[HN Gopher] The Textbook That Unleashed Ramanujan's Genius
___________________________________________________________________
The Textbook That Unleashed Ramanujan's Genius
Author : cbracketdash
Score : 252 points
Date : 2021-05-19 03:58 UTC (19 hours ago)
(HTM) web link (books.google.com)
(TXT) w3m dump (books.google.com)
| est wrote:
| Is there a modern equivalent of this book?
| dartharva wrote:
| Why? It's pure mathematics, that book can't ever get obsolete.
| pbhjpbhj wrote:
| Not going obsolete doesn't mean not improvable. Seems a
| reasonable question.
| masklinn wrote:
| 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.
| commandlinefan wrote:
| > that book can't ever get obsolete
|
| Math doesn't change, but language and printing technology do.
| pmoriarty wrote:
| 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.
| wbl wrote:
| 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.
| dartharva wrote:
| 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.
| eeegnu wrote:
| 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.
| open0 wrote:
| Not really the case, mathematical terminology and conventions
| change over time.
| [deleted]
| cratermoon wrote:
| 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
| voldacar wrote:
| 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.
| lern_too_spel wrote:
| 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.
| celerity wrote:
| 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...
| khazhoux wrote:
| 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.
| fao_ wrote:
| 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.
| commandlinefan wrote:
| 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.
| philiplu wrote:
| 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.
| dataangel wrote:
| 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!
| annexrichmond wrote:
| 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
| AlexCoventry wrote:
| Yeah, the exercises in that book were wonderful.
| xNeil wrote:
| I'm sure you'd enjoy _What is Mathematics?_ by Robbin and
| Courant. Take a look at it, hope it 's kind of what you're
| looking for.
| khazhoux wrote:
| Thanks. Looks pretty fantastic.
| xNeil wrote:
| Sounds good!
| kenny87 wrote:
| MAA has its Basic Library List: https://www.maa.org/press/maa-
| reviews/the-basic-library-list...
| khazhoux wrote:
| The list contains 2,963 books!
| ctchocula wrote:
| 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.
| xNeil wrote:
| 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.
| [deleted]
| lqet wrote:
| 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 thus also depends on the height above ground of the
| gun.
| flaubere wrote:
| 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.
| tyleo wrote:
| 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.
| xNeil wrote:
| In the JEE, you generally assume the range to be the
| distance the projectile covers before reaching the launch
| height again, unless specified otherwise.
| xNeil wrote:
| 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!
| alex_smart wrote:
| 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.
| nindalf wrote:
| 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.
| [deleted]
| pmoriarty wrote:
| _" 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?
| alex_smart wrote:
| >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.
| boruto wrote:
| > : I was top 10 in JEE
|
| This should be anti-source if you say you don't need to
| prepare hard enough.
| alex_smart wrote:
| 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.
| rob74 wrote:
| 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)...
| alex_smart wrote:
| >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.
| pmoriarty wrote:
| _" 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.
| reachtarunhere wrote:
| 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.
| timewarrior wrote:
| 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.
| alex_smart wrote:
| 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...
| timewarrior wrote:
| 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!
| xNeil wrote:
| 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 :)
| fizwhiz wrote:
| I hate to be that guy, but this isn't Quora my guy.
| xNeil wrote:
| I get at what you're saying, but I figured I could give
| it a shot since he replied to my thread :)
| nindalf wrote:
| 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.
| flaubere wrote:
| 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.
| Ntrails wrote:
| 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.
| dr_zoidberg wrote:
| 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
| [deleted]
| alex_smart wrote:
| 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.
| nindalf wrote:
| > 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.
| alex_smart wrote:
| >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.
| random314 wrote:
| > 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.
| valarauko wrote:
| > _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.
| alex_smart wrote:
| >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.
| xNeil wrote:
| >How much would it cost the Indian government to develop
| detailed coaching videos by IIT professors and upload it
| for free to YouTube?
|
| That's EXACTLY what they did. Look at IIT-PAL on YouTube.
| 1024core wrote:
| 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.
| rdedev wrote:
| 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.
| alex_smart wrote:
| 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.
| TeMPOraL wrote:
| > _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.
| flaubere wrote:
| 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.
| ItsMonkk wrote:
| 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.
| flaubere wrote:
| 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.
| Asymmetryk wrote:
| shouldn't everyone attending a top school be decidedly
| coasting along in some way about their education, so they
| can optimise preferred areas?
| alex_smart wrote:
| >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?
| ItsMonkk wrote:
| 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.
| alex_smart wrote:
| >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.
| ItsMonkk wrote:
| 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.
| valarauko wrote:
| While I largely agree with your argument, I'm curious if
| you have a solution in mind that could work in the Indian
| context.
| ItsMonkk wrote:
| Use the start-up model whenever possible.
|
| 1. Take as many bets as you can.
|
| 2. Pay a great deal of attention to those bets. Guide
| them.
|
| 3. As soon as you know the bet failed, let it fail.
|
| Entrance exams are an anti-pattern. They commit to much
| to early. This means they have to be correct, so they get
| more strict. This squeezes out exactly who they were
| hoping to find. Same problem with interviews. Same
| problem everywhere.
| alex_smart wrote:
| >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.
| valarauko wrote:
| > _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.
| alex_smart wrote:
| >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.
| [deleted]
| tmsh wrote:
| TIL "surds" https://www.mathsisfun.com/surds.html
|
| Such a fun language, math.
| rmk wrote:
| I always thought that surds is short for 'absurds' :)
|
| Nice to read the etymology of the word!
| mellosouls wrote:
| This takes too long to load and with no context or explanation
| for the title.
| elcapitan wrote:
| 43MB scanned PDF, just in case you're trying to read it on
| mobile.
| daveslash wrote:
| 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.
| tkgally wrote:
| 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
| etiam wrote:
| 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!
| philip1209 wrote:
| The book is still in print: "Synopsis of Elementary Results in
| Pure and Applied Mathematics: Volume 1: Containing Propositions,
| Formulae, and Methods of Analysis,"
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