Showing posts with label Mathematics. Show all posts
Showing posts with label Mathematics. Show all posts

Friday, January 15, 2010

Winds of Change: CCD in Kgp


Just in case you didn't know, Kharagpur has a brand new Cafe Coffee Day. Not that it is something to be really proud of or boast of. But I am just stating the facts.

The Pre-Kgp Days

The fact that Kharagpur didn't have a state of art eating joint had surprised me in the first place. Whenever I thought about IIT in my Pre-Kgp days, images of CCDs filled with geeky people in specs sitting on tables involved in some esoteric conversation would come to my mind.

One imagines a lot of things before going to places. Unfortunately, things aren't always as you imagine them to be.

As a "Faccha"

So when I finally landed up in Kgp, I was in for a shock. Even I (who has an amazing capability to do with any kind of comestibles and rarely make a fuss about it) found the Mess food Yuck!

So on Saturdays when the Mess would be officially closed, I would go have dinner at some eating joint - Sahara to start with, Billoos, Veggies/Eggies or some Canteen or the other. But rarely could I find the kind of food that I was looking for. Or for that matter, that ambience to sit down and Bhaat.

A lot can happen over Tea Coffee

One golden rule which I learnt at my first visit to CCD was - More isn't merry. If you dish out the bucks aka $$$$, you wouldn't necessarily get what you seek.

As I sat down on the table wondering how the fellow who passed by me could dish out 2147 rupees (yeah, I remember the figure) to have coffee - I knew it wouldn't be long before I got my answer.

The stuff that I ordered (Chicken Pizza and Garam Masala Tea) arrived 20 minutes after I ordered.

The Tea was a bowl of hot water into which I had to dip the teabags and put the milk, sugar ... blah blah blah. Although I knew this was the latest fad --- I never knew I would have to pay 20 rupees for preparing a cup of tea.

The pizza although yummy just went on to show how ignorant those people were about Mathematics. For one, their cuts didn't go through the center. On top of that, the cuts didn't go through and through. So I really couldn't apply the Pizza Theorem. As a result, my poor friend to be satisfied with whatever he had ordered (which was just about palatable).

But those people are here for a reason

They know how to do their business. As we finished our plates, we found something written on the plate.

Would You Like to Have Some Coffee?

That was written on his plate. Inscribed on my plate were the words "Want Some More?" in funky fonts.

My roommate says that Bengali blood runs in me. Even though I have lived out of Bengal all my life, my nature is the same. So as I sat back to enjoy the ambience, my friend ordered some more and hmm... had it not been for me... I really wonder how much he would ended up spending.

Our bill ended up at 200 bucks and I really marvel that we could have so much after all for just about 1/10th that the other guy ended up paying.

The final verdict

If you are looking to grab some coffee during the upcoming fest, you might be have to wait. I really doubt if there would be any space in their for Kgpians, let along non-Kgpians (Have your coffee before or after the fest!). It is the hottest thing in campus presently and its going to take some time before things begin to settle down.

And if you are looking for some good Water Tea, I would advise you to head off to Tikkas which is hardly a 10 minutes walk from CCD.

Ciao!

Friday, June 5, 2009

Mathematical PJs

The trouble with Mathematics is - we first learn the formulae and then the application.

The education system is such that we treat these two aspects - theory and application as separate entities when they should be going hand in hand.

For instance, when we learn complex numbers in our +2 course, its applications are not apparent till our electrical course in 1st year.

In such cases, one has to look for simpler applications.

1. Multiplication by iota

I can very well recall how our Mathematics teacher in class was well known for his PJs (poor jokes).

Some, though were quiet useful!

Once, while a student had turned to gossip with the fellow behind him, our Maths teacher quipped, "Ashish, please multiply yourself by iota squared."

[Whenever a complex number is multiplied by iota, it is rotated anticlockwise by 90o. Hence, multiplying it by iota squared would rotate it by 180o]

2. The Exponential Function

Unfortunately for Ashish, he had to bear the brunt of most of the PJs as he was quiet irregular to class.

Once, while Ashish was giving some lame excuse for remaining absent from class, our Maths teacher remarked, "You are like the exponential function. Whether you differentiate it or integrate it doesn't really matter. It never changes."

I am unable to recall many of his other PJs. If you know of any interesting Maths PJs, do let me know.

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Monday, June 1, 2009

Scientific Guessing

Mathematics is often considered an exact science.

2+2 is always 4. cos2x + sin2x is always 1.

However, this is not always the case. Mathematics also deals with probability - a deterministic science.

Why Guess?

Objective examinations are considered a test of analytical skills and a test of nerves.

Now, it also tests your knowledge of probability. (Didn't it always test that?)

Regardless of the syllabus, objective pattern exams will test how well you apply probability.

Surprised?

Consider this. JEE in 2008 had 132 questions. In these, I would reckon there were 20 questions where I had a doubt. I wasn't sure. It was 50-50.

Did I guess?

Of course, I did.

Guessing in JEE

The objective questions had a +4/-1 marking pattern (+4 if you get it right, -1 if you get it wrong).

I figured out - even if I got 4 questions right out of 20, I wouldn't be losing out. (4x4 - 16x1 = 0).

How much probable is that?

Probability of getting exactly no question right = 20C0(1/2)20
Probability of getting exactly one question right = 20C1(1/2)20
Probability of getting exactly two questions right = 20C2(1/2)20
Probability of getting exactly three questions right = 20C3(1/2)20
Probability of getting exactly three questions right = (1/2)20 { 20C0 + ... + 20C3} = (1/2)20 (1351) = 1.28 x 10-3
Probability of getting at least 4 right = 1 - 1.28 x 10-3 ≈ 1

Once I figured this out, my JEE paper was practically finished.

I guessed left-right and finished with a rank of 1594.

Double Check

Still cynical?

Feel that something somewhere is wrong.

Let us double check.

Probability of getting either none right or one right or... 20 right = (1/2)20 { 20C0 + ... + 20C20}

How much is 20C0+20C1+...+20C19+20C20?

It is 220!

We then get the probability = 220 / 220 = 1

That is what we should be getting!

What if I had no idea and simply guessed?

Probability of getting exactly
none right would then become 20C0(3/4)20
one right=20C1(3/4)19(1/4)1
two right = 20C2(3/4)18(1/4)2
three right = 20C3(3/4)17(1/4)3

Probability of getting less than 3 right = (3/4)17 { 20C0(3/4)3 + 20C1(3/4)2 (1/4)1 + 20C2(3/4)1 (1/4)2 + 20C3(1/4)3 } = 0.225

Probability of getting at least 4 right now becomes 1 - 0.225 = 0.775

It isn't as safe to guess now, even though the probability is still in the candidate's favour.

AIEEE/BITSAT etc.

AIEEE has the +3/-1 marking scheme.
If you use the same method to calculate, you'll find that

the probability of scoring non-negative in case of 50-50 ≈ 1
when one has no idea = 0.61

BITSAT has bonus questions if you complete all the questions. Suppose you have 20 questions left out. Should you guess and go for the bonus questions?

You are now empowered to decide for yourselves!

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Tuesday, May 26, 2009

Real Life Applications of Mathematics - Traffic Rules

Mathematics is often viewed as a subject which has no real life application.

I disagree with this view. One has to look at Mathematics in the right light. Only then one can discover the joy of Mathematics.

Consider, for instance - traffic rules. Very practical, you would agree. However, very few people appreciate the disadvantages of zig-zag movement.

Let us consider it in the light of two well known mathematical axioms.

1. Two sides of a triangle are greater than the third side

It is a very well known mathematical axiom that two sides of a triangle are always greater than the third side.

We can use that axiom to show how travelling in a straight line is a better option than travelling zig-zag. Going by the axiom,

CB + BA > CA

A vehicle travelling CB and then BA would travel more and hence consume more fuel than a vehicle going by CA.

Travelling in a zig-zag fashion is not economically viable.

2. Parallel lines never intersect

A vehicle travelling in a zig-zag fashion would have a greater probability of colliding with other vehicles than vehicles travelling in parallel lines.

That is what is lane driving. Vehicles drive in their respective lanes - in parallel paths. That prevents collision.

What would otherwise seem not very practical at once appears to be plain common-sense because of Mathematics.

Know of any other real life applications of Mathematics? Do let me know. You may leave your suggestions as comments to this post.

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