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The Textbook That Unleashed Ramanujan's Genius

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Re: The Textbook That Unleashed Ramanujan's Genius

#51

Post by alex_smart »

nindalf wrote: post #45
alex_smart wrote: post #42

Earlier quoted context omitted.

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 st…

>Only a person who did well in JEE would say this.

Please forgive me for considering, in a country fraught from top to bottom with corruption and casteism, an objective system that offers an opportunity for young, talented students, irrespective of their backgrounds, to devote two years of their lives to serious study and meaningfully transform their lives "beautiful". It MUST be because of my single-digit rank.

>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?

If you count Kota, there are plenty of students from small towns who do well in JEE by moving to a coaching center in a smaller town.

Why is "without moving to a different town" such an important consideration? Rural areas almost by definition don't have any scale.

>There are some rural students certainly, but not like the 80% you'd expect if the system was truly egalitarian.

Most rural students don't even have access to good primary schools. There is a huge information asymmetry between people from villages and big cities. That is not a problem an engineering exam can solve.

You replace JEE with a less objective system, and much fewer rural/small-town students will get in.

Re: The Textbook That Unleashed Ramanujan's Genius

#52

Post by xNeil »

lqet wrote: post #30
xNeil wrote: post #2

It's interesting to note that Ramanujan also completed SL Loney's books on Coordinate Geometry and Trigonometry before he turned 12. These books are today used by almost every aspirant in the IIT-JEE, the engineering entrance exam in India. I'm trying to complete them, they're genuinely wonderful books. I believe they are also available on archive.org, although I use print editions.

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…

You have to assume the angle of projection is 45 degrees, in which case the range of the projectile becomes (u^2/g). (Since Range = (u^2)(sin2(theta))/g) Hope I helped!

Re: The Textbook That Unleashed Ramanujan's Genius

#53

Post by xNeil »

tyleo wrote: post #41
flaubere wrote: post #33

Earlier quoted context omitted.

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.

In the JEE, you generally assume the range to be the distance the projectile covers before reaching the launch height again, unless specified otherwise.

Re: The Textbook That Unleashed Ramanujan's Genius

#55

Post by pmoriarty »

rob74 wrote: post #29
alex_smart wrote: post #15

Earlier quoted context omitted.

I did have to prepare hard in those two years, but two years was more than enough. A lot about doing well in an exam as selective as this comes down to winning the genetic lottery. If you do not have the aptitude, then spending 5-6 years wholly devoted to an exam you are not going to crack is going to be an extremely demotivating way to spend your entire teenage life.

Well, this is not a binary classification: there are those fortunate few who have, as you say, won the "genetic intelligence lottery" and sail through school and exams such as this with little to no effort, then there are those who have to study hard for x years in order to make it, then there are those who need extra tutoring, and then there are of course some who even with all the help their parents can afford will…

"there are those fortunate few who have, as you say, won the "genetic intelligence lottery" and sail through school and exams such as this with little to no effort"

Is that just genetics? What about these kids' family lives? How about the interests kindled in them when they were young? How did their teachers treat them, and was there something in their experience in school, with tutors or parents which ignited a love for that subject? Did these kids' friends and family also value their learning? How much encouragement did they get?

We can't assume that kids who take the same exams differ in nothing except their genes.

Re: The Textbook That Unleashed Ramanujan's Genius

#56

Post by eeegnu »

dartharva wrote: post #14
est wrote: post #9

Is there a modern equivalent of this book?

Why? It's pure mathematics, that book can't ever get obsolete.

Note the massive errata list which is very likely just the scratching the surface. Later editions tend to either implement these corrections, or have a more complete list.

Re: The Textbook That Unleashed Ramanujan's Genius

#57

Post by lern_too_spel »

voldacar wrote: post #25

I love it. It's literally just a barrage of math, separated into little bite-sized chunks. Modern textbooks can have a so much fluff with all the flashy pictures and icons and the text on the page being brightly colored or having bubbles drawn around it to be more "engaging" etc. I found it super annoying as a kid, wish I had something like this.

This is a book of mathematical results without derivation. Most textbooks that people learn from include proofs.

It's easy to understand how a person with no formal mathematics training could read this book, try to figure out why these results are true, and in doing so, gain an intuitive sense about numbers and operations on them without developing the rigor to be able to state proofs for why anything should be true.

Re: The Textbook That Unleashed Ramanujan's Genius

#58

Post by pmoriarty »

dartharva wrote: post #14
est wrote: post #9

Is there a modern equivalent of this book?

Why? It's pure mathematics, that book can't ever get obsolete.

Books can have mistakes. Other editions could correct these mistakes, provide more elegant proofs, more fruitful approaches to solving problems, more understandable language, or more standard terminology.

Re: The Textbook That Unleashed Ramanujan's Genius

#59

Post by pmoriarty »

nindalf wrote: post #3
xNeil wrote: post #2

It's interesting to note that Ramanujan also completed SL Loney's books on Coordinate Geometry and Trigonometry before he turned 12. These books are today used by almost every aspirant in the IIT-JEE, the engineering entrance exam in India. I'm trying to complete them, they're genuinely wonderful books. I believe they are also available on archive.org, although I use print editions.

For an international audience, the Joint Entrance Examination (JEE) is more like the Chinese gaokao than the SATs. In my day it took 4 years of preparation starting age 14. Nowadays kids start at 11 or earlier. The stakes are pretty high, and only the top 1% get through. The remaining 99% try to move on with their lives or spend another entire year preparing full time for the exam.

"the Joint Entrance Examination (JEE) is more like the Chinese gaokao than the SATs"

As someone not familiar with the JEE nor the gaokao, might I ask how they differ from the SAT?

Re: The Textbook That Unleashed Ramanujan's Genius

#60

Post by ItsMonkk »

alex_smart wrote: post #43
ItsMonkk wrote: post #39

Earlier quoted context omitted.

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?

While I am not Indian and the only thing that I know of this is what I have read here and from having watched 3 Idiots(2009), all metricization is the same. You can not test intelligence, you can only test knowledge. But everyone wants to know intelligence.

The examples you cite are finding the farthest distance in their field, and the only people capable of going that distance are people who move fast AND work hard. It only works when the participants are geeks for exactly the thing that is being tested.

As the people who study for a long time keep increasing their studying, the scores naturally improves, and therefore they need to make the test harder to keep the same pass rate. This only works so long as the juice is worth the squeeze.

We see this with the interview circuit. Top engineers, instead of studying up on CICO choose to interview elsewhere where real problems are asked. They have turned down working on esoteric problems that no one faces in the real world, even though if they were to face it would easily be able to solve it - likely by themselves from first principles.

We care about intelligence. The only way to learn someones intelligence is by seeing them work. It's by seeing them understand a problem new to society. Tests can not measure intelligence. Only personal accountability will work, but personal accountability doesn't scale.

The key is living in a society that doesn't scale.

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