The Textbook That Unleashed Ramanujan's Genius
books.google.com
books.google.com
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.
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.
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.
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.
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
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.
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.
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.
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.
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 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 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 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.
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.
That's EXACTLY what they did. Look at IIT-PAL on YouTube.
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.
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.
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.
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.
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 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 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.
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.
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.
You want several gradual sorts from the bottom up where each sortation relies on personal accountability between the different teachers and administrations. It would probably look much closer to the European football leagues. You would have gradual promotions and relegations every year.
Is there an example where this system is employed for the purpose of college admissions?
> each sortation relies on personal accountability between the different teachers and administrations
How would such a system actually work? As an illustrative example, the year I graduated High School I was one among about ~ 300K graduating students in my province. There were only ~ 35K college seats across all undergraduate courses (including Women's Colleges, Evening Colleges, etc) in my province up for grabs. If I was interested in medicine, there were ~ 400 seats, of which ~ 150 are female only. How would 'personal accountability' between teachers & administrations work in this scenario? I still fail to grasp how you suggest one kid should go to college vs another. School grades? I had the highest grades in the science exam nationwide, but so did 10 other kids just in my school. All of us could have gotten glowing letters of recommendation from our teachers, and I think that's a terribly subjective way to evaluate large numbers of people.
If your football league analogy is meant to suggest that students should move into and between colleges based on performance, that still doesn't resolve how one gets into a college in the first place without an exam. Even with continual evaluation at the school level, you're still left with many more eligible students (100X) than you have capacity for.
By 3rd grade you would be filtered into the best class in your city. By the 9th grade you would be filtered into the top province level school. By college, you would be filtered into the position that you already earned. In America we call this system the magnet schools. All I am suggesting is to make this more fluid, and with digital schools coming to be as a result of CO-VID, is the perfect time to experiment with such a system.
More importantly than attempting to fix the Indian education system is what can you do to help against metricification. Do not rely on others scores. If you are hiring and get a resume from someone who did not go to a prestigious school, do not throw it away without looking. People are more than a number. The best often do not look like the best.
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.
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.
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.
Sure, the very top students are likely to be both talented & hard working, and would perhaps have still gotten on the list without coaching (though perhaps not high enough to have their pick). It's in the minutiae of small differences in raw scores where the benefits of coaching likely help. If coaching gives me an additional 10 points, that could mean the difference between getting a seat vs not for a bright student.
I think you're suggesting that joining a coaching centre is a strong signal of seriousness, rather than a material benefit from the actual classes. Possible, but as others in this subthread have pointed out, access to coaching is something out of reach for many students, irregardless of their seriousness. To pose the question another way: how many of the 50K people who got a seat would not if coaching (in its current form) did not exist? Perhaps the top 100 names would be redistributed within the top 5000, but they'd still have a seat. There's likely a lot more students in the long tail whose fortunes were determined by access to coaching. My concern is less with the top 100 and more with students at the precarious end.
13 students getting top scores!!
My God, it has been a while since I wrote the exam, has the situation changed that much since then? At my time, there was a 25 marks difference between the top two ranks.
Is there any chance you are talking about JEE Mains and not the JEE Advanced? JEE Mains is supposed to be the easier test that serves as a "prelims" to the more difficult Advanced exam. For Mains itself, it is not all that important to distinguish between the top students.
>I think you're suggesting that joining a coaching centre is a strong signal of seriousness, rather than a material benefit from the actual classes
I am also suggesting that there are other benefits from joining coaching that are probably more important than the much hyped "tricks" for solving problems. For one, joining a coaching class means that you are part of a community of other students with similar goals and aptitude.
Otherwise, I agree with your overall argument (although not in its entirety). Yes, at the lower end of the ladder, small difference in scores can result in big jumps in ranks and yes, coaching would definitely have a significant impact on the prospects of these students.
The point I do not agree with is lack of access to coaching. Even middle class families of Bihar, the poorest state of India, find the resources to send their kid to Kota for a couple of years. So, it is not that inaccessible. Plus there is apparently free material available on youtube now, created by the IITs itself.
I would also argue that people much below this threshold have bigger worries in life. We as a society definitely need to ask ourselves why it is not possible to have a dignified, livable wage for the majority of people in our country when many other countries seem to have solved this problem. Solving such hard socio-economic problems is a ridiculous expectation from a measly entrance exam.
> Even middle class families of Bihar, the poorest state of India, find the resources to send their kid to Kota for a couple of years. So, it is not that inaccessible.
I wonder, though. Quora answers about the cost of coaching in Kota from 2018 yields figures in the range of 2.6 - 3.3 lakhs annually (ie, coaching + accommodation + food, etc). That's a median additional expenditure of 25K per month, for two years. Yes, some families from Bihar are able to muster up the amount, but I suspect there is some survivorship bias here. Even if Kota were to be filled by Bihari students, it doesn't necessarily follow that it is accessible to the average bright motivated Bihari student. My guess it is not.
> I would also argue that people much below this threshold have bigger worries in life.
No argument there.
Not "some". It is literally lakhs of families every year. And if you look at the data of total number of JEE candidates from Bihar, that is actually a very significant percentage.
Even if you believe that coaching is not accessible to the average bright motivated Bihari student, the very fact that so many people from the poorest, most backward part of the country look at this exam as an instrument to better their lives should tell you something.
Across all the coaching centres in Kota, you have about ~ 150K students annually, so about 1.5 lakhs in total from all states. Even if the overwhelming majority were Bihari, it doesn't generalize. That's tells us more about the network effect operating in Bihar rather than something about dedicated students in general. That's a lot of kids for a tiny town like Kota, but a drop in the ocean when dealing with the scale of the JEE.
> the very fact that so many people from the poorest, most backward part of the country look at this exam as an instrument to better their lives should tell you something.
Yes, that the exam needs reform. The fact that so many students who 'succeed' at the exams benefited from enrolling in coaching classes suggests that the exam needs to be reformulated to eliminate that variable. It's not the only thing in the education system that needs reform, but it is one among many. If as you suggest serious students benefit from the community of other like minded kids, then self organizing study groups can happen and still save 25K/month.
According to me, the goal of the JEE is to identify ~ 10K kids with the right combination of aptitude & dedication, in a manner that's not blind to their wide ranging social & economic backgrounds. Attending a coaching centre is a signal for their family's desire, but I think we can find much better signals for aptitude & dedication.
You keep repeating this misdirection everywhere. Students studying in Kota from the poorest and most backward states are not themselves from poor and backward families. India has tremendous wealth inequality as does Bihar. If they were, they wouldn't be able to afford 2 years of coaching and lodging in Kota.
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.
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.
This should be anti-source if you say you don't need to prepare hard enough.
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)...
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.
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.
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.
As well as having educated supportive parents with a decent budget, and being part of an ecosystem where education is prioritized.
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.
https://timesofindia.indiatimes.com/city/lucknow/Youngest-II...
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!
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.
As someone not familiar with the JEE nor the gaokao, might I ask how they differ from the SAT?
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.
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.
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.
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
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.
Google scan: https://archive.org/details/asynopsiselemen00carrgoog
MSN scan: https://archive.org/details/synopsisofelemen00carrrich
Thank you!
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.
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.
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".
Such a fun language, math.
Nice to read the etymology of the word!
So a modern version would at most be a different idea of what the core theorems should be.
Math doesn't change, but language and printing technology do.