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The Textbook That Unleashed Ramanujan's Genius

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Re: The Textbook That Unleashed Ramanujan's Genius

#41

Post by tyleo »

flaubere wrote: post #33
lqet wrote: post #30

Earlier quoted context omitted.

A bit off-topic, but I just googled some IIT-JEE questions and found the following: A large number of bullets are fired in all directions with same speed u. What is the maximum area on the ground on which these bullets will spread. The provided answers all depend only on u, pi, and g. How can this be possible? Obviously, if I fire the gun from a tower, this area will be larger than when I fire it from the ground, and…

Not sure why you are asking this in this thread, but the implication is that the bullets are fired from ground level, not necessarily horizontally. The maximum distance a projectile can travel when fired from ground level is the basic first result of ballistics.

I think I understand. From height 0 figure out what gun angle gives the largest distance and then calculate the area of the circle with that distance as radius.

Re: The Textbook That Unleashed Ramanujan's Genius

#42

Post by alex_smart »

dr_zoidberg wrote: post #24
Ntrails wrote: post #11

Earlier quoted context omitted.

So, here's my thinking. The goal of the exams is not to find the children who are middle of the pack. The goal of the exams is to find the outliers. The unusually bright. What I think actually happens is you capture the top 0.1% because they're too smart not to make it, but the other 0.9% of passes is a mixture of highly trained, hard working kids alongside the intended targets. I guess I always wonder what could be…

I've caught the exceptional by being a commited teacher. You notice that they are ahead of the pack, by different signs: some make great questions in class, others barely say a word but utterly ace the exams, others are incredibile driven and tell you about their interests, others aren't, but when challenged they respond with interesting solutions. Of course, that may not be a scalable way to find them. But if you ha…

The problem with this approach is that it is too dependent on the goodness and honesty of said teachers. Anytime you rely more on human beings, you also bring in the typical human problems like self-interest, politics, biases, connections etc.

Your approach is not going to work in a country like India. We are a resource-starved nation where people have the mentality of securing every little advantage they can find for themselves without spending half a thought about social consequences. What happens if I am a talented student but I go to a school in a smaller town and references from teachers there carry a lot less weight that teachers from famous schools. What happens if my math teacher wants to promote a student of his own caste over other more qualified students. Will secondary-school teachers with laughably low salaries not feel incentivized to sell their recommendations to the highest bidder?

In a country where most systems are fraught with such human problems from head to toe, the beauty of JEE is that it is a completely objective system.

Re: The Textbook That Unleashed Ramanujan's Genius

#43

Post by alex_smart »

ItsMonkk wrote: post #39
flaubere wrote: post #35

Earlier quoted context omitted.

Yes, what people competing to get their children into the 0.9% miss is that 1. There are going to be other tests and hurdles in the future which differentiate your child from those with very high natural aptitude. 2. If your child worked 10 times as the top achievers to attain a similar level, at the next stage they will have to work 20 times as hard, then 100 times as hard, until it simply becomes impossible. 3. Whi…

Unless this is the bottleneck and Standford isn't harder than NJIT and at Google you work at on some project that gets cancelled and you never actually had to be all that good to stay with the Elite. Intelligence is speed. Knowledge is distance. If you are very smart and other kids are not as smart, if you give them more time then they can reach the same benchmark as you. When metrics become targeted, it is a sign th…

>When a measure becomes a target, it ceases to be a good measure.

The success of JEE in selecting excellent students year after year is evidence to the contrary.

When the measure is set high enough, it actually becomes an excellent motivating factor in itself. Do you think the people participating in the various Olympiads (IMO, IPhO etc) not benefit from the experience? How about the Olympics?

Re: The Textbook That Unleashed Ramanujan's Genius

#44

Post by flaubere »

ItsMonkk wrote: post #39
flaubere wrote: post #35

Earlier quoted context omitted.

Yes, what people competing to get their children into the 0.9% miss is that 1. There are going to be other tests and hurdles in the future which differentiate your child from those with very high natural aptitude. 2. If your child worked 10 times as the top achievers to attain a similar level, at the next stage they will have to work 20 times as hard, then 100 times as hard, until it simply becomes impossible. 3. Whi…

Unless this is the bottleneck and Standford isn't harder than NJIT and at Google you work at on some project that gets cancelled and you never actually had to be all that good to stay with the Elite. Intelligence is speed. Knowledge is distance. If you are very smart and other kids are not as smart, if you give them more time then they can reach the same benchmark as you. When metrics become targeted, it is a sign th…

I'm sure there are lots of bright people who are coasting at either Stanford or Google. If that's your goal, you might well achieve it. But at the same time, there are people who are going to be vastly more successful than that. The ones who revolutionize whole fields.

Re: The Textbook That Unleashed Ramanujan's Genius

#45

Post by nindalf »

alex_smart wrote: post #42
dr_zoidberg wrote: post #24

Earlier quoted context omitted.

I've caught the exceptional by being a commited teacher. You notice that they are ahead of the pack, by different signs: some make great questions in class, others barely say a word but utterly ace the exams, others are incredibile driven and tell you about their interests, others aren't, but when challenged they respond with interesting solutions. Of course, that may not be a scalable way to find them. But if you ha…

The problem with this approach is that it is too dependent on the goodness and honesty of said teachers. Anytime you rely more on human beings, you also bring in the typical human problems like self-interest, politics, biases, connections etc. Your approach is not going to work in a country like India. We are a resource-starved nation where people have the mentality of securing every little advantage they can find fo…

> The beauty of JEE

Only a person who did well in JEE would say this. You talk about disadvantages for rural students. This is important, because the vast majority of people in India live in villages or small towns, not the big cities. Tell me though, how many students from villages and small towns do well in JEE without moving to a coaching centre in a bigger town?

Personal anecdotes aside, you'll find that urban students are disproportionately represented in the top engineering institutes. There are some rural students certainly, but not like the 80% you'd expect if the system was truly egalitarian. You rail against the possibility of some students getting ahead because of advantages other than academic performance, but fail to consider that the current system is also based on the lottery of birth.

Re: The Textbook That Unleashed Ramanujan's Genius

#46

Post by commandlinefan »

khazhoux wrote: post #7

I'd love to see recommendations of similarly "powerful" math books in circulation today. And I mean books that actually taught you a ton of math, not books that contain a ton of interesting-looking math but mostly sit unread. Tim Gowers' Princeton Companion to Mathematics comes to mind, but I don't own it and I'm not sure if it's breadth-over-quality.

Not quite math, but TAOCP was like that for me: rather than having to force myself to work through it, I actually looked forward to spending time reading it or working the exercises.

Re: The Textbook That Unleashed Ramanujan's Genius

#48

Post by kenny87 »

khazhoux wrote: post #7

I'd love to see recommendations of similarly "powerful" math books in circulation today. And I mean books that actually taught you a ton of math, not books that contain a ton of interesting-looking math but mostly sit unread. Tim Gowers' Princeton Companion to Mathematics comes to mind, but I don't own it and I'm not sure if it's breadth-over-quality.

MAA has its Basic Library List: https://www.maa.org/press/maa-reviews/the-basic-library-list...

Re: The Textbook That Unleashed Ramanujan's Genius

#49

Post by AlexCoventry »

annexrichmond wrote: post #13
khazhoux wrote: post #7

I'd love to see recommendations of similarly "powerful" math books in circulation today. And I mean books that actually taught you a ton of math, not books that contain a ton of interesting-looking math but mostly sit unread. Tim Gowers' Princeton Companion to Mathematics comes to mind, but I don't own it and I'm not sure if it's breadth-over-quality.

Spivak's Calculus, which is really an introduction to Analysis, was that book for me. The way to approach it was to forget everything you learned about math in high school and learn it from the ground up in this book, as it will provide you with so much more insight and appreciation for how it all comes together Some of the book's best content is actually the exercises; notoriously difficult, but incredibly rewarding…

Yeah, the exercises in that book were wonderful.

Re: The Textbook That Unleashed Ramanujan's Genius

#50

Post by fao_ »

khazhoux wrote: post #7

I'd love to see recommendations of similarly "powerful" math books in circulation today. And I mean books that actually taught you a ton of math, not books that contain a ton of interesting-looking math but mostly sit unread. Tim Gowers' Princeton Companion to Mathematics comes to mind, but I don't own it and I'm not sure if it's breadth-over-quality.

I found Precalculus Mathematics In A Nutshell by Simmons to be extremely valuable (as someone who got so stressed out by my maths teachers in primary school that I literally was not able to add up in my head until the age of 14).

It teaches the concepts and cuts out all of the crap, but the diagrams and the clearly stated formulas make a lot of the implicit knowledge, explicit and extremely elucidating.

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