these chapters. An independently posed question should practice your general ability to solve problems and find the necessary theorems and techniques on your own, which is much closer to an exam situation. Phantasy and flexibility are as important as the theorems themselves are. So, no, solving problems is never senseless, it might just train different qualities.

 

[Vanadium 50]

The institute where I'm studying consists of books, problems and exams which seems to me completely senseless.

Then why did you pick it?

 

[Adesh]

There is a basic difference between problems in a textbook and those being posed independently. The former are usually related to a certain chapter and their purpose is to tighten the theorems and techniques of these chapters. An independently posed question should practice your general ability to solve problems and find the necessary theorems and techniques on your own, which is much closer to an exam situation. Phantasy and flexibility are as important as the theorems themselves are. So, no, solving problems is never senseless, it might just train different qualities.

Actually, we have those type of questions for each chapter. Sir, the way they teach is like this : First they pretend to teach the concept (I'm too rude over here but it's true) I mean they complete the theory part in just around 10-15 minutes and then they move completely to problem-solving. If I take the example of limits then, it hardly takes them 25 minutes to complete each every part of theory of limits and then suddenly we move to questions like this :

So, they are not like a single problem book rather their books on each chapter is consists of self posed problems. I hope you will reply me further.

 

[fresh_42]

It is really hard to tell. There always have been and probably will be different types of teaching. The gap that I saw at my time was between east and west, to make it short. While we concentrated on an understanding of the underlying principles, Soviet students concentrated on problem solving and calculations, training for the next exam. It's pointless to discuss which one is better. As usual, the truth is probably somewhere in between. What you described sounds similar. Now every person has different abilities and likes, hence tends towards one or another way of teaching. Here it is generally the case, that technical universities, those for engineers and other technical professions tend towards problem solving, since this is what engineers will finally do, whereas general universities have their focus on the general viewpoint.

I'm afraid there is no way out within the given circumstances. All you could do is learn other stuff in parallel according to the method which fits you best. Even books are written differently, will say emphasize on different aspects.

 

[cnh1995]

The institutes in which I'm right now have something which I hate

Are you in one of those JEE coaching institutes?

 

[Adesh]

Are you in one of those JEE coaching institutes?

Yes. I think you know what my problem is ?

 

[Adesh]

It is really hard to tell. There always have been and probably will be different types of teaching. The gap that I saw at my time was between east and west, to make it short. While we concentrated on an understanding of the underlying principles, Soviet students concentrated on problem solving and calculations, training for the next exam. It's pointless to discuss which one is better. As usual, the truth is probably somewhere in between. What you described sounds similar. Now every person has different abilities and likes, hence tends towards one or another way of teaching. Here it is generally the case, that technical universities, those for engineers and other technical professions tend towards problem solving, since this is what engineers will finally do, whereas general universities have their focus on the general viewpoint.

I'm afraid there is no way out within the given circumstances. All you could do is learn other stuff in parallel according to the method which fits you best. Even books are written differently, will say emphasize on different aspects.

Sir your answer is so nice that it has given me such a relief which is hard to define. I'm grateful to you.

 

[cnh1995]

Yes. I think you know what my problem is ?

Yes, I can relate to your situation.
Their approach is quite exam-oriented. You may enjoy a concept because of its scientific/mathematial/logical beauty, but for them, this concept is just another potential JEE question. In the end, what matters is whether or not you can solve JEE problems with the desired speed and accuracy. Their job is to "coach" you to achieve this level.
You might find it "pleasant" to solve a multiple-choice mechanics problem using Newton's laws and some fancy calculus. But some other student who doesn't know Newton's laws might still be able to solve it by the process of elimination of the options using just common-sense. As far as the JEE is concerned, the other student is smarter than you, because, even though he does not know Newton's laws, he knows a better "technique" to solve this problem.
Coaching institutes will help you become a good problem solver. They will make you solve plenty of problems using different techniques, some of which you will find silly.
But that is necessary to make it to the top given the highly competitive nature of the exam.
You can manage this situation if you just start following your teachers' instructions. Improve your problem solving skills with the help of coaching, and parallely, explore the concepts on your own under the guidance of experts here on PF. I think this is the right place for you to learn science the way you want to.