"this is one of those things where if you were born early enough you get your name on an algorithm" damn why you gotta throw shade on my boy karatsuba like that

Karatsuba starts at 33:54

02:56 irrationals 06:56 Catalan numbers (fun digression) 18:08 Newton's method 24:12 quadratic convergence 32:52 high precision multiplication 38:02 Karatsuba algorithm 42:13 demo: fun geometric problem Spoiler: plot twist in demo is related to Catalan numbers.

Dr Devadas reminds me of Sheldon Cooper whenever he laughs XD

46:17 What a twist!

Cool demo - I have seen it many times in this lecture and still amazed!

He's so much more fun in this class

Catalan number thing is dope! Pretty cool lecture.

After all the great lectures up to this point, this is a truly confusing and incoherent one. Let's hope Victor clears things up :)

Speaking from 2020! Multiplication is now proved to be computable in nlogn time complexity

36:49 error Z2 = X2*Y2 - should be z2 = x1*y1 .. also 2^log(3) is a transcendental number and not just irrational

wow, cool end of the lecture

Last 2 mins blew my mind. Numbers are MindBlowing 🤯🤯🤯🤯🤯🤯🤯🤯🤯

Thank you MIT.

Love your concern towards india🇮🇳

Ok, completely blown away in the last 5 mins, not gonna lie!

Professor’s shirt is glittering in video 💥

x-Sqr(x^2-1)==1/(x+Sqr(x^2-1)~1/2x in this case, it's about 1E-12.

40:00 z2 supposed to be x1y1 not x2y2, x2, y2 are undefined

i head about MIT ...what a big peace of chulck

3:05 Among the Pythagoreans, Hippasus was likely the first to realize some numbers where not rational. According to legend he discovered this at sea, and his fellow pythagoreans responded by throwing him overboard.

if don't know about catalan numbers. at 6:30 pause the video and read this en.wikipedia.org/wiki/Catalan_number he is terrible in this part. better read wikipedia .

thank you sir.

magic design shifting shirt

qudratic convergence using newton methos

Let's see if the professor was right. >>> def cn(x): ... if x < 2: return 1 ... sum = 0 ... for k in range(x): ... sum = sum + cn(k)*cn(x-1-k) ... return sum ... >>> cn(2) 2 >>> cn(3) 5 >>> cn(4) 14

I like this guy... ! [with the observation that the original (long) 3x3 split would need 9 dm (digit multiplications), not 8 :P (and you can multiply them in only 6 dm, see karatsuba on wiki, asymmetric formulae), which is just a bit better than 2x2 split (where you make 6 dm instead of 8 dm). Toom-3 can get 5 dm instead of 9 dm in that case, etc (see Toom-Cook on wiki).]

goog ting ur middle shool hs teachers arent her elik eim so gladdd

when you break up into 3 chunks why are you trying to get away with less than 8 multiplications ? I think it should be 9 (100a+10b+c )(100d +10e+f) involves ad,ae,af, bd,bd,bf, cd,ce,cf or it should be 5 as log(6)/log(3)>1.58

46:30 THIS IS WITCH CRAFT!! How the hell did he get the catlan numbers in there!!! Sorcery !!!

Excellent lecture ( except for initial explanation of Catalan numbers ) - great teaching nevertheless

Now that is some sorcery at the end of lecture.

3:30 Hindu-Arabic numerals are more important than Pythagoras' triangle theorem, so there's that.

"42 is on the list!" That was very funny.

I was so X[i]-ted

37:31, 39:00 z2 = x2*y2 should be z2 = x1*y1

At MIT, "five hundred thousand" equals "five hundred billion".

16:34 : I came in early.. lol

i have problem understanding from 33:39 onwards

God I want to be in the class of Srini Devadas

this lecture was directed by christopher nolan lol(last min was more than crazy)

his shirt is giving my phones gpu tough time

36:49

I hope you all recovered from the quiz LOL

what is this? some kinda genjutsu!

anyone knows any link where I can read about the appearance of catalan numbers in the last circle calculation?

His shirt is trippy... :D

The problem with his exposition in this lecture is how he abstract the concept even before the viewers know what he will do. For example is when he introduced the high precision multiplication, he started pulling random variables z_2, z_1, z_0, without any context instead of showing how x times y would lead to the derivation of their values: x*y = (r^(n/2) * x_1 + x_0) (r^(n/2) * y_1 + y_0) = (r^(n) * x_1 * y_1) + (r^(n/2)(x_1*y_0 + x_0*y_1)) + (x_0*y_0) [through the distributive property] which is the values of z_2, z_1, z_0 summed up with each other, i.e.: x*y = (r^n * z_2) + (r^(n/2) * z_1) + z_0. If you want to better understand Karatsuba Algorithm, I highly recommend this video: kzfaq.info/get/bejne/gKmSjcSqq9idgnk.html

I am a bit surprised that the professor keeps questioning the existence of irrational numbers throughout this lecture, as if advances in computing could in the future reveal a cycle in, say sqrt(2) [sure old Pythagoras would have been delighted if such a hope had ever existed]. If there is one thing I learned from 6.042 (also in youtube), is that what makes mathematical proof superior to other proof methods, like the scientific method, is that you can prove propositions about numbers once and for all without having to enumerate any concrete numbers, just by a chain of logical deductions starting from a set of axioms; such proofs are theorems. As an example, there was a proof by contradiction of the irrationality of sqrt(2) in one 6.042 lecture, apparently the same that was already known by the pythagoreans, which as I have said, must be independent of any advances in computation, by definition of mathematical proof. Have I missed anything? Of course, maybe my mistake is believing that not having a cycle (definition given in this lecture) is the same as claiming that then a number cannot be expressed as the fraction of two whole numbers, which is how irrational numbers were defined in 6.042.

#properties#Soll#Liebe#schönen#Highlight#Episode#awarded Liebe und zu Videos#so#schönes#

didn't know professors could really make u laugh =D

#POW

4862

That wasn't the smartest choice for a shirt :J

Catalan number explanation is the worst explanation he's given of anything in this course.

how did he get the derivative at 22:09?

🙏🙏🙏💞💓💞👍🐉

How can I CS professor at MIT make such a glaring mistake? It can be proved that square root(2) can never have repeating patterns, because it can never be expressed as (p/q) where p,q are integers. That's elementary stuff which we learned at school. Quality of education at US universities must be really going down.

Are these Catalan numbers of any real importance? Hmmmmmmm - I don't think so, but who knows.

Sadly not many people these days understand the significance of 42

If you want to save nearly 40 minutes of your life, the actual Karatsuba multiplication is as far as at 38:19 :P But if you want to save even more, skip this video entirely and go somewhere else, because this dude's explanation is terribly bad :P

He is not as good as Erik