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The Textbook That Unleashed Ramanujan's Genius

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Re: The Textbook That Unleashed Ramanujan's Genius

#11

Post by Ntrails »

nindalf wrote: post #6
alex_smart wrote: post #5

Earlier quoted context omitted.

>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…

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 prob…

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.

Re: The Textbook That Unleashed Ramanujan's Genius

#13

Post by annexrichmond »

khazhoux wrote: post #7

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

Spivak's Calculus, which is really an introduction to Analysis, was that book for me. The way to approach it was to forget everything you learned about math in high school and learn it from the ground up in this book, as it will provide you with so much more insight and appreciation for how it all comes together

Some of the book's best content is actually the exercises; notoriously difficult, but incredibly rewarding as spending the time to solve them them really prepares you for upcoming chapters

Re: The Textbook That Unleashed Ramanujan's Genius

#15

Post by alex_smart »

boruto wrote: post #8
alex_smart wrote: post #5

Earlier quoted context omitted.

>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…

> : I was top 10 in JEE 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.

Re: The Textbook That Unleashed Ramanujan's Genius

#19

Post by masklinn »

pbhjpbhj wrote: post #18
dartharva wrote: post #14

Earlier quoted context omitted.

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

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.

Re: The Textbook That Unleashed Ramanujan's Genius

#20

Post by alex_smart »

xNeil wrote: post #2

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

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.
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