Learn Mathematics Like Ramanujan Did
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- čas přidán 27. 09. 2023
- My Courses: www.freemathvids.com/ || Every time I think of Ramanujan I am always shocked at how he was able to learn math from the book in this video. It is called A Synopsis of Elementary Results in Pure and Applied Mathematics (Volume I).
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Thank you:)
Ramanujan is one of the greatest mathematians of all time.
There are no one who can be claimed to be the BEST mathematician of all time, but there are so many audacious born from the very first beginnings of the humanity that motivate us (modern mathematicians) to keep going and improving! From the Legendre identities, Ramanujan equations for obtaining as much PI digits as you want, to Delta of Dirac and topology. An universal language that make us comprehend better the world where we live, without even being able to see stuffs that it can explain perfectly, such as R^n planes. I hope you have a good day, and everyone who reads this. FIGHT for what you love and that can make the world better than "yesterday".
@@Mewingmaster42 yea no one (if you don't count euler)
Pure genius. Way ahead of time
He left this world way too early. Imagine what he'd accomplish if he had more time.
He was poor deprived of nutrition, no money to buy books and paper to practice. Still his brain worked as max capacity or even more to understand, compute and interpret those equation. Yes astounding. Also for the fact he lived only for 32 years and made such a significant impact. Imagine what would have happened if he lived till 70 years. Ramanjan, Bodhi dharman, Jagadish Chandra bose, CV Raman are the sages among few Bharat has produced.
India*
@@syedmuheeb2409 ?????
@@syedmuheeb2409kiddo India is a newer term in comparison to Bharat.
@@gravity.inescapable okay so? The point?? Mr gravity sir??
@@syedmuheeb2409 what was purpose behind dropping a comment like " India* "??
Seems like you have problem with Bharat. (Which is not a sign of deshpremi)
"The Man Who Knew Infinity" was great. I'd encourage anyone who is interested in mathematics - a group which presumably includes pretty much anybody watching Math Sorcerer videos - to watch it. It's very moving and very inspirational, IMO.
That movie was way, way to slow. I didn’t like it.🤷
@@calicoesblue4703 watch in 2x then
@@calicoesblue4703watch hindi movie
Amazing movie. Loved it.
I love stories of genius like The Man Who Knew Infinity. Whether a true biography (like that or Theory of Everything) or a fantasy spin (Tolkien or Contact, granted Contact is much further removed from the inspiration). I feel like they all have that slightly slower pacing too. Even realistic stories of drive in intellect like Queen's Gambit. Wish I knew how to search for that genre.
Thank you for continuing to produce these videos! You are an inspiration to many, myself included.
Ramanujan was such a rock star legendary mathematician. The way he saw mathematics was as if he could see the Matrix (pun very much intended!😁).
It's such a tragic story about his life being cut so short. Imagine what he could have achieved if he had lived to old age.
I have the two-volume hardcover edition in my private math library! Thank you, MS, for doing a video about this classic work that awakened the genius of one of my math heroes, Srinivasa Ramanujan (1887-1920)!!
While Ramanujan did study a lot from one this book, another book from which he studied was a trigonometry book by SL Loney. He was able to solve very complex trigonometry by the age of 13 with its help. Would love to see you review that!
I think he also had one or two more books that he could get access to (it is pretty hard to find the names as everyone just says this book).
He was a genius nevertheless, a true bright mathematician.
Also, paper was very scarce for him. He wrote with chalk on the floor of temples and only wrote the final and most important results on paper(to mail it to other people. Like he did to Hardy). This is probably why he didn't care about writing proofs.
Even when he was in Cambridge, it was very difficult to find paper due to world war 1 (that is what I heard from someone. Not really sure but seems probable)and this might be one of the reasons why we don't really know what all he discovered. We have his notebooks but it only included the really selected ones with little proofs. Imagine if we were able to access all of his works.
And here I was struggling at Trig prove questions. I was 14y/o when I was struggling.
@@user-qc9cd5iz3lIt's okay bro. Not everyone is a genius. I'm sure even Ramanujan struggled a lot but figured it out by spending a lot of time into it :)
@@user-qc9cd5iz3l if someone is a genius, that's the power he got by birth. But hard work is in your hand how much you can improve yourself, it matters.
I think ramanujan also do read and learn a lot more stuff over there and so. Is imposible for Simeone who don't know what a integer sign is to just imaginé What that means. For example. Even through he was a genious with low resourses he do learn here and there at least the básics. He was at university in spite he does not finish it. And probably borrow books from library and Friends...the man was an absolute genious. No doubt. And a true magical guy. But he was a Spartan in what hard work means.
As a mathematician (PhD) myself, I’ve always been fascinated with Ramanujan since I was child. He was an exceptionally profound human being and it’s one of the greatest tragedies that he died at such a young age.
I always ask myself what else could he had achieved with a long life.
He actually died of TB which was curable even then.
@@homijbhabha8860depends on which part of the world you’re in
Great book. Great video. I’m so glad you emphasized the superhuman effort Ramanujan made to learn mathematics. He did pour his WHOLE life into math. My mind boggles at the depth of his intellect and his contribution to math. Thanks for bringing that forward. I would enjoy a review of a book that chronicles and/or catalogues his insights. It would be fascinating learn some of the pathways he took to results. Thank you for caring and teaching.
I almost cried when I saw Archimedes quote in the begining of the video and it gives me memories when I first fell in love with math.❤ Ramanujan is one of my idols.
My idol is Grigory Perelman
@@aki7162 My number one idol is Leonhard Euler
@@calculus988 have you heard about Perelman though?
@@aki7162 no, I learned something new though
Cool😎👍
One of my favourite mathematicians. Thanks for sharing this incredible book.
Working my way thorugh a multiple variable calculus course, I have no idea what most of your videos mean, but just the passion you talk about it is contagious and it keeps me going . Thanks Sorcerer!
Incredible story, incredible !
I am studying math and some of its history as my side-hobby but up until now i hadn't encountered myself, through my efforts, a stories about this brilliant mathematician. What a great finding!
For us Indians, he is legend
I find this book and learning process more attractive that the standard "here's the full thing, now memorize it and apply it".
It's like sorted puzzle pieces you have to think through, understand and connect.
You're free to explore them however you want, without a constrained order or list of X problems due in 2 days.
Very good.
This paper is about Carr's book and Ramanujan.
"The Influence of Carr’s Synopsis on Ramanujan" by Bruce C. Berndt.
which appeared in the conference proceedings "Number Theory and Discrete Mathematics" 2002.
Math Sorcerer, I just emailed you this paper.
Great video! Its amazing how much he did with so little. Imagine if he had a proper formal education at a young age 🤯! What an amazing mathematician and very inspiring!
Srinivasa Ramanujan Sir is a great devotee of Lord Vishnu and Namagiri Thayyar, which enabled him to learn Mathematics like understanding a spiritual truth
I think it’s nice to do some proofs and maths by yourself. It really helps to understand the concept
I want to mention that he also used
S.L loney book for trigonometry
Thanks for feeding our 🧠 . You are a true inspiration
He also feeds our hearts too ❤️
Mathematics and Physics are two subjects which require no country, no language, Nothing, only intellect and the university language Mathematics. ... Respect Ramanujan...sir .... And also Newton 🤎🤎🤎🤎🤎🤎🙌🏻🙌🏻🙌🏻🙌🏻🙌🏻
I loved "The Man Who Knew Infinity" !
Salute to great mathematician sir Ramanujan. 🙏
The difference between someone who studies maths grudgingly just to pass an exam and someone who likes maths genuinely.
Unfortunately with how school is set up it’s incredibly hard for anyone, even people who like math, to study math genuinely
He is an inspiration 😊
Love from India
That book and its presentation style looks very much like the trig book we used at univ; very lean and not fleshed out at all. We were expected to follow the definitions then apply them having first derived the proof. Took time and much effort but fun as I was offered trig in 7th grade and again as a junior in public h.s. Interestingly all my best teachers/profs for math were women, and for chem -- one woman taught chem & physics in hs. All chem profs were brilliant men but could not teach their way out of a paper bag.
v happy to see you cover Ramanujan
It just amazed how dense mathematics is, that’s one of the reasons I think it’s so hard.
He deserves noble prize
1. He "deserved"
2. as noble prize is not awarded to deceased
3. and we don't have noble prize in mathematics (as far as I know Fields medal is highest honor)
I learned about Ramanujan because of this channel and other sources in the web. He is definitely a legend. Massive respect and I will also look up to him. :)
He nu... 1x47.. Guy was a mathmagician. Guy wasn't gifted, just passed the blessings of his understanding, a true legend 🙏
he wasnt gifted, because he himself was the gift
If you wanna produce results, you better learn the content. But if you wanna produce new concepts, you better read about results
That is the greatest truth close to reality that i have ever read. Thank you bro.
How did it came in ur mind and why
This requires wider appreciation
He was not too poor exactly, he used chalk and slate to do mathematics. He learned mathematics by himself, though he always credited the Goddess of Namagiri. According to Ramanujan, she appeared to him in visions. Definitely, he was a genius
What I find interesting in the movie is that he had no idea how he knew everything, but simply the fact that he did.
I was also like that like
I don't know how I got the answer but I got it.
I like your comment, but at the same time, it makes me introspective: What I find interesting in my life is that I have no idea how I don’t know anything, but simply the fact that I do cry😢
thats pure god given talent
@@looooonooooooooooooooooooooongThe talent given to him by the lord Jesus Christ
@@calicoesblue4703 factually inaccurate
What I lack in IQ I will make up for in persistence and caffeine.
Also, the second volume is crazy. Plenty of graphs for multivariable calculus. I expend a lot of money to buy the originals but they are worthy.
Thanks for talking about S. Ramanujan. ❤
estaba intentando resolver algunas reespuestas jajaja, es dificil pero es gratificante al dar los pasos como se hicieron y ver donde estaba tu error y como concuerdan al final
You will enjoy the Nova documentary on Ramanujan made about thirty years ago.
H'actually the Vid was named "Letter from an Indian Clerk" and was made for the excellent science based series Equinox (sadly now defunct!), and broadcast on the UK's Channel Four, way back in 1987! I've still got the Vid. I think this formed the basis for the movie: "The Man who knew Infinity", which was also based on the book of the same name.
He is my inspiration ❤ , thank you for covering him in video ❤ . Namaste from india ❤,
AND WAS A BRAHMIN TOO
Inspiring ❤
Ramanujan is easily amongst the smartest who ever lived
I love the cat and mouse game that he played with British mathematician via letter exchange, incredible story, they doubted him first at first saying he had simple proofs but clearly he was "hiding something".
Oh pls elaborate this i wanna know too.
I guess he either never revealed intermediate steps at first or so heavily influenced by the Book he used to teach himself math that he followed it to derive
It would be great if you could Explain every mathematical results from this in series of videos from this book (Volume 1 & 2)
You smelled the book! I was waiting for that moment 😂👍
All book lovers smell the books first before open it. Next, check the back of the book, next open few pages and feel the freshness (and the knowledge that you gonna get from the book).
@@slhermit oh I do the same, I find it difficult to learn from online pdfs, I need the touch and olfactory sensations from a physical book to effectively learn the material :)
Cringe
You mention about if paper was scarce. I believe the "legend" goes that he did a great deal of his early work as a child in chalk on stone outside, before he could afford paper
Looking back based on biographical and documentary works on Ramanujan its kind of obvious he could have been a man diagnosed with savant syndrome. He struggled with lots of OCDs and he was not know to be a vocal man and social interaction was not his strong traits.
This book actually seems useful as quick review material.
True
He’s one of the reason why we should know more about cosmical intuition and understanding reincarnation
If you have genuine passion for something. You will become very good at it.
Men like Ramanujan advance human civilization in a big way while mere mortals like most of us can be only be in awe!!
Conservation of Spatial Curvature (Both Matter and Energy described as "Quanta" of Spatial Curvature. A string is revealed to be a twisted cord when viewed up close.)
Is there an alternative interpretation of "Asymptotic Freedom"? What if Quarks are actually made up of twisted tubes which become physically entangled with two other twisted tubes to produce a proton? Instead of the Strong Force being mediated by the constant exchange of gluons, it would be mediated by the physical entanglement of these twisted tubes. When only two twisted tubules are entangled, a meson is produced which is unstable and rapidly unwinds (decays) into something else. A proton would be analogous to three twisted rubber bands becoming entangled and the "Quarks" would be the places where the tubes are tangled together. The behavior would be the same as rubber balls (representing the Quarks) connected with twisted rubber bands being separated from each other or placed closer together producing the exact same phenomenon as "Asymptotic Freedom" in protons and neutrons. The force would become greater as the balls are separated, but the force would become less if the balls were placed closer together. Therefore, the gluon is a synthetic particle (zero mass, zero charge) invented to explain the Strong Force. An artificial Christmas tree can hold the ornaments in place, but it is not a real tree.
String Theory was not a waste of time, because Geometry is the key to Math and Physics. However, can we describe Standard Model interactions using only one extra spatial dimension? What did some of the old clockmakers use to store the energy to power the clock? Was it a string or was it a spring?
What if we describe subatomic particles as spatial curvature, instead of trying to describe General Relativity as being mediated by particles? Fixing the Standard Model with more particles is like trying to mend a torn fishing net with small rubber balls, instead of a piece of twisted twine.
Quantum Entangled Twisted Tubules:
“We are all agreed that your theory is crazy. The question which divides us is whether it is crazy enough to have a chance of being correct.” Neils Bohr
(lecture on a theory of elementary particles given by Wolfgang Pauli in New York, c. 1957-8, in Scientific American vol. 199, no. 3, 1958)
The following is meant to be a generalized framework for an extension of Kaluza-Klein Theory. Does it agree with some aspects of the “Twistor Theory” of Roger Penrose, and the work of Eric Weinstein on “Geometric Unity”, and the work of Dr. Lisa Randall on the possibility of one extra spatial dimension? During the early history of mankind, the twisting of fibers was used to produce thread, and this thread was used to produce fabrics. The twist of the thread is locked up within these fabrics. Is matter made up of twisted 3D-4D structures which store spatial curvature that we describe as “particles"? Are the twist cycles the "quanta" of Quantum Mechanics?
When we draw a sine wave on a blackboard, we are representing spatial curvature. Does a photon transfer spatial curvature from one location to another? Wrap a piece of wire around a pencil and it can produce a 3D coil of wire, much like a spring. When viewed from the side it can look like a two-dimensional sine wave. You could coil the wire with either a right-hand twist, or with a left-hand twist. Could Planck's Constant be proportional to the twist cycles. A photon with a higher frequency has more energy. ( E=hf, More spatial curvature as the frequency increases = more Energy ). What if Quark/Gluons are actually made up of these twisted tubes which become entangled with other tubes to produce quarks where the tubes are entangled? (In the same way twisted electrical extension cords can become entangled.) Therefore, the gluons are a part of the quarks. Quarks cannot exist without gluons, and vice-versa. Mesons are made up of two entangled tubes (Quarks/Gluons), while protons and neutrons would be made up of three entangled tubes. (Quarks/Gluons) The "Color Charge" would be related to the XYZ coordinates (orientation) of entanglement. "Asymptotic Freedom", and "flux tubes" are logically based on this concept. The Dirac “belt trick” also reveals the concept of twist in the ½ spin of subatomic particles. If each twist cycle is proportional to h, we have identified the source of Quantum Mechanics as a consequence twist cycle geometry.
Modern physicists say the Strong Force is mediated by a constant exchange of Gluons. The diagrams produced by some modern physicists actually represent the Strong Force like a spring connecting the two quarks. Asymptotic Freedom acts like real springs. Their drawing is actually more correct than their theory and matches perfectly to what I am saying in this model. You cannot separate the Gluons from the Quarks because they are a part of the same thing. The Quarks are the places where the Gluons are entangled with each other.
Neutrinos would be made up of a twisted torus (like a twisted donut) within this model. The twist in the torus can either be Right-Hand or Left-Hand. Some twisted donuts can be larger than others, which can produce three different types of neutrinos. If a twisted tube winds up on one end and unwinds on the other end as it moves through space, this would help explain the “spin” of normal particles, and perhaps also the “Higgs Field”. However, if the end of the twisted tube joins to the other end of the twisted tube forming a twisted torus (neutrino), would this help explain “Parity Symmetry” violation in Beta Decay? Could the conversion of twist cycles to writhe cycles through the process of supercoiling help explain “neutrino oscillations”? Spatial curvature (mass) would be conserved, but the structure could change.
=====================
Gravity is a result of a very small curvature imbalance within atoms. (This is why the force of gravity is so small.) Instead of attempting to explain matter as "particles", this concept attempts to explain matter more in the manner of our current understanding of the space-time curvature of gravity. If an electron has qualities of both a particle and a wave, it cannot be either one. It must be something else. Therefore, a "particle" is actually a structure which stores spatial curvature. Can an electron-positron pair (which are made up of opposite directions of twist) annihilate each other by unwinding into each other producing Gamma Ray photons?
Does an electron travel through space like a threaded nut traveling down a threaded rod, with each twist cycle proportional to Planck’s Constant? Does it wind up on one end, while unwinding on the other end? Is this related to the Higgs field? Does this help explain the strange ½ spin of many subatomic particles? Does the 720 degree rotation of a 1/2 spin particle require at least one extra dimension?
Alpha decay occurs when the two protons and two neutrons (which are bound together by entangled tubes), become un-entangled from the rest of the nucleons
. Beta decay occurs when the tube of a down quark/gluon in a neutron becomes overtwisted and breaks producing a twisted torus (neutrino) and an up quark, and the ejected electron. The production of the torus may help explain the “Symmetry Violation” in Beta Decay, because one end of the broken tube section is connected to the other end of the tube produced, like a snake eating its tail. The phenomenon of Supercoiling involving twist and writhe cycles may reveal how overtwisted quarks can produce these new particles. The conversion of twists into writhes, and vice-versa, is an interesting process, which is also found in DNA molecules. Could the production of multiple writhe cycles help explain the three generations of quarks and neutrinos? If the twist cycles increase, the writhe cycles would also have a tendency to increase.
Gamma photons are produced when a tube unwinds producing electromagnetic waves. ( Mass=1/Length )
The “Electric Charge” of electrons or positrons would be the result of one twist cycle being displayed at the 3D-4D surface interface of the particle. The physical entanglement of twisted tubes in quarks within protons and neutrons and mesons displays an overall external surface charge of an integer number. Because the neutrinos do not have open tube ends, (They are a twisted torus.) they have no overall electric charge.
Within this model a black hole could represent a quantum of gravity, because it is one cycle of spatial gravitational curvature. Therefore, instead of a graviton being a subatomic particle it could be considered to be a black hole. The overall gravitational attraction would be caused by a very tiny curvature imbalance within atoms.
In this model Alpha equals the compactification ratio within the twistor cone, which is approximately 1/137.
1= Hypertubule diameter at 4D interface
137= Cone’s larger end diameter at 3D interface where the photons are absorbed or emitted.
The 4D twisted Hypertubule gets longer or shorter as twisting or untwisting occurs. (720 degrees per twist cycle.)
How many neutrinos are left over from the Big Bang? They have a small mass, but they could be very large in number. Could this help explain Dark Matter?
Why did Paul Dirac use the twist in a belt to help explain particle spin? Is Dirac’s belt trick related to this model? Is the “Quantum” unit based on twist cycles?
I started out imagining a subatomic Einstein-Rosen Bridge whose internal surface is twisted with either a Right-Hand twist, or a Left-Hand twist producing a twisted 3D/4D membrane. This topological Soliton model grew out of that simple idea. I was also trying to imagine a way to stuff the curvature of a 3 D sine wave into subatomic particles.
I'm headed to Wikipedia to learn more about Ramanujan. Thanks for this video!
What did Wikipedia say about Ramanujan?
Proud to be an indian
Sir Ramanujan pride of india❤❤❤❤❤❤
Math books used to have a table of symbols where they put their meanings and where in the book is defined.
It was so useful.
Do you know why they don't include it anymore?
Why?
@@tagberli I don't know.
Books like Baby Rudin have them.
@TheMathSorcerer
Hello! How do we get 'A Synopsis of Elementary Results in Pure and Applied Mathematics (Volume 2)' by G.S. Carr ? Please tell.... because i tried to find the volume-2 in the net but i could not get it.
"Ramanujan's Place in the World of Mathematics" edited by Krishnaswami Alladi looks like a interesting read.
10:11 the formula of summation of r^4 is wrong.
The correct formula is n(n+1)(2n+1)(3n^2+3n-1)/30
If you know mathematics and think about the fact that he was able to learn mathematics basically all by himself with this kind of book. That’s just unbelievable . Have to agree with you that Einstein was smart but if you think of crazy smart think of Ramanujan.
Arguable. Perhaps Einstein is just an absolute genius
@@charlessimbolon7333 So was Ramanujan, he did all of this with just basic education. We cannot imagine what he wouldve done if he had access to everything einstein had.
@@yashvi2048 it is (Ramamujan) jjust overrated genius just like Terry Tao, and others. Because Ramanujan did not invent the most fundamemtal theorem in Math like Gauss, Euler and Newton or G.F.B Riemann
@@charlessimbolon7333yeah but most the scientists who discovered this thing not died at the age of 33 like ramanujan
@@charlessimbolon7333 But those mathematicians you named, the math actually wasn't new & was first done in Africa first.
“… some people think of Einstein…yeah”. Boy, what an understatement.
Ramanujan even discovered mystery of infinity but he died early of sickness. I feel bad for him. He could achieved many things if he lived longer not only him but whole mathematics
Ramanujan had some bizarre mutation. Even that doesn’t capture it. Once in a species event. But yes I can certainly pick up a book and teach myself.
Love the CZcams videos. I wanted to ask about the Udemy classes. The list to the links of the Udemy classes above, are these in any order. For example, would the Abstract Algebra Course be taken 1st? Thanks
Not in order 😊
Another genuine was the Armenian mathematician Sergey Mergelyan who made the mergerlyan’s theorem
I'm a math's teacher sir nice stuff but the problem is many people choose Engineering only for monetary purposes but seldom some people choose maths for the love of it ...
If right educator is there things can become more positive
Cool as can be
Sir check these formula for arithmetic sequence. (n+1_1/2 )n represent number of term plus1minus1divided by 2 ;n+1-1/n and n+1-1/n+1 only for interest in mathematics.thanks
As an Indian I am proud of that man(ramanujan sir)..
He was just a genius ❤️❤️
11:46 section 339 is about wallis' product but it doesn't seem to give the actual answer (which is 2/pi, and as they say, between 1/2 and 1)
I'd also say politely that dude was badass😂
my god, so its really just a crazy long formula book which that insane man used to teach himself math with. the respect i have for ramanujan grows every single day exponentially
intenta resolver las demostraciones
I have seen that this society on seeing people like ramanujan exclaim that he was gifted not knowing that the only bridge to even talent is hardwork and no more
Actually he was both hardworking and god gifted
Sir please make a video on Chemistry for beginners.....!!!
It's a request.....!!!!
Amazing movie. Want to read the book. (Not the math book, just the book that the movie was based on)
own it agreed on your take
Thanks for your videos
Impossible ko possible bharat krta hai🎉🎉🎉🎉 no one can beat bharat.......
I'm assistant professor of mathematics in Rajasthan state of India ❤
I only taught him to my maths honours students only my number theory class , he was brilliant because he was studying maths with free mind that is only reason he was untrained mathematician
Ramanujan was struggling to write proofs, because he "just knew", because it was in his head. But writing those thoughts into paper is hard. Einstein was very confident at that.
Most of his proofs were actually done on a slate which could be erased and used again coz he could only afford paper for the results.
I feel like this would be a great reference book.
Legendary
❤️ from 🇧🇩
I'm more curious about the first pages, the things you've shown needs a great base
Hey bro love you....... ❤
In India,he is a God like figure in mathematics. Due to his way of approach in maths and his romanticism with it.....
Hey Math Sorcerer! I really struggle with being slow processing math however I still do love solving it. Will that be a problem except for when in school?
Ramanujan had no formal training in undergraduate mathematics. When Hardy and Littlewood would try to tutor him during his Trinity college years , very soon they would be flooded with a deluge of original ideas. Ramanujan progressed from the very basics to top quality research level original insights within days and both his mentors found it extremely hard to tutor or teach him the usual way Cambridge Math students were taught.
So many equations and proofs. Mostly cultural arts of mathematics. So difficult to get when you are in a remote village. Lucky we have advanced in maths. I find it difficult.
The real movie on Ramanujan was done by Indian producers from Tamilnadu,from South India where You can see his real life for more than 2 hrs 45 minutes in the screen where Britishers and Indian Tamil fims actors have acted.Films name is Ramanujan
I kinda like to place him in tandem with the great Paul Erdos as an inventor /investigator of new things, continuously creating & questioning, but leaving the proofs up to others following the trail of secrets to be discovered.
However, make no mistake that Ramanujan's place in the vast pantheon of Mathematics is definitely in the top 10....IMO 🤔
I am Chintu Sharma and study in class 2-A. In my class I am math topper and I always get 20/20 😎😎😒😎😎😎😎
Good job keep studying hard and make your parents proud
Sir I am your subscriber.your mentioned some books are not available in amajon 3:32 n and Flipkart.please mention availability of those books which you mentioned.and it's price.
They say this is tre only film taken inside Cambridge.
Ladies and Gentlemen, these are just "basic" or "elementary" mathematical results, don't put too much effort and stress yourself learning this stuff....
this book have every thing
My birthday is on December 22 and ramanujan is also born on 22 December and iam very good at math😎 quite coincidence 😁
Hello Master, do you knw if exists Volumne nº 2 ????
I smell my books too! lol, I understand the habit. There is something about the smell of a freshly printed book.