The Textbook That Unleashed Ramanujan's Genius

https://books.google.com/books/download/A_Synopsis_of_Elementary_Results_in_Pure.pdf?id=JLmCAAAAIAAJ&output=pdf

by cbracketdash • 5 years ago

289 108 5 years ago

books.google.com

xNeil8• 5 years ago

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.

nindalf3• 5 years ago

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.

alex_smart18• 5 years 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.

pmoriarty3• 5 years 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?

alex_smart18• 5 years ago

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.

lqet• 5 years ago

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.

flaubere4• 5 years ago

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.

xNeil8• 5 years ago

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!

khazhoux3• 5 years ago

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.

ctchocula• 5 years ago

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.

annexrichmond• 5 years ago

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• 5 years ago

Yeah, the exercises in that book were wonderful.

xNeil8• 5 years ago

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.

khazhoux3• 5 years ago

Thanks. Looks pretty fantastic.

commandlinefan2• 5 years ago

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• 5 years ago

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.

kenny87• 5 years ago

MAA has its Basic Library List: https://www.maa.org/press/maa-reviews/the-basic-library-list...

khazhoux3• 5 years ago

The list contains 2,963 books!

fao_• 5 years ago

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.

est• 5 years ago

Is there a modern equivalent of this book?

dartharva2• 5 years ago

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

pbhjpbhj• 5 years ago

Not going obsolete doesn't mean not improvable. Seems a reasonable question.

wbl• 5 years ago

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.

open0• 5 years ago

Not really the case, mathematical terminology and conventions change over time.

commandlinefan2• 5 years ago

that book can't ever get obsolete

Math doesn't change, but language and printing technology do.

eeegnu• 5 years ago

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.

pmoriarty3• 5 years ago

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.

tkgally• 5 years ago

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• 5 years ago

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!

tmsh• 5 years ago

TIL “surds” https://www.mathsisfun.com/surds.html

Such a fun language, math.

rmk• 5 years ago

I always thought that surds is short for 'absurds' :)

Nice to read the etymology of the word!

elcapitan• 5 years ago

43MB scanned PDF, just in case you're trying to read it on mobile.

voldacar• 5 years ago

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• 5 years ago

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• 5 years ago

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...

mellosouls• 5 years ago

This takes too long to load and with no context or explanation for the title.

philip1209• 5 years ago

The book is still in print: "Synopsis of Elementary Results in Pure and Applied Mathematics: Volume 1: Containing Propositions, Formulae, and Methods of Analysis,"

cratermoon• 5 years ago

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

daveslash• 5 years ago

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.

The Textbook That Unleashed Ramanujan's Genius

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