The Textbook That Unleashed Ramanujan's Genius(books.google.com)
books.google.com
The Textbook That Unleashed Ramanujan's Genius
https://books.google.com/books/download/A_Synopsis_of_Elementary_Results_in_Pure.pdf?id=JLmCAAAAIAAJ&output=pdf
102 comments
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.
>In my day it took 4 years of preparation starting age 14. Nowadays kids start at 11 or earlier.
That's more due to Indian coaching companies preying on Indian's parents' extreme sense of desperation and FOMO for their children rather than any real need to start that early. I don't think any more than two years are required or recommended for preparation of the exam. The longer you stretch the preparation, the longer you have to get completely bored and burnt-out by the process.
Source: I was top 10 in JEE and personally know more than half the people who were in top 100 in my year.
That's more due to Indian coaching companies preying on Indian's parents' extreme sense of desperation and FOMO for their children rather than any real need to start that early. I don't think any more than two years are required or recommended for preparation of the exam. The longer you stretch the preparation, the longer you have to get completely bored and burnt-out by the process.
Source: I was top 10 in JEE and personally know more than half the people who were in top 100 in my year.
That’s not a great source. Sounds like extreme sampling bias to me. What I’m saying is, you don’t know what it’s like being mediocre at school. I do.
In my experience, being at the top is extremely motivating. It encourages you to put in even more effort. The opposite is also true - when you feel like you’ve given it everything but you’re still in middle of the pack, you get burned out. It’s easy for someone who probably never needed any coaching to tell people “nah it’s just FOMO”. It’s not. As distasteful as the industry is, a small edge means you do better than others at 14, which can motivate you to put in more effort. That effect compounds over time.
In my experience, being at the top is extremely motivating. It encourages you to put in even more effort. The opposite is also true - when you feel like you’ve given it everything but you’re still in middle of the pack, you get burned out. It’s easy for someone who probably never needed any coaching to tell people “nah it’s just FOMO”. It’s not. As distasteful as the industry is, a small edge means you do better than others at 14, which can motivate you to put in more effort. That effect compounds over time.
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 done differently to capture just aptitude. Is that even a good idea? I myself was bright but didn't have much drive, so would have done poorly. I don't think that's a group you want to capture either.
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 done differently to capture just aptitude. Is that even a good idea? I myself was bright but didn't have much drive, so would have done poorly. I don't think that's a group you want to capture either.
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 had all the teachers in line with that "pay attention to the exceptional" objective, you'd probably find more than the current[0] "grind students forward into formal education" approach.
[0] I say this being fully aware that may not be the particular case in a region/group, but it certainly seems like the broadly taken "strategy" by most of the education system where I live
Of course, that may not be a scalable way to find them. But if you had all the teachers in line with that "pay attention to the exceptional" objective, you'd probably find more than the current[0] "grind students forward into formal education" approach.
[0] I say this being fully aware that may not be the particular case in a region/group, but it certainly seems like the broadly taken "strategy" by most of the education system where I live
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.
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.
My issue with JEE and the entrance examination system as a whole in India is that it grades students based on a combination of just 3 subjects, physics, chemistry and maths. It dosent matter if you are passionate about computer science and you have the talent to code well, it won't get you a seat into the CS department at any IIT. Atleast it was like this when I was preparing for it. I don't know if the system is the same currently. It would be nice if there was some other optional exam that you could take to prove your competence in other subjects.
If you spend five minutes thinking about the problem at hand, you will yourself realize why things have to be the way they are.
Anyway, you can take heart in the fact that if your goal is just to learn programming, a computer science department at an IIT is probably the last place you want to be. I'm only half joking. The curriculum is tilted heavily towards theory, reflecting the attitudes of the professors who obviously come from an academic background (most of them have probably never programmed professionally).
There was only one course where anyone is actually going to even try to teach you programming, but that is actually a pretty basic programming course in the first semester. Everything else you are supposed to learn on your own, through "assimilation". There are several courses in your third year that require significant programming skills, so if you haven't learnt those skills on your own outside the classroom by that time, you're kind of fucked.
Anyway, you can take heart in the fact that if your goal is just to learn programming, a computer science department at an IIT is probably the last place you want to be. I'm only half joking. The curriculum is tilted heavily towards theory, reflecting the attitudes of the professors who obviously come from an academic background (most of them have probably never programmed professionally).
There was only one course where anyone is actually going to even try to teach you programming, but that is actually a pretty basic programming course in the first semester. Everything else you are supposed to learn on your own, through "assimilation". There are several courses in your third year that require significant programming skills, so if you haven't learnt those skills on your own outside the classroom by that time, you're kind of fucked.
I don't understand why universities can't give a certain weightage to some specialized examinations. Like some international Olympiad for CS. We already have something like this if you are a KVPY scholar. But all universities only look at your entrance exam marks. Other than just trying to maintain the status quo I don't know why they can't change this current system.
Also even if the subject taught at IIT is not worth it it opens a lot more doors than what my college can ever do. In things like research.
Also even if the subject taught at IIT is not worth it it opens a lot more doors than what my college can ever do. In things like research.
> 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.
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.
>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.
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.
> irrespective of their backgrounds, to devote two years of their lives to serious study
I don't know how you can make such a statement with a single digit rank.
JEE offers the middle and upper middle class an opportunity to leap into the rich class. What percentage of India is middle class?
How many lower middle class and poor folks can send their kids to kota to study for JEE?
How much would it cost the Indian government to develop detailed coaching videos by IIT professors and upload it for free to YouTube? Yes JEE is a good entrance exam, but let's not romanticize it as something that can cross boundaries of caste and class. If so, we can also claim that capitalism doesn't care about your caste and class either! The harrassment faced by students of lower caste who get in through affirmative action is also well known.
I don't know how you can make such a statement with a single digit rank.
JEE offers the middle and upper middle class an opportunity to leap into the rich class. What percentage of India is middle class?
How many lower middle class and poor folks can send their kids to kota to study for JEE?
How much would it cost the Indian government to develop detailed coaching videos by IIT professors and upload it for free to YouTube? Yes JEE is a good entrance exam, but let's not romanticize it as something that can cross boundaries of caste and class. If so, we can also claim that capitalism doesn't care about your caste and class either! The harrassment faced by students of lower caste who get in through affirmative action is also well known.
> How much would it cost the Indian government to develop detailed coaching videos by IIT professors and upload it for free to YouTube?
I realize this is entirely tangential to the thrust of this sub-thread, but I don't think the government really should be encouraging coaching (with some caveats). The goal of the JEE is to identify the top 1% of applicants, or more accurately the top n number of candidates. In 10 years the JEE might have to pick the top 0.5% of applicants as the population grows and the seats do not. Making the JEE more equitable doesn't change that - more seats aren't created to meet demand. The difficulty of the JEE has to scale & adapt to the level of the students who appear in the exam. Yes, coaching classes can teach tricks that exploit weak patterns within the JEE. I would much rather see the JEE continually redesigned to be resistant to coaching in general.
I realize this is entirely tangential to the thrust of this sub-thread, but I don't think the government really should be encouraging coaching (with some caveats). The goal of the JEE is to identify the top 1% of applicants, or more accurately the top n number of candidates. In 10 years the JEE might have to pick the top 0.5% of applicants as the population grows and the seats do not. Making the JEE more equitable doesn't change that - more seats aren't created to meet demand. The difficulty of the JEE has to scale & adapt to the level of the students who appear in the exam. Yes, coaching classes can teach tricks that exploit weak patterns within the JEE. I would much rather see the JEE continually redesigned to be resistant to coaching in general.
Coaching classes actually do teach physics. It is not simply a shop teaching tricks. You cannot simply qualify for JEE by learning tricks for 2 years.
I should probably have used the word "teaching" instead of "coaching".
The problem is that the quality of science education in India at the high school level is really poor. To make the exam more equitable, we have to push for higher quality educational content accessible to everyone.
To give an example of how poor high school science education is - I was taught ohm's law in 8th grade when I didn't know what voltage was? Voltage was actually defined 3 years later, which is super ridiculous.
This causes students to believe that science is about memorizing equations and learning how to apply simple templates to solve problems derived from the same template. They are not even aware that they don't understand the terms they use. These students confuse familiarity with understanding. I have met so many electrical engineers who don't know what voltage is. They simply repeat the definition they learned in 8th grade. Voltage is potential difference. However, they don't know what potential difference is. They don't think they even need to know that. The actual definition is simply physics esoterica for them.
Such a student will be completely stumped on how to solve a simple ohms law problem, if we change the wording of the question from voltage to force and distancing and electric current to the speed of charged particles.
I should probably have used the word "teaching" instead of "coaching".
The problem is that the quality of science education in India at the high school level is really poor. To make the exam more equitable, we have to push for higher quality educational content accessible to everyone.
To give an example of how poor high school science education is - I was taught ohm's law in 8th grade when I didn't know what voltage was? Voltage was actually defined 3 years later, which is super ridiculous.
This causes students to believe that science is about memorizing equations and learning how to apply simple templates to solve problems derived from the same template. They are not even aware that they don't understand the terms they use. These students confuse familiarity with understanding. I have met so many electrical engineers who don't know what voltage is. They simply repeat the definition they learned in 8th grade. Voltage is potential difference. However, they don't know what potential difference is. They don't think they even need to know that. The actual definition is simply physics esoterica for them.
Such a student will be completely stumped on how to solve a simple ohms law problem, if we change the wording of the question from voltage to force and distancing and electric current to the speed of charged particles.
>I don't know how you can make such a statement with a single digit rank.
I don't quite follow why having a single digit rank should stop me from having an opinion on the subject.
I come from a middle class family from the poorest part of the country. I have a lower caste background (OBC), and my father was the first in my family to receive a university education. For innumerous Biharis, JEE and other competitive examinations have been the road to salvation.
I know someone who literally learnt swimming by hanging on to the tail of buffalos and went to a CS program of a top IIT.
>How many lower middle class and poor folks can send their kids to kota to study for JEE?
A lot more than you think. Kota is probably at least 30% students from UP and Bihar, the most backward states of the country.
>but let's not romanticize it as something that can cross boundaries of caste and class
It crosses boundaries of caste and class by a, being objective and b, not testing based on criteria (such as extra-curricular activities, knowledge of English) that only the upper urban class have access to.
>If so, we can also claim that capitalism doesn't care about your caste and class either!
I don't quite follow the analogy, but capitalism cares much less about caste than the feudal systems that it replaces.
>The harrassment faced by students of lower caste who get in through affirmative action is also well known.
It is also more exaggerated than real. A few bad cases should not be taken to represent the system in its entirety.
I don't quite follow why having a single digit rank should stop me from having an opinion on the subject.
I come from a middle class family from the poorest part of the country. I have a lower caste background (OBC), and my father was the first in my family to receive a university education. For innumerous Biharis, JEE and other competitive examinations have been the road to salvation.
I know someone who literally learnt swimming by hanging on to the tail of buffalos and went to a CS program of a top IIT.
>How many lower middle class and poor folks can send their kids to kota to study for JEE?
A lot more than you think. Kota is probably at least 30% students from UP and Bihar, the most backward states of the country.
>but let's not romanticize it as something that can cross boundaries of caste and class
It crosses boundaries of caste and class by a, being objective and b, not testing based on criteria (such as extra-curricular activities, knowledge of English) that only the upper urban class have access to.
>If so, we can also claim that capitalism doesn't care about your caste and class either!
I don't quite follow the analogy, but capitalism cares much less about caste than the feudal systems that it replaces.
>The harrassment faced by students of lower caste who get in through affirmative action is also well known.
It is also more exaggerated than real. A few bad cases should not be taken to represent the system in its entirety.
> I don't quite follow why having a single digit rank should stop me from having an opinion on the subject.
Rather, I expected someone with a single digit JEE rank to have a better, more rational perspective on JEE; instead of over the top romanticism. I know a few folks with a similar JEE ranks and their perspective is different.
> A lot more than you think. Kota is probably at least 30% students from UP and Bihar, the most backward states of the country.
Introspect on what I said and what your reply was. Families that are able to send their kids away to a different state for lodging and coaching for 2 years are at the very minimum middle class, if not rich or upper middle class. In fact, most American families can't do this at all. The fact that there are a lot of poor people in Bihar or India in general does not invalidate what I am saying.
My dad earned 500$ per month as an engineer in India. I am not going to pretend that I rose up via some extremely objective and meritocratic system inspite of tremendous economic disadvantage. The simple fact is that my dad was an engineer, while most of the kids in India at the time had illiterate parents.
> It crosses boundaries of caste and class by a, being objective
There are several exams of these kind in India, all entrance exams can be considered objective by default by this narrow definition. The exception of the JEE, UPSC etc. is the high bar. However, the amount of parental support, financial and otherwise - clearly shuts out the vast majority of India - the lower middle and the poor (SC/ST and some OBCs). With politicians expanding the scope of OBC, going beyond Shudras to include Vaishyas, OBC has been quite diluted. Significant population of OBCs also belong to the creamy layer.
I reiterate that, the JEE is a vehicle for the middle and upper middle to move to the rich class. For the vast majority of Indians, it is not an option. Better than the American system, but not some magic elixir.
> It is also more exaggerated than real. A few bad cases should not be taken to represent the system in its entirety.
It was quite common to bring up the affirmative action boost of these kids in newsgroups. The DASA students were also not spared. Posts like "Apna Mahesh problem solve kar diya. Aaj galati se tube light jal gaya :D". AIR was in the lifeblood of these students. You brought it up as well, while it was quite unnecessary.
> My father was the first in my family to receive a university education
Same here. No surprise.
Rather, I expected someone with a single digit JEE rank to have a better, more rational perspective on JEE; instead of over the top romanticism. I know a few folks with a similar JEE ranks and their perspective is different.
> A lot more than you think. Kota is probably at least 30% students from UP and Bihar, the most backward states of the country.
Introspect on what I said and what your reply was. Families that are able to send their kids away to a different state for lodging and coaching for 2 years are at the very minimum middle class, if not rich or upper middle class. In fact, most American families can't do this at all. The fact that there are a lot of poor people in Bihar or India in general does not invalidate what I am saying.
My dad earned 500$ per month as an engineer in India. I am not going to pretend that I rose up via some extremely objective and meritocratic system inspite of tremendous economic disadvantage. The simple fact is that my dad was an engineer, while most of the kids in India at the time had illiterate parents.
> It crosses boundaries of caste and class by a, being objective
There are several exams of these kind in India, all entrance exams can be considered objective by default by this narrow definition. The exception of the JEE, UPSC etc. is the high bar. However, the amount of parental support, financial and otherwise - clearly shuts out the vast majority of India - the lower middle and the poor (SC/ST and some OBCs). With politicians expanding the scope of OBC, going beyond Shudras to include Vaishyas, OBC has been quite diluted. Significant population of OBCs also belong to the creamy layer.
I reiterate that, the JEE is a vehicle for the middle and upper middle to move to the rich class. For the vast majority of Indians, it is not an option. Better than the American system, but not some magic elixir.
> It is also more exaggerated than real. A few bad cases should not be taken to represent the system in its entirety.
It was quite common to bring up the affirmative action boost of these kids in newsgroups. The DASA students were also not spared. Posts like "Apna Mahesh problem solve kar diya. Aaj galati se tube light jal gaya :D". AIR was in the lifeblood of these students. You brought it up as well, while it was quite unnecessary.
> My father was the first in my family to receive a university education
Same here. No surprise.
I grew up in a small village and hadn't heard of JEE before I entered the 12th grade. I tried to prepare by myself and failed spectacularly. A lot of the questions rely on tricks or insights that you typically learn only in coaching classes. My neighbor's son, who actually went to school in a nearby big town, had signed up for coaching classes. He did much better than me, and from chatting with him (post-exam), I could tell he had learned these tricks in his coaching classes.
So, clearly, lack of coaching classes hurt my chances.
In any case, I never joined the IITs, but joined another engineering college thanks to my scoring very well in the final exam.
So, clearly, lack of coaching classes hurt my chances.
In any case, I never joined the IITs, but joined another engineering college thanks to my scoring very well in the final exam.
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> Of course, that may not be a scalable way to find them.
That's the crux, though - the common theme behind failures of modern education, among other things. It seems to me that becoming a developed country comes with the desperate need to make everything scalable, and losing the ability to do things that do not scale.
That's the crux, though - the common theme behind failures of modern education, among other things. It seems to me that becoming a developed country comes with the desperate need to make everything scalable, and losing the ability to do things that do not scale.
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. While they are sacrificing their youth for this, they are missing out on discovering what they are good at and do want to do.
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 that your community has scaled beyond what it can handle, and you have lost personal accountability. When a measure becomes a target, it ceases to be a good measure.
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 that your community has scaled beyond what it can handle, and you have lost personal accountability. When a measure becomes a target, it ceases to be a good measure.
>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?
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.
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.
>You can not test intelligence, you can only test knowledge.
You absolutely can test for a combination of intelligence and knowledge.
>But everyone wants to know intelligence.
Seldom do people actually care about intelligence in isolation. What use is intelligence without the discipline and ability to apply yourself towards a goal for a considerable length of time?
>As the people who study for a long time keep increasing their studying, the scores naturally improve
That simply does not work. Even with the coaching industry trying to lure parents into sending kids to them since Kindergarten, year after year it turns out that the students who do best in the JEE have only had two years of dedicated preparation. Because that is all the time that is needed for a talented student to prepare for the material that is being tested.
> and therefore they need to make the test harder to keep the same pass rate
If anything, the JEE has gotten easier with time.
Honestly, your entire argument seems to be based on dogma and not evidence. Selecting for the top 1% students by their aptitude for math/engineering, within an acceptable error margin, is not really as difficult a problem as you are making it out to be.
You absolutely can test for a combination of intelligence and knowledge.
>But everyone wants to know intelligence.
Seldom do people actually care about intelligence in isolation. What use is intelligence without the discipline and ability to apply yourself towards a goal for a considerable length of time?
>As the people who study for a long time keep increasing their studying, the scores naturally improve
That simply does not work. Even with the coaching industry trying to lure parents into sending kids to them since Kindergarten, year after year it turns out that the students who do best in the JEE have only had two years of dedicated preparation. Because that is all the time that is needed for a talented student to prepare for the material that is being tested.
> and therefore they need to make the test harder to keep the same pass rate
If anything, the JEE has gotten easier with time.
Honestly, your entire argument seems to be based on dogma and not evidence. Selecting for the top 1% students by their aptitude for math/engineering, within an acceptable error margin, is not really as difficult a problem as you are making it out to be.
I know more about the South Korean system.
They grade to a curve. When the students get better, the test gets harder. Their students spend 16 hours a day studying for their university exams, and start at the age of 12. 46% of students are depressed. Suicide is the leading cause of death in both 10-19 and 20-29 population, mostly due to the stress.
The goal of all students is to pass the test so that they can make it into Seoul University so that Samsung will hire them. The bottleneck is the test. Life afterwards is easy.
Rigorous testing does not give you the best 1% of the population, it filters the people willing to go through the system down to the top 1%. Some of them will be of the .1% best, and others will be those who worked harder as they did not have to help their little sister get home, or their parents clean the restaurant after school.
You can not know your false positives. You can not know your false negatives. Every Einstein born to a poor family who does not get to study is wasted potential to humanity. Every Einstein whose passion is in Machine Learning and spends all of his time on that topic will fail this test.
They grade to a curve. When the students get better, the test gets harder. Their students spend 16 hours a day studying for their university exams, and start at the age of 12. 46% of students are depressed. Suicide is the leading cause of death in both 10-19 and 20-29 population, mostly due to the stress.
The goal of all students is to pass the test so that they can make it into Seoul University so that Samsung will hire them. The bottleneck is the test. Life afterwards is easy.
Rigorous testing does not give you the best 1% of the population, it filters the people willing to go through the system down to the top 1%. Some of them will be of the .1% best, and others will be those who worked harder as they did not have to help their little sister get home, or their parents clean the restaurant after school.
You can not know your false positives. You can not know your false negatives. Every Einstein born to a poor family who does not get to study is wasted potential to humanity. Every Einstein whose passion is in Machine Learning and spends all of his time on that topic will fail this test.
>The goal of all students is to pass the test so that they can make it into Seoul University so that Samsung will hire them. The bottleneck is the test. Life afterwards is easy.
That sounds quite similar to the JEE tbh. Won't you say that a significant cause of the stress is the cultural expectation that all parents have that their should be able to get into Seoul University and eventually a job at Samsung?
In India there is a good reason for this mindset, because we do not have many good universities and base salaries are very low and of course there is not much of a social security net. I wonder what causes a similar mindset in a developed country like South Korea.
> Every Einstein whose passion is in Machine Learning and spends all of his time on that topic will fail this test.
Any person who does not have a basic understanding of his background and social situation is not an Einstein.
Regardless, that is a very strange example indeed. I really don't understand what kind of a person has the background and social circle that enables him to do top quality research in a highly specialized field of engineering (that also requires considerable funds to run any sort of experiments) at the age of 17 but also doesn't have the connections that will help him get into a decent university.
That sounds quite similar to the JEE tbh. Won't you say that a significant cause of the stress is the cultural expectation that all parents have that their should be able to get into Seoul University and eventually a job at Samsung?
In India there is a good reason for this mindset, because we do not have many good universities and base salaries are very low and of course there is not much of a social security net. I wonder what causes a similar mindset in a developed country like South Korea.
> Every Einstein whose passion is in Machine Learning and spends all of his time on that topic will fail this test.
Any person who does not have a basic understanding of his background and social situation is not an Einstein.
Regardless, that is a very strange example indeed. I really don't understand what kind of a person has the background and social circle that enables him to do top quality research in a highly specialized field of engineering (that also requires considerable funds to run any sort of experiments) at the age of 17 but also doesn't have the connections that will help him get into a decent university.
While I largely agree with your argument, I'm curious if you have a solution in mind that could work in the Indian context.
>Even with the coaching industry trying to lure parents into sending kids to them since Kindergarten, year after year it turns out that the students who do best in the JEE have only had two years of dedicated preparation. Because that is all the time that is needed for a talented student to prepare for the material that is being tested.
Do we have any figures (anecdotal or otherwise) of how many students in the top rankings have had coaching?
I am of the opinion that the JEE (and every other competitive exam: AIIMS, etc) should be much much harder, and designed with a specific eye to defeat coaching. I'd go so far as to draw an analogy with crypto algorithms designed to be ASIC - resistant.
Do we have any figures (anecdotal or otherwise) of how many students in the top rankings have had coaching?
I am of the opinion that the JEE (and every other competitive exam: AIIMS, etc) should be much much harder, and designed with a specific eye to defeat coaching. I'd go so far as to draw an analogy with crypto algorithms designed to be ASIC - resistant.
Several of the candidates qualifying for the exam have appeared multiple times for the exam. Very often the students have been studying for more than 2 years.
>Do we have any figures (anecdotal or otherwise) of how many students in the top rankings have had coaching?
I would say 90%. Probably even higher. That's also because pretty much anyone who is serious about taking the exam gets some coaching. However, I know at least a few people that cracked JEE without any coaching. Even a guy who got rank 1 without coaching (Piyush Srivastava).
> I am of the opinion that the JEE (and every other competitive exam: AIIMS, etc) should be much much harder, and designed with a specific eye to defeat coaching
I am not sure how making the exam harder would defeat coaching. The value of the hard problems is that it helps you distinguish better between the very top of the top students. At least at my time there were always a number of such problems thrown in for that purpose.
I also don't quite understand what you hope to achieve here. The whole "coaching centers teach you tricks to solve problems" idea is way exaggerated. (Honest to God, I have a terrible memory and I actually derived half the formulae I needed during the exam itself.) There are many other ways in which coaching centers add value. The most important of which being that you surround yourself with and compete against other talented, motivated students.
I would say 90%. Probably even higher. That's also because pretty much anyone who is serious about taking the exam gets some coaching. However, I know at least a few people that cracked JEE without any coaching. Even a guy who got rank 1 without coaching (Piyush Srivastava).
> I am of the opinion that the JEE (and every other competitive exam: AIIMS, etc) should be much much harder, and designed with a specific eye to defeat coaching
I am not sure how making the exam harder would defeat coaching. The value of the hard problems is that it helps you distinguish better between the very top of the top students. At least at my time there were always a number of such problems thrown in for that purpose.
I also don't quite understand what you hope to achieve here. The whole "coaching centers teach you tricks to solve problems" idea is way exaggerated. (Honest to God, I have a terrible memory and I actually derived half the formulae I needed during the exam itself.) There are many other ways in which coaching centers add value. The most important of which being that you surround yourself with and compete against other talented, motivated students.
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.
shouldn't everyone attending a top school be decidedly coasting along in some way about their education, so they can optimise preferred areas?
It seems like you are advocating, for a bright but not exceptional child, that they do get pushed to the point where they burn out, just in case they manage to win the lottery of appearing to be in the exceptional group. Even if this dubious plan succeeds, sooner or later it will become clear that they are not as good as their results.
You were not mediocre, school told you that you are mediocre.
I am 14 and i do want to give JEE as I want to be a cs student. I do coding and i love it, but i am at such a place that i think jee is the only option. I have not even studied more than 2 hour from a year because of our schools are close. People always demotivate me and they tell that if you won't have good college (especially IIT), you will fail and all you coding will not worth. And they are not wrong because I have heard this 10 thousand times. Is IIT JEE really needed to learn CS. If you are any boy here, he will say he want to "become jee", how can he become jee. Elders tell that if you get into IIT you will get 10 crore of package. Is is real? I am telling this from view of a kid who lives in this NEET/JEE only world.
I am 14 and i do want to give JEE as I want to be a cs student. I do coding and i love it, but i am at such a place that i think jee is the only option. I have not even studied more than 2 hour from a year because of our schools are close. People always demotivate me and they tell that if you won't have good college (especially IIT), you will fail and all you coding will not worth. And they are not wrong because I have heard this 10 thousand times. Is IIT JEE really needed to learn CS. If you are any boy here, he will say he want to "become jee", how can he become jee. Elders tell that if you get into IIT you will get 10 crore of package. Is is real? I am telling this from view of a kid who lives in this NEET/JEE only world.
>Elders tell that if you get into IIT you will get 10 crore of package
That's nonsense. I'm from CS at a top IIT, and only a handful of my batchmates have that kind of compensation, and that is after >5 years of experience. Absolutely nobody is going to give you a 10 crore salary fresh out of college.
For students from other not so popular streams, in India, a salary of Rs 10-20 lakh a year is more realistic. Again, this is after 4-5 years of industry experience. Even after IIM, the average salary is around 20-30 lakhs.
That's nonsense. I'm from CS at a top IIT, and only a handful of my batchmates have that kind of compensation, and that is after >5 years of experience. Absolutely nobody is going to give you a 10 crore salary fresh out of college.
For students from other not so popular streams, in India, a salary of Rs 10-20 lakh a year is more realistic. Again, this is after 4-5 years of industry experience. Even after IIM, the average salary is around 20-30 lakhs.
I agree with this. Most people need just 2 years during grade 11 and 12. Starting earlier might give minor edge at best but more damage to other aspects of personality and growth!
In IIT, in under 1000 rank, most people who spent more than 2 years were people who were intelligent but didn't take preparation seriously during their grade 11-12 but put in effort after that.
I also know people who were extremely intelligent who could crack under 100 if they gave the exam in grade 8. But they were outliers.
In IIT, in under 1000 rank, most people who spent more than 2 years were people who were intelligent but didn't take preparation seriously during their grade 11-12 but put in effort after that.
I also know people who were extremely intelligent who could crack under 100 if they gave the exam in grade 8. But they were outliers.
Haha I know somebody who cracked JEE at the age of 14. I met him and found out that he was homeschooled with zero social skills. Warms my heart to know that he is doing well in life.
https://timesofindia.indiatimes.com/city/lucknow/Youngest-II...
https://timesofindia.indiatimes.com/city/lucknow/Youngest-II...
I always wonder about kids who skip too many grades or who get college degree at 12. Even if they are intellectually there, socially life would be a nightmare. Imagine being a 12 year old which 17 year old peers. I can't imagine the emotional trauma!
I didn't do any IIT coaching and was able to prepare for IIT only for one year in my grade 11. After that I got some major health issue and was harassed by armed bullies in my school, so couldn't study at all in Grade 12. This made me miss Top 200 rank.
But this ended up being a blessing in disguise, because I couldn't get Computer Science at IIT. I have been passionate about computers since I was 8 years old. If I had studied Computer Science as a part of the course curriculum, I might have ended up hating it.
Instead I pursued Computer Science on mine own, based on my interest. I have loved it every single day!
I look forward to my work, versus most of my friends who feel trapped in their jobs!
I didn't do any IIT coaching and was able to prepare for IIT only for one year in my grade 11. After that I got some major health issue and was harassed by armed bullies in my school, so couldn't study at all in Grade 12. This made me miss Top 200 rank.
But this ended up being a blessing in disguise, because I couldn't get Computer Science at IIT. I have been passionate about computers since I was 8 years old. If I had studied Computer Science as a part of the course curriculum, I might have ended up hating it.
Instead I pursued Computer Science on mine own, based on my interest. I have loved it every single day!
I look forward to my work, versus most of my friends who feel trapped in their jobs!
>Imagine being a 12 year old which 17 year old peers. I can't imagine the emotional trauma!
In my experience, these kids are homeschooled so at least they get sheltered from bullying at school. Of course they also get "sheltered" from any opportunity to learn how to navigate social situations. And when the get into real life, it is into an academic environment that at least somewhat supports such eccentrics.
To a smaller extent, I think almost everyone makes sacrifices in their social life and hobbies during that time period for a boost in career. For pretty much my entire first year, I had a single point agenda in life: get laid!
>If I had studied Computer Science as a part of the course curriculum, I might have ended up hating it.
You can pursue Computer Science on your own even while being enrolled in CS program and just use the curriculum as sort of a sanity check that you're making enough progress. That's pretty much what I did.
In my experience, these kids are homeschooled so at least they get sheltered from bullying at school. Of course they also get "sheltered" from any opportunity to learn how to navigate social situations. And when the get into real life, it is into an academic environment that at least somewhat supports such eccentrics.
To a smaller extent, I think almost everyone makes sacrifices in their social life and hobbies during that time period for a boost in career. For pretty much my entire first year, I had a single point agenda in life: get laid!
>If I had studied Computer Science as a part of the course curriculum, I might have ended up hating it.
You can pursue Computer Science on your own even while being enrolled in CS program and just use the curriculum as sort of a sanity check that you're making enough progress. That's pretty much what I did.
> : I was top 10 in JEE
This should be anti-source if you say you don't need to prepare hard enough.
This should be anti-source if you say you don't need to prepare hard enough.
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 not be able to make it.
I (born in Romania, was programming as a hobby since age 12) was in the "extra tutoring" group BTW, then I barely passed the maths, physics etc. exams of the first semesters, but when the actual CS courses started I got better and graduated with pretty passable grades (not that any employer looks at those)...
I (born in Romania, was programming as a hobby since age 12) was in the "extra tutoring" group BTW, then I barely passed the maths, physics etc. exams of the first semesters, but when the actual CS courses started I got better and graduated with pretty passable grades (not that any employer looks at those)...
>Well, this is not a binary classification
You are missing that the context here is getting through an extremely selective competitive examination. Only the top 5% students by aptitude for math/science/engineering have any significant chance of getting through. The rest are just fodder for the coaching industry selling increasingly more and more extreme and ridiculous products. Soon they might start selling products for coaching the unborn baby by teaching maths to the mother too.
None of what I am saying is intended to apply to the practice of actually being a professional engineer or having a successful career.
You are missing that the context here is getting through an extremely selective competitive examination. Only the top 5% students by aptitude for math/science/engineering have any significant chance of getting through. The rest are just fodder for the coaching industry selling increasingly more and more extreme and ridiculous products. Soon they might start selling products for coaching the unborn baby by teaching maths to the mother too.
None of what I am saying is intended to apply to the practice of actually being a professional engineer or having a successful career.
"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.
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.
There is a belief among folks who cleared the JEE that this is a pure consequence of their inner genius - they are mini-Einsteins.
They forget the investments their parents made - including sending them away for 2 years at a coaching and lodging centre - Something most folks cant afford. Or they forget that they had to appear twice or thrice. Surprisingly the entrance exam failed to recognize their genius the first time around.
They forget the investments their parents made - including sending them away for 2 years at a coaching and lodging centre - Something most folks cant afford. Or they forget that they had to appear twice or thrice. Surprisingly the entrance exam failed to recognize their genius the first time around.
Agree 2 years is more than enough. Within the first 6 months of those 2 years the ones who had been there longer had no advantage. Guys who had been top at their local schools quickly caught up if they studied hard.
> winning the genetic lottery
As well as having educated supportive parents with a decent budget, and being part of an ecosystem where education is prioritized.
As well as having educated supportive parents with a decent budget, and being part of an ecosystem where education is prioritized.
Bragging about JEE rank (called AIR) is almost unavoidable with folks from IIT. In this case it would invalidate his argument, because he is an outlier sample. But they can't help themselves :)
Well that bragging made my first year the worst year at college. I would have enjoyed more had I opted for a less prestigious IIT.
Hi! I'm a JEE aspirant - is there any way I could contact you to have a bit of a chat? Of course, only if you're kind enough to accept - I'll understand if you don't, however :)
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"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?
As someone not familiar with the JEE nor the gaokao, might I ask how they differ from the SAT?
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The best part of these books were the exercises. I have very fond memories of spending hours trying to solve every single problem at the end of each chapter. You get more from solving those last two difficult problems you couldn't solve than solving hundreds of easy problems mechanically.
A bit off-topic, but I just googled some IIT-JEE questions and found the following:
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 thus also depends on the height above ground of the gun.
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.
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 thus also depends on the height above ground of the gun.
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.
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!
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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.
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 as spending the time to solve them them really prepares you for upcoming chapters
Some of the book's best content is actually the exercises; notoriously difficult, but incredibly rewarding as spending the time to solve them them really prepares you for upcoming chapters
Yeah, the exercises in that book were wonderful.
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.
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.
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.
If you think you'd like TAOCP, but with just the math, not the programming (hah), take a look at Concrete Mathematics by Graham, Knuth, and Patashnik. I haven't read anything else by Graham or Patashnik, so I don't know how much their voice comes through, but Knuth's playfulness and joy in the material comes through strongly. It's a blast just to read for fun.
I must be built differently, I found Concrete Mathematics insanely inapproachable. I have a math stack exchange question where I ask for clarity on WTF he means on one question and got upvotes and comments from his students who were similarly flummoxed taking the course from him in real life!
Seconded.
This brings to mind "Disturbing the Universe", a selection of autobiographical essays by physicist Freeman Dyson, where he mentions he learned differential equations as a 12-year-old by working through 700 problems in Piaggio's "Differential Equations" over the summer vacation, after which learning general relativity became a breeze.
This brings to mind "Disturbing the Universe", a selection of autobiographical essays by physicist Freeman Dyson, where he mentions he learned differential equations as a 12-year-old by working through 700 problems in Piaggio's "Differential Equations" over the summer vacation, after which learning general relativity became a breeze.
MAA has its Basic Library List: https://www.maa.org/press/maa-reviews/the-basic-library-list...
The list contains 2,963 books!
The book is easier to read in a browser at the Internet Archive:
Google scan: https://archive.org/details/asynopsiselemen00carrgoog
MSN scan: https://archive.org/details/synopsisofelemen00carrrich
Google scan: https://archive.org/details/asynopsiselemen00carrgoog
MSN scan: https://archive.org/details/synopsisofelemen00carrrich
Wonderful. I was hoping there was a version without the obnoxious commercial branding, and indeed, these are both free of it. (And the MSN scan also without the harsh thresholding)
Thank you!
Thank you!
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.
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.
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.
If you want to get a taste of some of what Ramanujan seems to have been occupied with, the mathematical physicist John Baez explained "Ramanujan's easiest formula" in an approachable way https://johncarlosbaez.wordpress.com/2020/11/18/ramanujans-e...
Ramanujan: Srinivasa Ramanujan. born December 22, 1887, Erode, India—died April 26, 1920, Kumbakonam
in 1913, the English mathematician G. H. Hardy received a strange letter from an unknown clerk in Madras, India. The ten-page letter contained about 120 statements of theorems on infinite series, improper integrals, continued fractions, and number theory .... Every prominent mathematician gets letters from cranks, and at first glance Hardy no doubt put this letter in that class. But something about the formulas made him take a second look, and show it to his collaborator J. E. Littlewood. After a few hours, they concluded that the results "must be true because, if they were not true, no one would have had the imagination to invent them".
https://www.usna.edu/Users/math/meh/ramanujan.html
in 1913, the English mathematician G. H. Hardy received a strange letter from an unknown clerk in Madras, India. The ten-page letter contained about 120 statements of theorems on infinite series, improper integrals, continued fractions, and number theory .... Every prominent mathematician gets letters from cranks, and at first glance Hardy no doubt put this letter in that class. But something about the formulas made him take a second look, and show it to his collaborator J. E. Littlewood. After a few hours, they concluded that the results "must be true because, if they were not true, no one would have had the imagination to invent them".
https://www.usna.edu/Users/math/meh/ramanujan.html
TIL “surds” https://www.mathsisfun.com/surds.html
Such a fun language, math.
Such a fun language, math.
I always thought that surds is short for 'absurds' :)
Nice to read the etymology of the word!
Nice to read the etymology of the word!
Is there a modern equivalent of this book?
Why? It's pure mathematics, that book can't ever get obsolete.
> that book can't ever get obsolete
Math doesn't change, but language and printing technology do.
Math doesn't change, but language and printing technology do.
Not going obsolete doesn't mean not improvable. Seems a reasonable question.
Assuming it’s Carr’s, IIRC it’s a rather odd style of work, it’s a summary of the state of basic mathematics rather than a textbook per se, with pages of theorems with little explanation.
So a modern version would at most be a different idea of what the core theorems should be.
So a modern version would at most be a different idea of what the core theorems should be.
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When I was starting college I took an analysis course based on Kolmogorov and Fomin. We didn't work with all sorts of special functions, but focused much more on functional analysis, measure, and multidimensional functions. Later we did Fourier transforms for any locally compact abelian group. What's important in math changes.
But this specific book only covers elementary-to-intermediate topics in Algebra, Geometry and Calculus from the looks of it. It isn't likely to change as much at all.
Not really the case, mathematical terminology and conventions change over time.
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.
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.
43MB scanned PDF, just in case you're trying to read it on mobile.
The book is still in print: "Synopsis of Elementary Results in Pure and Applied Mathematics: Volume 1: Containing Propositions, Formulae, and Methods of Analysis,"
As I understand this, this book is the one that Ramanujan read that helped him unleash his inner genius. When I first read the link title, I thought this was a book written by (or at least co-written by) Ramanujan that unleashed his genius to the greater Mathematical world. I now understand this to be the former, not the latter.
This takes too long to load and with no context or explanation for the title.
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.