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The Textbook That Unleashed Ramanujan's Genius
- xNeil 5y agoIt'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.
- nindalf 5y agoFor 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.
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- alex_smart 5y ago>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.
- nindalf 5y agoThat’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.
- Ntrails 5y agoSo, 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 5y agoI'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
- pmoriarty 5y ago"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?
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- alex_smart 5y agoThe 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.
- lqet 5y agoA 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 5y agoNot 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 5y agoI 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 5y agoIn the JEE, you generally assume the range to be the distance the projectile covers before reaching the launch height again, unless specified otherwise.
- xNeil 5y agoYou 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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- khazhoux 5y agoI'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.
- ctchocula 5y agoSeconded. 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.
- annexrichmond 5y agoSpivak'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 5y agoYeah, the exercises in that book were wonderful.
- xNeil 5y agoI'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 5y agoThanks. Looks pretty fantastic.
- est 5y agoIs there a modern equivalent of this book?
- dartharva 5y agoWhy? It's pure mathematics, that book can't ever get obsolete.
- pbhjpbhj 5y agoNot going obsolete doesn't mean not improvable. Seems a reasonable question.
- masklinn 5y agoAssuming 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.
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- wbl 5y agoWhen 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 5y agoBut 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.
- open0 5y ago
- tkgally 5y agoThe book is easier to read in a browser at the Internet Archive: Google scan: https://archive.org/details/asynopsiselemen00carrgoog https://archive.org/details/asynopsiselemen00carrgoog MSN scan: https://archive.org/details/synopsisofelemen00carrrich https://archive.org/details/synopsisofelemen00carrrich
- etiam 5y agoWonderful. 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!
- tmsh 5y agoTIL “surds” https://www.mathsisfun.com/surds.html https://www.mathsisfun.com/surds.html Such a fun language, math.
- rmk 5y agoI always thought that surds is short for 'absurds' :) Nice to read the etymology of the word!
- elcapitan 5y ago43MB scanned PDF, just in case you're trying to read it on mobile.
- voldacar 5y agoI 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 5y agoThis 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 5y agoIf 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-easiest-formula/ https://johncarlosbaez.wordpress.com/2020/11/18/ramanujans-e...
- mellosouls 5y agoThis takes too long to load and with no context or explanation for the title.
- philip1209 5y agoThe book is still in print: "Synopsis of Elementary Results in Pure and Applied Mathematics: Volume 1: Containing Propositions, Formulae, and Methods of Analysis,"
- cratermoon 5y agoRamanujan: 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 https://www.usna.edu/Users/math/meh/ramanujan.html
- daveslash 5y agoAs 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.