I love how every lecture so far they managed to come up with a new and creative way to record sound. It's cute buy annoying.####[['lecture', 'Course_General_Feedback', 'POS'], ['way to record sound', 'Teaching_Setup', 'POS']]
1 minute in and I'm bored fuck this..math is lame.####[['math', 'Mathematical_Related_Concept', 'NEG']]
I think he is a chinese teacher####[]
Lmfao he is good but his french accent make his lecture  weird####[['NULL', 'Instructor', 'NEU']]
Why does the method for Ex 3 have dtheta, it makes sense to me when you find the integral wrt dx you multiply the function by dx to form a series of rectangles, but why are we multiplying the height given by sintheta by the angle?####[['dtheta', 'Mathematical_Related_Concept', 'NEU'], ['height', 'Mathematical_Related_Concept', 'NEU']]
got another way of slightly less clumsy integrating to pi/8cos^4(t)=cos^2(t) - cos^2(t) sin^2(t)=cos^2(t)-1/4 sin^2(2t)double angle formulae again, original integrand becomes3/8+1/2 cos(2t) +1/8 cos(4t)happy integrating####[]
The bus inter-arrival time example is a bad/counteractive example. If buses are running at the rate of 4 per hour, You go at a random time for many days and your average waiting time should be  7.5 minutes. Why would the bus company foll people by saying we are running buses whose time is determined by poisson process and not a uniform/predetermined time?####[]
wonderful lecture thank you so much!!!####[['lecture', 'Course_General_Feedback', 'POS']]
Those paradoxes and the addressal of them: so good!####[['paradoxes', 'Other', 'POS']]
Great lecture! But aren't we supposed to make an orthogonal projection? Instead he did a projection parallel to the Y-axis because he calculates p1, p2 and p3 by taking t-values 1, 2 and 3. You can also see it on his drawing. Why does he take this projection instead of the orthogonal one? And how can e turn out to be orthogonal to p anyway?####[['lecture', 'Course_General_Feedback', 'POS'], ['orthogonal projection', 'Mathematical_Related_Concept', 'NEU']]
Python code for the Markov chain n-step transition example: http://nbviewer.jupyter.org/github/YoungxHelsinki/jupyter-notebook-cheatsheet/blob/master/Markov%20chain%20n-step%20transition%20example.ipynb####[]
@[USERNAME]i think the cameraman usually falls asleep. maybe he's a professional who doesnt understand a word of maths, so he gets annoyed and takes small naps####[['cameraman', 'Teaching_Setup', 'NEG'], ['NULL', 'Instructor', 'POS']]
God bless MIT! Thank you very much!####[['MIT', 'Other', 'POS']]
sweet, did this like a term and a half ago in higshcool. aced the test for it too :Dgosh calculus is awesome!####[['calculus', 'Mathematical_Related_Concept', 'POS']]
Thanks this is priceless.Great interview.####[['interview', 'Teaching_Setup', 'POS']]
I never thought I would be able to comment "first" on any Strang lecture O__O Lucky me XD####[['comment', 'Other', 'POS']]
The proof of A^tA being invertible around 39:00 was great!####[['proof', 'Mathematical_Related_Concept', 'POS'], ['A^tA', 'Mathematical_Related_Concept', 'POS'], ['invertible', 'Mathematical_Related_Concept', 'POS']]
Professor Strang this lecture explains  in great detail Clusters in Graphs and how Eigenvectors  determine Clusters. The role of Spectral Clustering and it's start with the Laplacian Matrix. Thanks to MIT for all these fantastic lectures.####[['lecture', 'Course_General_Feedback', 'POS'], ['MIT', 'Course_General_Feedback', 'POS']]
"this is more than just a dead end; it's a crash, burn AND SELF DESTRUCT"####[]
Oh.. my god.. the board and chalk are phenomenal..!####[[' board ', 'Teaching_Setup', 'POS'], ['chalk', 'Teaching_Setup', 'POS']]
Wtf, i learnt this when I was 15. How is MIT one of the best uni in the world??####[['MIT', 'Other', 'NEG'], ['NULL', 'Other', 'NEG']]
i like this teacher but he has explained very badly the related rates problems. Is very difficoult to see the beuty of maths with this man but is ok for practical instances.Thanks MIT####[['NULL', 'Instructor', 'NEU']]
why did he use the third derivative of x(theta) but only the second derivative for y(theta) in the taylor approx?####[['derivative', 'Mathematical_Related_Concept', 'NEU']]
The Lecture has become immortal, sir! Thank you!(Ref - first sentence of Prof. Strang in the lecture)####[['Lecture', 'Course_General_Feedback', 'POS'], ['Prof. Strang', 'Instructor', 'POS']]
this is the beauty of life, thank you so much Professor Strang and MIT!####[['Professor Strang', 'Instructor', 'POS']]
This man is a great teacher!####[['NULL', 'Instructor', 'POS']]
@[USERNAME] This is so wrong man....you mean (X-Xo) --> 0????it will make sense if you say what I just wrote...you CAN NOT bring -Xo over the other side since  --> is not >DUH.####[['NULL', 'Other', 'NEG']]
I don't understand the thing about the convergence rate :S ..You take the difference and then what..?####[['convergence rate', 'Mathematical_Related_Concept', 'NEU'], ['difference', 'Mathematical_Related_Concept', 'NEU']]
Just want to thank him and say that I love the sparkle in his eyes when he teach####[['NULL', 'Instructor', 'POS']]
nothing makes me happier than seeing Dr. Casey Rodriguez eating a cookie and drinking a can of liquid####[['Dr. Casey Rodriguez ', 'Other', 'POS']]
I can imagine that the algorithm where you subtract a1 from all subsequent a would also be much easier to parallelize.####[['algorithm', 'Mathematical_Related_Concept', 'POS']]
Great improvement on video quality compared with 18.06####[['video', 'Course_General_Feedback', 'POS']]
Well, you've convinced me of the autism at least.####[]
learning linear algebra with you is like watching movies. it's fascinating, exciting, convincing and fun. thank you so much Professor Strang! Im so lucky to be learning this subject with you!####[['Professor Strang', 'Instructor', 'POS']]
The application of the Fundamental Theorem of Linear Algebra is the constant theme of Professor Strang's lectures:http://mathworld.wolfram.com/FundamentalTheoremofLinearAlgebra.htmlI never heard of this theorem before these lectures, and I'm an Old Bastard. So this has been a fun learning experience!####[['Fundamental Theorem of Linear Algebra', 'Mathematical_Related_Concept', 'POS'], ['lectures', 'Course_General_Feedback', 'POS']]
Use headphones and set the sound mode to Mono Audio.####[]
prof gilbert strang : teaching the beauty of linear algebra me : wondering how we are going to get those erasers stuck behind the backboard ........####[['prof gilbert strang', 'Instructor', 'POS'], ['NULL', 'Other', 'NEG']]
At 41:54, Strang gets the eigenvalues correct from memory.  I'm impressed!####[['Strang', 'Instructor', 'POS']]
I am very happy to why the fuck is this full of bots in space and curl. Thank you, it really helps####[['bots', 'Other', 'POS'], ['curl', 'Other', 'POS']]
@[USERNAME]why would there be a square root 2 pi there, I don't get the significance of what he is saying when there are no fudge factors and this is the true asymptotic variance. Why would there be any of that?####[['square root 2 pi', 'Mathematical_Related_Concept', 'NEU']]
These courses are the best in the Math.####[['courses', 'Course_General_Feedback', 'POS']]
Interesting proof: showing  probability of two separate coincidental events being larger than  the probability of a single event occurring in the universe of events by saying that they are not coincidental events, however,  but 1 single event with a larger probability than a single event occurring in the specific universe. Very clever.####[['proof', 'Mathematical_Related_Concept', 'POS']]
This would be much better had a noise-cancelling microphone been used.####[['NULL', 'Teaching_Setup', 'NEG'], ['noise-cancelling microphone', 'Teaching_Setup', 'POS']]
Inputting 100 cubic centimeters and 1 cubic meter yielded different answers because _the inputs were different._One cubic meter equals one million cubic centimeters because we're calculating in the 3rd dimension. In the 2nd dimension, one square meter equals ten thousand square centimeters, and in the 1st dimension, one meter does equal one hundred centimeters.When converting units in higher dimensions, you _square or cube the conversion factor._####[]
I highly disagree with the resolution of the "notation problem" at 19'13". The problem is well stressed, but ill solved, if a cat ought to be called a cat! A little "mess" indeed is runing around there, in the lecture notation, and confusion is rising with paradox from a rather different cause than the one stressed out, if RIGOUR is to be called RIGOUR!The little "mess" that is at the core of these confusions is simply that, through the change of variables, though f(x,y) = x+y = 2u+v = g(u,v), which are NUMERICAL EQUALITIES and which are NUMERICALY true, nevertheless the functions f and g ARE NOT the same sincef : (x,y) --> f(x,y)=x+y, and g : (u,v) --> g(u,v) = 2u+v, WHICH IS equivalently written (since variables are "DUMMY VARIABLES") g : (x,y) --> g(x,y) = 2x+y.From this rigourous functional (or algorithmical) way of looking at it,  it's obvious that f and g are DIFFERENT algorithms, that is DIFFERENT functions!With things clarified this way, all confusions, danger, paradox... simply vanish : (df/dx)y = 1, and (dg/du)v=2 No more pb!...More over, be now clearly aware that we can write, with absolute rigour : (dg/du)v = (dg/dx)y, BUT ONLY IF YOU READ THIS IDENTITY IN THE PROPER WAY ONE SHOULD READ IT, THAT IS THROUGH "FUNCTIONS SPIRIT", AND NOT "number spirit". Why that? Because variables in these expressions, ARE AND MUST BE LOOKED AT, AS "DUMMY VARIABLES"! More precisely, what both of these expressions (dg/du)v or (dg/dx)y, trully mean, is simply and unambiguously : DIRIVE WITH RESPECT TO THE FIRST VARIABLE (OF THE ORDERED PAIR, OF THE CROSS PRODUCT OF SETS), KEEPING THE SECOND "VARIABLE" CONSTANT. Therefore we could equivalently have written (dg/dk)@  (or any crazy other "names" of variables), if we had defined the function "in such CHART", labeled (k,@),  by :g : (k , @) --> 2k+@THIS is the only way of puting things trully clearly and rigourously, without ever giving rise to any notation confusion or paradox! Simply by calling a function a function, and NOT "a cat a dog", messing around with words and concepts, through rather "physicist" lasy notations wich turns sometime to prove to be "bad" habits. It's in fact a CHAIN RULE MISTAKE that is arising when one misleadingly identify f with g. If one realy wants to differentiate with respect to the same variable, x for instance, keeping y constant, it is possible! But to perform that without any mess and mistake, one SHOULD NOT naively compare  (df/dx)y=1 with (dg/du)/v=2, wich are clearly DIFFERENT (and nothing wrong about it!). But instead, one SHOULD think "functionaly" instead of "numericaly"! That means one has to compute clearly the "CHAINED FUNCTION" G, which is different from g, but which is related to g by the Change of Variable. We thus express, first the change of variable in the PROPER WAY! That is, as the following FUNCTION :C : (x,y) --> C(x,y) = (u,v) = (x, y - x)We thus recall that the FUNCTION g is defined as the following algorithm :g : (@,#) --> 2@ +#,or equivalently (since what any function trully IS, IS it's defining ALGORITHM!), but more conveniently (for our CHAINING FUNCTIONS GOAL)  :g : (u,v) --> g(u,v) = 2u+vThese two FUNCTION are now wisely CHAINED to build the FUNCTION G defined as follow :G(x,y) = g(u,v) = g( (u,v) ) = g(C(x,y)) = (goC)( (x,y) ) = (goC)(x,y)We now clearly see what is this FUNCTION G : THE CHAINED FUNCTION OF g and C :G = goCThe central "o" meaning the CHAINING (COMPOSITION) OPERATION ON FUNCTIONAL SPACE, defined, in general, for any two function A : E--> F, and B : F --> G, very simply as :BoA : E --> G , x --> BoA(x) = B(A(x))Which could thus, aternatively be named "THE BOA RULE" instead of the usual "fog" and "gof" of "FUNCTION CHAINING"... (joke!)In our exemple we then get, finaly, since u=x and v=y-x :G(x,y) = (goC)(x,y)  = g(C(x,y)) = g( (u,v) ) =  g(u,v) = g(x, y-x) = 2x + (y-x) = x +ySO WE "DISCOVER" THAT for all x and all y, we have :G(x,y) = f(x,y)That means FUNCTIONAL EQUALITY :G=fSo what have we done? Turning around? Yes, in a sens, because we have INSISTED in differentiating g with respect to x, IN A NUMERICAL SENS, instead of doing it in a FUNCTIONAL PROPER WAY that is, differentiating with respect to its FIRST variable in the ALGORITHM g : (@,#) --> g(@,#) = 2@ + #Thus, in this NUMERICAL SENS, x is no longer a DUMMY VARIABLE, but a "NUMBER ATTACHED TO f"! The physicist would call it a "physical observable". This way of looking at things makes it complicate and cand lead to confusions if one doesn't clearly understand the CHAIN FUNCTION KEY AND THE IN FACT THE MANIFOLD CHARTS MAPPING (THUS CHANGE OF CHARTS TRANSFORMATIONS, often differentiable for a regular manifold) laying under all this...  We thus have, in a sens, "turned around", leading to G=f! But doing so we nevertheless HAVE CLEARLY WRITEN THINGS IN CHAIN FUNCTION PROPER WAY, that reveal to be EXTREMELY USEFULL in higher and more abstract DIFFERENTIAL GEOMETRY, where crucial concepts of COVERING and UNIVERSAL COVERING, TANGENT SPACE, GROUP, LIE ALGEBRA, LIE DERIVATIVE, COVARIANT DERIVATIVE, CONNEXIONS, DIFFERENTIAL FORMS,..for instance, are usefully springing, needing CHAINING FUNCTION PROCESS to be clearly understood and mastered!Finally, often, this abuse of notation which misleadingly sets f=g, will be handled without damage by the "human computer", with some habits and agility. BUT only in rather easy area. On the contrary it will lead to catastrophic confusions, misconceptions, darmatically false results and chear non sens interpretations, in more suttle area...alike, not for naming them, general relativity, riemanian differential geomedry, condensed matter, plasma, etc...CHAINING FUNCTION OPERATION is one of the most simple, but important one in all mathematics! It's the building block of nested structures, one inside the others alike Pandora box, BUT "BOXES" THAT REVEAL FASCINATING STRUCTURES ALIKE GROUP, ALGEBRA, CLIFFORD,...TOPOS... : PointsFunctions, from points to pointsFunctional (or Operator), from functions to functions, etc...All included IN...CATEGORY Groetendick SPIRIT...deap!####[]
Fantastic way to introduce Pseudoinverse.  GS is a great teacher.   Thanks OCW for making this available####[['GS', 'Instructor', 'POS']]
the chalk is about three times thicker than his thumb####[]
I want to thank MIT for putting this up and Sir Gilbert Strang for such an amazing lecture####[['Sir Gilbert Strang', 'Instructor', 'POS'], ['lecture', 'Course_General_Feedback', 'POS']]
is it just me or do state colleges have a completely different syllabus?####[]
I've just noticed that my teacher never taught me the entire steps...just the short cuts. This is great!####[['NULL', 'Course_General_Feedback', 'POS']]
Emergency question! Can we describe a basis for non-subspaces? For example a plane doesn't go through the origin???####[]
So far this is simple####[]
If Denis Auroux was my math teacher all my life Euler would be eating my dust.####[['Denis Auroux', 'Instructor', 'POS'], ['NULL', 'Other', 'NEU']]
i didn't catch "rangle" until the students pointed it out####[]
What a gem of a teacher! A legend. I did not learn C of calculus in 5 years of my engineering studies way back in 1974-79. Then came the blessing in disguise and by the way I had to teach some calculus to my daughter in her graduate course in economics. And that is how I landed onto Professor Gilbert Strang's video and I fell in love with calculus which all these years was kind of a terror to me. What a beautiful and stylish way of teaching mathematics. I never have seen any teacher with such a vast knowledge and at the same time  comfortable teaching beginners. God bless Professor Strang with health a d happiness.RegardsAnup Kumar GuptaIndia####[]
hoah this lecture is tough but very interesting at the same time :3####[['lecture', 'Course_General_Feedback', 'POS']]
13:22 , lucky to sleep in mit lecture hall####[]
If you don't understand professor explanation at 15:00 the angular velocity is 1 because v = wr and v is equal to r basically since r vector rotated 90 degree becomes v; so w = 1####[]
Would love to see more from Alex Townsend. What a fantastic lecturer!####[['Alex Townsend', 'Instructor', 'POS'], ['lecturer', 'Course_General_Feedback', 'POS']]
If you enjoy Khan, you might also like a channel called PatrickJMT; although, you probably know him already.####[]
I am confused with Thm2, the instructor said and explained like x is coarser than x' but since x' is contained in x and considering the definition of the partition, isn't his explain should be opposite while he is proving Thm2? so x contains x' and more I think####[['Thm2,', 'Mathematical_Related_Concept', 'NEU']]
Thank you very much Prof. Gilbert####[['Prof. Gilbert', 'Instructor', 'POS']]
Made it here from Lec 1. Very satisfied####[['NULL', 'Course_General_Feedback', 'POS']]
Does anybody know what movie or book title he is talking about in the last minutes of the lecture at 43:47 ?####[]
can anyone provide me notes####[]
It's real algebraist hours, my dudes.####[['algebraist hours', 'Course_General_Feedback', 'NEU']]
Thank you, Prof. Gilbert Strang and MIT.####[['Prof. Gilbert Strang', 'Instructor', 'POS']]
MIT has done great service to mankind, by recording his lectures and sharing them online. This are so beautiful, future generations will remember him as the Mozart of this subject####[['MIT', 'Course_General_Feedback', 'POS']]
My left ear is learning while my right ear is getting bored cause it already learned this.####[['NULL', 'Other', 'NEU']]
At 31:20does a dfa converted from nfa always contain 2^q states ?I mean , Q' is equal to P(Q)  or Q' is a subset of P(Q) ?####[['dfa', 'Mathematical_Related_Concept', 'NEU'], ['nfa', 'Mathematical_Related_Concept', 'NEU'], ['2^q states', 'Mathematical_Related_Concept', 'NEU'], ['P(Q)', 'Mathematical_Related_Concept', 'NEU'], ["Q'", 'Mathematical_Related_Concept', 'NEU']]
To anyone considering watching all 35 lectures, do it. Professor Auroux teaches better than anyone I've ever seen before. Everything is structured, thought out, and flows from one topic to the next so effortlessly that you'll be amazed you just sat through 50+ minutes of math.####[['Professor Auroux', 'Instructor', 'POS'], ['lectures', 'Course_General_Feedback', 'POS']]
Partial fractions starts at 0:45 until 18:20, which is also important.####[['Partial fractions', 'Mathematical_Related_Concept', 'POS']]
It's clear that he likes physics. That's good.####[['physics', 'Other', 'POS']]
There are a lot of comments that some of the Prof.'s explanations are not rigorous enough. MIT has 2 or 3 levels of introductory calculus. This one is for freshmen with little or no high school calculus, and who will probably major in eng. where the key is to get the right answer rather than to be rigorously correct. If you go to the OCW website, you can find the one aimed at students who want to major in math or physics. It's totally different and much harder.####[['comments', 'Course_General_Feedback', 'NEG'], ["Prof.'s", 'Instructor', 'NEG']]
Thank you so much, sir. From India.####[['NULL', 'Instructor', 'POS']]
dang i am in precal class, wanting to get a jump start on calculus, and none of this or lecture one made any sense, he kept talking about limits and derivitaves and even showed examples, but never explained how to get them that well, or even what they were....have the ppl in this class had previous exposure to this stuff?####[['lecture', 'Course_General_Feedback', 'NEG'], ['NULL', 'Instructor', 'NEG'], ['calculus', 'Mathematical_Related_Concept', 'NEU'], ['limits', 'Mathematical_Related_Concept', 'NEU'], ['derivitaves', 'Mathematical_Related_Concept', 'NEU'], ['ppl', 'Other', 'NEU']]
32:36 anyone notice that he did not say that ? :D####[['NULL', 'Instructor', 'NEU']]
Sir ,in the last of lecture How those two column vector passes through the origin ????####[['column vector', 'Mathematical_Related_Concept', 'NEU']]
33:31 Minnie Mouse learns Calculus 2. Great lecture!####[['lecture', 'Course_General_Feedback', 'POS']]
100 students in a class. each pay 50USD a day aprox for university. perhaps 25USD for this lecture alone. (2500USD total!) And we get it for free!This really helps those without opportunities to learn and advance.####[['lecture', 'Course_General_Feedback', 'POS']]
3:13  "going way back to greeks..." :) well, sir, i think greeks are still in the world.####[['sir', 'Instructor', 'NEU']]
What would any if this be used for?####[]
6 people dont have brains####[['people', 'Other', 'NEG']]
This guy is great.  I studied engineering at a university less prestigious than MIT, and I remember professors refusing to explain their algebra steps.  They were like "you should know this already".####[['NULL', 'Instructor', 'POS']]
And the audience was speechless.####[]
how is 27:55 2 dimesional ?####[]
do people do vector calculus just for fun?well my friend says he enjoys it.####[['vector calculus', 'Mathematical_Related_Concept', 'NEU']]
Absolutely legendary. Professor Strang explains linear algebra 10 times better than my own professor at school. : )####[['Professor Strang', 'Instructor', 'POS'], ['linear algebra', 'Course_General_Feedback', 'POS'], ['professor', 'Instructor', 'NEG']]
This guy is a legend. I love him. The neatness of his lectures is just like the beauty of mathematics, and 18.02 is definitely my favorite MIT open course.####[['NULL', 'Instructor', 'POS'], ['lectures', 'Course_General_Feedback', 'POS'], ['MIT open course', 'Other', 'POS'], ['mathematics', 'Mathematical_Related_Concept', 'POS']]
@[USERNAME]so he plugged in the WHOLE term, which was multiplied with X - Xo, to the derivative formula?####[]
This professor is a pure legend####[['professor', 'Instructor', 'POS']]
Very good lecture.  Very simple to understand.  Thanks for sharing.####[['lecture', 'Course_General_Feedback', 'POS']]
You can even derive the law of cosines purely from elementary geometry and the mere definition of the sine and cosine. Just use Pythagoras and you'l get there.####[['Pythagoras', 'Mathematical_Related_Concept', 'POS']]
This is more of a revision of Linear Algebra and Multivariate Calculus, for the actual contenton PCA, go to lecture 20 herehttps://www.youtube.com/watch?v=a1ZCeFpeW0o####[]
The instructor got Confused? with the cos term, C dot C has an angle of zero so, cos (0) is 1, this is why no cos appears in C dot C, has nothing to do with going back to definition of dot product, (so simple!)####[['instructor', 'Instructor', 'NEU']]
Any faces with combination Eigenfaces!!!####[]
Started this course today. Hope to complete it soon. Loving the journey of learning.####[['NULL', 'Other', 'POS']]
MIT please provide water and sponges for your professor's blackboard cleaning needs wtf####[['blackboard', 'Teaching_Setup', 'NEG']]
Best chalk I have ever seen####[['chalk', 'Teaching_Setup', 'POS']]
This series is Breaking Bad level high. Same highs and lows and tension and mystery and excitement####[['series', 'Course_General_Feedback', 'POS']]
I love how everybody cheers when he erases the board faster than the pulley moves it : P####[['cheers', 'Other', 'POS']]
Nice lecture sir.Love from India🇮🇳🇮🇳####[['lecture', 'Course_General_Feedback', 'POS']]
@[USERNAME](First of all, I don´t speak english as a native language, so, sorry for my mistakes) I think that is kinda stupid to criticize these videos that are free, I mean, if Somebody were paying it would be ok to give "not flattering" comments...There is a expression in my country "A caballo regalado, no le mires el diente" (Never look a gift horse in the mouth)This is free men/woman...don´t worry, I know you are just making a observation and not criticizing####[['comments', 'Other', 'NEG']]
Why does he call it a "vector"  ??####[['NULL', 'Instructor', 'NEU'], ['vector', 'Mathematical_Related_Concept', 'NEU']]
Hlo sir  My question is that Why we use exponential####[['exponential', 'Mathematical_Related_Concept', 'NEU']]
Stat is very hard sub..####[['Stat', 'Course_General_Feedback', 'NEG']]
I Really Like The Video From Your Elimination with Matrices####[['Video From Your Elimination with Matrices', 'Course_General_Feedback', 'POS']]
Thanks for these lectures and for the effort in putting together these videos!####[['lectures', 'Course_General_Feedback', 'POS']]
informative without excess fluff, intrinsically entertaining, and well paced. i hope the rest of the lecture series is as well done as this first introduction####[['introduction', 'Course_General_Feedback', 'POS'], ['lecture series', 'Course_General_Feedback', 'POS']]
same content as my non ivy league university. in fact because the professor is so good here and i had to teach my self everything i would say it was harder.####[['professor', 'Instructor', 'POS'], ['non ivy league university', 'Other', 'NEU']]
I've yet to take Calculus, many people make it out to be the achilles heel of those who seek higher learning. I hope that's not the truth.####[['Calculus', 'Mathematical_Related_Concept', 'NEU']]
A good video to supplement the gradient and rate of learning :-) : https://www.youtube.com/watch?v=NomUbVmmyro####[['video', 'Course_General_Feedback', 'POS']]
I'm an economist, but if with this professor, I can also become an engineer in 6 months. I also wonder if these profs take any drawing lessons. His circles are good!####[['professor', 'Instructor', 'POS']]
Can't help but notice that someone in that lecture hall has a bad cough.####[['NULL', 'Other', 'NEG'], ['lecture', 'Course_General_Feedback', 'NEU']]
At 11:00, he is doing the univariate case, so the det part can be omitted. For the multivariate case, you need the additional fact that det(AB) = det(A)*det(B), and the result follows similarly.####[]
Which book does they follow?####[]
o, man...so many words, so many lines, useful for self confusion...relax, man, votka martini will do the job...####[['NULL', 'Instructor', 'NEG']]
23:30  ".... including slightly more legit businesses like insurance", lmao!####[]
@[USERNAME]dude be thankful  , we do not have a professor we have the exam finally lol####[['exam', 'Other', 'NEG']]
This is what I like about these good schools - that the teachers are devoted to teaching. Most other teachers are lousy and dull, and they end up naturally being egocentric. I love you guys.####[['teachers', 'Instructor', 'POS'], ['other teachers', 'Instructor', 'NEG']]
God, I love this man!####[['NULL', 'Instructor', 'POS']]
Dear sir,isn't the linear approximation formula the first two terms of the Taylor Expansion? Is Linear approximation like Taylor Series but for linear functions?####[['linear approximation formula', 'Mathematical_Related_Concept', 'NEU'], ['Taylor Expansion', 'Mathematical_Related_Concept', 'NEU'], ['Linear approximation', 'Mathematical_Related_Concept', 'NEU'], ['Taylor Series', 'Mathematical_Related_Concept', 'NEU'], ['linear functions', 'Mathematical_Related_Concept', 'NEU']]
Yeah, he could have covered the ratio test in just as much time as it took to explain why he wasn't covering the radius of convergence.####[['NULL', 'Instructor', 'NEU'], ['radius of convergence', 'Mathematical_Related_Concept', 'NEU']]
but then WHAT IS DETERMINANT?####[['DETERMINANT', 'Mathematical_Related_Concept', 'NEG']]
if someone could explain what he is saying at 34:35, that would be great. I don't really understand it. I  wish I could be more specific in explaining my confusion!####[['NULL', 'Teaching_Setup', 'NEU']]
why won't the rest be uploaded?####[]
At 40:46, if b is the greatest of lower bounds, should it say b < b_0, whereas it says b ≤ b_0 for both second cases of least upper bound and greatest lower bound? I checked the notes for the lecture after and the second case; whilst using c and c_0, it says c < c_0. I wondered if it should strictly be less given c_0 or b_0 is considered the greatest lower bound.####[]
Why center of mass of Cn+1 block= Cn+1####[[' block= Cn+1', 'Mathematical_Related_Concept', 'NEU']]
This is some nice chalk####[['chalk', 'Teaching_Setup', 'POS']]
god bless gilbert strangand also thanks to MIT for putting them on  the webwhat on earth  did we do before the internet  ?####[['gilbert strang', 'Instructor', 'POS'], ['MIT', 'Other', 'POS'], ['NULL', 'Teaching_Setup', 'POS']]
so this is that Michael Sipser whose book we all read and love####[['book', 'Other', 'POS'], ['Michael Sipser', 'Other', 'POS']]
@[USERNAME]Yeah you're right, basically first year at Uni is a lot easier than A levels. Second year is a rude awakening, you work your ass off. Of course all the genius' posting here were discovering dark energy in their freshman year (or you would think that was the case the way they act so patronising and smug about this lecture.) It hasn't dawned on them that MIT have some experience in educating some of the brightest minds and recapping first principles might just have a valid purpose####[['lecture', 'Course_General_Feedback', 'POS'], ['posting', 'Other', 'NEG']]
This comment section is so surprisingly positive... almost makes me suspicious :,D####[['comment section', 'Other', 'NEG']]
@[USERNAME]Maybe it's because i already understand lagrange multipliers, but they should not be that lost. this explanation is pretty decent, imho####[['lagrange multipliers', 'Mathematical_Related_Concept', 'NEU'], ['explanation', 'Teaching_Setup', 'POS']]
@[USERNAME]Sorry, now i think i got what u were saying. i think u meant to write "I think P U L is a subspace only IF ( not 'in') line L lies in the plane." That makes completely sense. Thanks.####[]
We are already study in class 11thAnd they study in collegeIndian education is higher than America####[]
33:01 after watching the 3blue1brown serie and being on this video on this serie I'm a huge fan of columns, and find they make much more sense than rows.If you want to understand the geometrical meaning of linear algebra I recommend everyone to watch the 3blue1brown playlist, everything you use on linear algebra has a geometrical equivalent, why matrices that have determinant equal to 0 doesn't have an inverse, how linear transformations (matrices) modify space, how the basis vectors generates the space, how the determinant of a linear transformation is the factor by which the area of something in that space changes, and so forth.####[]
Amazing ending to an amazing series. Thank you MIT OpenCourseWare, thank you Professor David Jerison and thank you Professor Haynes Miller####[['series', 'Course_General_Feedback', 'POS'], ['Professor David Jerison', 'Instructor', 'POS'], ['Professor Haynes Miller', 'Instructor', 'POS']]
Why didn’t he explain method of washers? They mention it in the recitation vid.####[['method of washers', 'Mathematical_Related_Concept', 'NEU'], ['vid', 'Mathematical_Related_Concept', 'NEU'], ['vid', 'Course_General_Feedback', 'NEU']]
I wish I would have watched this videos back in my Engineering. No problem I will watch it now though I am 26 now.####[['videos', 'Other', 'POS']]
i just spent 8 hours looking at this videos and now that i check the problems from my school i am on the start again just wasted 8h...how can USA and EU have such different uses and concepts of matrix it suks donkey balls####[['uses', 'Other', 'Neg'], ['concepts', 'Other', 'Neg']]
nice, we covered a lot of multivariable calculus this year (a first for junior students in Hawaii) it was awesome, but since we also took AP Calculus BC during this year, it was a bit difficult to switch back for the exam and I ended up trying to use MV calc on the BC exam lol.  Smart idea to spend time reviewing the course materials ^^####[]
it was really funny when he saw his mistake :D:D####[['NULL', 'Instructor', 'NEU']]
Great guy in the planet####[]
Every lecture, the number of views is going down. For everyone else doing all the problems, watching the lectures, etc. - you have my respect. I'll see you at the end!####[['everyone else', 'Other', 'POS']]
In many linear algebra courses that I have seen, the student is simply told about the various relationships between the fundamental subspaces. But in this course these ideas are convincingly yet accessibly presented. This is very important because it allows students to really understand such key ideas of linear algebra to the point where they become intuitive, instead of simply memorizing properties and formulas. Another great lecture by professor Strang!####[['course', 'Course_General_Feedback', 'POS'], [' professor Strang', 'Instructor', 'POS']]
29:10 Here's the paper covering the proof for anyone wondering:- https://www.cse.iitk.ac.in/users/manindra/algebra/primality_v6.pdf####[]
why is phi limited from 0 to 180####[['phi', 'Mathematical_Related_Concept', 'NEU']]
@[USERNAME]The parabola doesn't matter in terms of bounds because we know it becomes the unit circle in the xy plane. The double integral cares only about the xy plane, and so that's all you need to know in order to set up the integral.####[['parabola', 'Mathematical_Related_Concept', 'NEG']]
What is understanding the concepts he's presenting in comparison to being able to explain them to someone else? It's not nothing, to use a double negative, but you get the idea. It's of course not the only difference between professors and students, but if you can find someone interested enough, try explaining it to them, and you'll never forget the lesson. If you're not a professor, one difficult task is finding someone who's interested, in order to practice. Normally, the way to do this on your own is to write proofs.####[]
I Really Like The Video Lecture 16: Differential equations, separation of variables From Your####[['Video Lecture', 'Course_General_Feedback', 'POS'], ['Differential equations', 'Mathematical_Related_Concept', 'NEU'], ['separation of variables', 'Mathematical_Related_Concept', 'NEU']]
And thanks MIT for this content####[]
it is very nice lecture i appreciate his hard work####[['lecture', 'Course_General_Feedback', 'POS'], ['work', 'Other', 'POS']]
Glad to see this posted. Hoping of going to the Eastern Half of Australia next semester so that I can study this.####[['posted', 'Other', 'POS'], ['this', 'Other', 'POS']]
Professor Strang, I would like to humbly thank you for sharing this invaluable knowledge with all of us. And of course, thank you MIT for uploading such amazing content. I spent the last 2.5 months watching all the videos, preparing all 10 problem sets, 3 quizzes, and the final exam. I even uploaded my solutions here - https://github.com/alivay/mit_1806_linear_algebra in latex and pdf formats.####[['Professor Strang', 'Instructor', 'POS'], ['videos', 'Course_General_Feedback', 'POS']]
Why the camera is wobbling? Why not focusing on the board? more distractions####[['camera', 'Teaching_Setup', 'NEG']]
The girl who raised her hand in the first row when he asked what the name of the matrix is... :'( College is just a high level Dora the Explorer where the teacher asks a question, stares at you for 15 seconds, then answers it himself####[['teacher', 'Instructor', 'NEU']]
me: "So....What?  Can you explain it again?"him: "Which part?"me: "All of it"him: "MIT OCW...Okay, so next..."####[]
So... I was feeling kind of hip so I started simplifying the 1/8 - cos(4x) /8 into terms with only x and I ended up with just sin^2(x) cos^2(x).. Now that's pretty interesting right cause it's the same as the integrand plus a constant. Anyone tried this?####[['sin^2(x) cos^2(x)', 'Mathematical_Related_Concept', 'POS'], ['NULL', 'Mathematical_Related_Concept', 'POS']]
Excellent relationship between parabola and normal curve.####[['relationship', 'Other', 'POS']]
why these video lectures are not to be downloaded?####[['video lectures', 'Other', 'NEU']]
You could say that about a lot of math, the trick isn't usually in doing the algebra. It's understanding the relationships between numbers and equations.####[]
Gilbert Strang, the name that all college students around the world know. He's a genius and a great teacher####[['Gilbert Strang', 'Instructor', 'POS']]
Just finished after 11 weeks of watching all the lectures, doing all the homeworks, and taking all the exams.  Cannot thank Prof. Strang and MIT enough for creating and posting this series of lectures.  It's so rare to find an obviously brilliant mathematician who actually seems to enjoy teaching introductory-level courses, and Prof. Strang was such a joy to spend ~30 hours with through these videos.  I've taken Linear Algebra before but needed a refresher after 10 years, and this course was perfect for walking me through the concepts.####[['lectures', 'Course_General_Feedback', 'POS'], ['Prof. Strang', 'Instructor', 'POS']]
now doubt sir you are the blessing for mathematicians and also for related to this field,i often enjoy your lectures  in my vocations####[['lectures', 'Course_General_Feedback', 'POS'], ['sir', 'Instructor', 'POS']]
19:00 Proof by mathematical induction.41:41 Pumping lemma.####[['Pumping lemma.', 'Mathematical_Related_Concept', 'NEU']]
At the last proof (A'A is invertible), why is he allowed to multiply both sides by a row vector? Shouldn't that change the solution set?For example, suppose [x1 x2 x3 x4]' = 0. Then x = 0 vector. But if I multiply both sides by [1 -1 0 0], then [1 1 0 0]' becomes a solution. Should I assume that this operation can only add solutions, so the proof is still valid (since after the operation, only 0 is in the nullspace)?####[['row vector', 'Mathematical_Related_Concept', 'NEG'], ['operation', 'Mathematical_Related_Concept', 'NEU']]
is sir Gilbert strang still alive??####[['Gilbert strang', 'Instructor', 'NEU']]
@[USERNAME]hey, do you understand the first part when he stated that ( d/dx +x ) y = 0, translates to dy/dx +xy = 0? I'm a little confused about that. i see from the first equation that was a give that dy/dx = f(x) = y. Therefore y should equal dy/dx, so shouldn't the equation be (d/dx)(dy/dx) = -xy?####[['( d/dx +x ) y = 0', 'Mathematical_Related_Concept', 'NEU'], ['dy/dx +xy = 0', 'Mathematical_Related_Concept', 'NEU']]
25:24 To prove AB and BA share the same eigenvalues, I think here the proof only proves the case when B is invertible. So this is not a general proof.####[['AB', 'Mathematical_Related_Concept', 'NEU'], ['BA', 'Mathematical_Related_Concept', 'NEU'], ['eigenvalues', 'Mathematical_Related_Concept', 'NEU'], ['invertible', 'Mathematical_Related_Concept', 'NEU']]
Why u_0 can be written as a linear combination of eigenvector of A? 29:55####[['u_0', 'Mathematical_Related_Concept', 'NEU'], ['linear combination ', 'Mathematical_Related_Concept', 'NEU']]
I am taking linear algebra class at my own college. It's a top 20 university, but the professor totally messes stuff up! He didn't even emphasize the closure of linear combination when he introduced vector space! I thought linear algebra is super hard but I realized it's actually not after I watched this video!####[['professor', 'Instructor', 'NEG'], ['linear algebra class', 'Course_General_Feedback', 'NEG'], ['video', 'Teaching_Setup', 'POS']]
at 38:40 "has anyone seen this before?"  I mean...HOW DID YOU GET INTO    M  I  T    if you don't know what the Law of Cosines is????####[['NULL', 'Other', 'NEG']]
I got 70 out of 75 in my final linear algebra exam thanks MIT...####[['MIT', 'Course_General_Feedback', 'POS']]
Love this guy. I did get a bit lost on the Taylor stuff but I need to review it and was here mainly for the parametric representation part.####[['Taylor stuff ', 'Instructor', 'POS']]
I don't know why but I feel kinda sad knowing that this course is over.####[['course', 'Course_General_Feedback', 'POS']]
The professor is looking rather green. He must sick.####[]
@[USERNAME]He talks about it in lec 2. He doesnt prove it, though.####[['NULL', 'Instructor', 'POS'], ['NULL', 'Mathematical_Related_Concept', 'NEU']]
in india we study all this in standard 10####[]
Gil's talking to himself here-####[]
Is this course for beginners.####[]
Can someone please help me with the drawing of the column space at the end of the video? Is he saying that if I summed up all the possible linear combinations of the two columns made from matrix A, I'd end up with a 2D plane in a 3D space?####[]
Think of it this way. Let's say the wheel did not turn but was simply dragged. The curve describing the path of a point on the wheel would be equal to the displacement of the wheel. Similarly, if the wheel did not move but simply turned in place the arc length would be 2pi for each revolution. The cycloid includes both the revolution and the translation as part of its length.####[]
What about inverses of non-square matrices?####[]
MIT blackboards tend to infinity####[['blackboards', 'Teaching_Setup', 'POS']]
Thank you so much MIT OCW!####[]
Salute this man, he has taught more students linear algebra than anyone in history, and is likely to continue to do so eternally!####[['NULL', 'Instructor', 'POS'], ['linear algebra', 'Mathematical_Related_Concept', 'POS']]
46:31 Use the Cofactor Formula from the beginning.####[['Cofactor Formula', 'Mathematical_Related_Concept', 'NEU']]
Don't  act confused guy, i'm not saying anything about the teaching capabilities if the lecturers or the work they cover at MIT. All i'm saying is that the title of being one of the greatest engineering schools in the world is due to talented students every now and then and a wide range of resources available to them.####[]
In italian calculus courses there are better proofs for limits sinx/x=1 and (cosx-1)/x=0... here the explanation is very confused, and in particular how can I say that the limits would be 1 and 0 and not, for example, 0.99 and 0.01? We use instead the theorem of comparison for the first limit (sin x < x < tan x) and a trick for the second limit (1-cos x = 2sin^2(x/2)). Very simpler and clearer.####[]
@[USERNAME]The fact that A^T * A and A * A^T have the same non-zero eigenvalues is blowing my mind right now. I guess this is intimately related to the fact that det(B) = det(B^T), since det is where we get the characteristic polynomial/egenvalues...####[['A^T * A', 'Mathematical_Related_Concept', 'NEU'], ['A * A^T', 'Mathematical_Related_Concept', 'NEU'], ['det(B) = det(B^T),', 'Mathematical_Related_Concept', 'NEU']]
Today i completed this course, i'm not a science major I'm an Eco student and just started learning Maths so that i can pursue Masters later and this is the 1st course that i took and it truly inspired me to learn more maths and never leave Linear Algebra, This could not have been possible without  Prof. Stang and MIT OCW. Thank you so much words cannot express my gratitude.####[['Prof. Stang', 'Instructor', 'POS'], ['MIT OCW', 'Other', 'POS'], ['course', 'Course_General_Feedback', 'POS'], ['Linear Algebra', 'Mathematical_Related_Concept', 'POS']]
Wa... Wa... Wa... Are these students really MIT's students?  Wa.... I am flabbergasted by their questions.  How many of them have full SAT scores? :0####[['questions', 'Other', 'NEU'], ['students', 'Other', 'NEG']]
in determining the range of of the area, the function depends on x....####[]
Instead of using the double angle formula and expanding the square he could've used complex exponentials to linearize cos theta to the fourth, right?####[['NULL', 'Instructor', 'NEU']]
I think the grad(f) at 16:00 should be 0.5(S+S tranpose)x-a , right? anyway, thank you for the amazing lecture!####[['lecture', 'Course_General_Feedback', 'POS'], ['NULL', 'Instructor', 'POS'], ['grad(f)', 'Mathematical_Related_Concept', 'NEU'], ['0.5(S+S tranpose)x-a', 'Mathematical_Related_Concept', 'NEU']]
24:31 the guy's tee on the bottom right. A good MIT student.####[['student', 'Other', 'POS']]
In love with course outline####[['course outline', 'Course_General_Feedback', 'POS']]
at 28:10 why are we stuck using (*) to find y.it seems easily solvable to me?####[['(*)', 'Mathematical_Related_Concept', 'NEG']]
Thank you for this lecture: https://www.youtube.com/richcoast####[['lecture', 'Course_General_Feedback', 'POS']]
Blessing to all peoples those are related to mathematics field####[['NULL', 'Other', 'POS']]
When i connected dots in my head around 15 minutes when professor was talking about why we do this projection thing, it was one of the most mind fucking blown moments in my mind. I felt like going from top to bottom in the tiny brain - galaxy brain meme in a span of a second. Amazing course####[['course', 'Course_General_Feedback', 'POS'], ['professor', 'Instructor', 'POS']]
this is the big stuff####[]
I was wondering if a semicircle is differentiable at x=+1. I would say no, since it becomes minus infinity.####[['semicircle', 'Mathematical_Related_Concept', 'NEU']]
As an avid Rick and Morty fan (200 IQ.) i thought id visit calculus videos to see if the profs were doing a good job.####[['calculus videos', 'Course_General_Feedback', 'NEU'], ['profs', 'Instructor', 'NEU']]
How I understood the beginning example about the mean: We defined our sample space to be Omega = { [a,0] , [0,b] }. We defined the distribution over this sample space to be uniform (hence the 1/2). Now each sample can be seen as a random variable which takes on one of the values in Omega. By definition, the expectation is the sum of the products of each outcome with its probability. However, if we define a random variable to be the sum of the samples then we get the expectation of the new random variable is sum of the expectations of each sample. Each sample has the same expectation thus we can reduce the sum to a multiplication by s. PS I don't have very advanced knowledge of probability theory (I'm taking a course right now). If I have made a mistake let me know.####[]
About pi. I find it funny that people say that one can calculate the periphery of a circle but not of an ellipse when the periphery of circle is 2*pi*r and ellipse is 4*a*E(e), where r is the radius of the circle, a is the larger semiaxis of the ellipse and e is the excentricity of the ellipse. pi and E(e) are both as difficult to calculate exactly but somehow people say that the other equation is explicit and the other is not.####[]
americans do this in college?LOLin australia we do this in year 11 / sometimes year 10####[]
im confused with top z and bottom z can someone help me with it/####[['top z', 'Mathematical_Related_Concept', 'NEU'], ['bottom z', 'Mathematical_Related_Concept', 'NEU']]
the professor is really into the subject and is really explaining   good. i guess he is a pupil of albert einstien.wallah professor####[['professor', 'Instructor', 'POS'], ['albert einstien', 'Other', 'POS']]
If only probability questions had half the clarity in their information as the way Professor talks..!As he mentioned at the end, it is very easy to get confused while solving the probability questions based on real situations because the information provided can easily have multiple interpretations if utmost clarity is not maintained.####[['Professor', 'Instructor', 'NEU'], ['probability questions', 'Mathematical_Related_Concept', 'NEU']]
Knowing that the class is empty, 19:09 becomes incredibly hilarious.####[['class', 'Teaching_Setup', 'NEU']]
fair enough it may be a review in some way but in my uni this is all very basic pre-requisites before your even allowed on the course!####[['uni', 'Other', 'NEU'], ['NULL', 'Mathematical_Related_Concept', 'NEU']]
I would agree with you were it not for the FACT that MIT is asking not the Chinese, not Europeans, not those in the Southern hemisphere, nor the Northern hemisphere, but specifically Americans to foot the bill to, as you said, increase global standards, help mankind, educate ALL students, blah, blah, blah.  Americans should not be continually asked to sacrifice their own flesh for such endeavors.  Why should I pay taxes to pay for schools who turn out only foreign grads?####[['foreign grads', 'Other', 'NEG']]
Great video, finally I understand! :) thanks, MIT!!!####[['video', 'Course_General_Feedback', 'POS']]
The vector space part sounded like intro to abstract algebra. Nice!####[['vector space', 'Mathematical_Related_Concept', 'POS'], ['abstract algebra', 'Mathematical_Related_Concept', 'NEU']]
The meat starts at 09:56 for those who don't want to waste their time.21:50 I'm not sure if this is correct :p The probability of 0 assigned to each of these points would mean that there is _absolutely no chance_ I hit _any_ of them :P So I wouldn't be allowed to hit anywhere inside that square, and I'm also not allowed to hit outside of it, so I simply am not allowed to throw the dart at all :P What would be correct to say, I think, is that if the precision _approaches_ infinity, the probability _approaches_ 0, but it is not _exactly_ 0, just something arbitrarily close to it.####[]
Glad to see he's well!Much better than the 240p quality of the original linear algebra videos.####[['linear algebra videos', 'Course_General_Feedback', 'NEG'], ["he's", 'Course_General_Feedback', 'POS']]
This guy taught me more than I learned when I studied Maths for four years.####[['NULL', 'Instructor', 'POS']]
Around 18:02 when prof strang shows when we would get a symmteric matrix, he mutiplies R^t with R .  Didn't he wrote the order in reverse? wouldnt it be R into R^t??####[['R into R^t?', 'Mathematical_Related_Concept', 'NEU'], ['prof strang ', 'Instructor', 'POS']]
what is a relation in 3 d?????####[]
It's so important to develop a geometric view of linear algebra.####[['linear algebra.', 'Mathematical_Related_Concept', 'NEU']]
why is this lecture not being downloaded by Idm and only some of lectures of these lectures are able to be downloaded.####[['lecture', 'Teaching_Setup', 'NEU']]
at 6:07 he writes E2 is approx the square of E1 . But Shouldn't it be E1 is approx the square of E2?####[['E2', 'Mathematical_Related_Concept', 'NEU'], ['E1', 'Mathematical_Related_Concept', 'NEU']]
MIT students haven't seen the law of cosines ... smh####[['law of cosines', 'Mathematical_Related_Concept', 'NEU']]
38:38 I did not get what he meant. Y is a random variable indicating the time we have to wait. And for time, isn't it continuous? Then Y should also be a continuous RV. Why did he mention PMF rather than PDF?####[['Y', 'Mathematical_Related_Concept', 'NEU'], ['PMF', 'Mathematical_Related_Concept', 'NEU'], ['PDF', 'Mathematical_Related_Concept', 'NEU'], ['NULL', 'Instructor', 'NEU'], ['continuous RV', 'Mathematical_Related_Concept', 'NEU'], ['continuous', 'Mathematical_Related_Concept', 'NEU'], ['random variable', 'Mathematical_Related_Concept', 'NEU']]
Dang - Prof Tsitsiklis is good! Reminds me of Gilbert Strang and Walter Lewin. Probably all MIT profs are good, eh?####[['Prof Tsitsiklis', 'Instructor', 'POS'], ['Gilbert Strang and Walter Lewin', 'Instructor', 'POS']]
I do not understand the fact that why the summation of expected values gives mean?? Could u please help Thanks in advance.####[['summation of expected values', 'Mathematical_Related_Concept', 'NEU']]
Con someone help me understand what happens in 12:30? cant understand what he did there.####[['NULL', 'Instructor', 'NEU']]
oh god, prof. strang is so funny. he is acting natural. like him so much.####[['prof. strang', 'Instructor', 'POS']]
sir your style of explaining is outstanding...Thanks, to MIT for doing this noble work which benefits hundreds of thousands of students in the world......keep up the great work!!####[['NULL', 'Instructor', 'POS'], ['MIT', 'Other', 'POS']]
Thankyou Dr. Strang, been here from Lec 1 to 34. Amazing course####[['Dr. Strang', 'Instructor', 'POS'], ['course', 'Course_General_Feedback', 'POS']]
Thank you prof I'm writing a exam tomorrow morning####[['prof', 'Instructor', 'POS']]
45:00in the case r = m < n,  then  rref (A)  = [  Id.  F ] , if we allow permutation of columns.####[]
I blessed to see the prof.Gilbert strang  lecture. Very thankful to u.####[['lecture', 'Course_General_Feedback', 'POS'], ['prof.Gilbert strang', 'Instructor', 'POS']]
Very good. Thank you. But in the first example at min. 29:30 , why you go (-1) in the " X "direction ? I think it's (+1) , so the Vector will be < 1, 1, 0  >.####[['(-1)', 'Mathematical_Related_Concept', 'NEG'], ['NULL', 'Instructor', 'POS']]
colombia exploded because a welder slacked on an o ring u idiot dont fuck up facts. columbia exploded causee of power point lol wow u are smart####[['NULL', 'Instructor', 'NEG']]
Very good content to understand Bayesian inference. Thanks prof.####[['prof', 'Instructor', 'POS'], ['content', 'Course_General_Feedback', 'POS'], ['Bayesian inference', 'Mathematical_Related_Concept', 'NEU']]
Why does a 4x4 matrix have 24 Permutationmatrices when a 3x3 Matrix has 6? I don't get how they calculated it so quickly.####[['4x4 matrix', 'Mathematical_Related_Concept', 'NEU'], ['3x3 Matrix', 'Mathematical_Related_Concept', 'NEU']]
cook up numbers till they burn####[['numbers', 'Other', 'NEG']]
x/lnx IS DEFINED at x=0.ln(0+) approaches –infinite = -1/0so if f(x) = x/(lnx)f(0) = 0/(ln0) = x/(-1/0) = x*(-0/1) = 0Despite popular belief here in the comments, x=0 need not be an open dot, but closed as displayed.####[]
31:40  In the case of A = [2, 6; 6, 7] for example, when setting z = 0, what we actually get is a cross (an 'X' shape) ; when z euqals other values, then we get a hyperbola.####[]
my lecturer is so smart he thought us all these 35 lectures in one lecture am i the only one who knows such Jenious####[['lecturer', 'Instructor', 'NEG'], ['lecture', 'Course_General_Feedback', 'NEU']]
My professor isn't bad, but he doesn't hold a candle to this professor.  Zero obfuscation.####[['professor', 'Instructor', 'NEU']]
6:23 "that long, infinite series" hmmm....####[]
damn girl didn't want to take a seat. disrupting my learning environment.####[['girl', 'Other', 'NEG']]
LOL - those annoying computer-generated comments are all over the MIT videos I've been viewing. Any theories why they exist?####[['videos', 'Teaching_Setup', 'NEG'], ['computer-generated comments', 'Other', 'NEG']]
I guess I don't understand how the last vector set creates a subspace / plane.  Since x, y, and z are utilized in both vectors, wouldn't the subspace essentially be all of R3 with linear combinations being able to extend through that plane infinitely due to z?####[['vector set', 'Mathematical_Related_Concept', 'NEU']]
Clear, concise, coherent so who disliked this####[['NULL', 'Course_General_Feedback', 'POS']]
Holy crap this is a good lecture####[['lecture', 'Course_General_Feedback', 'POS']]
16:20 small signal analysis? hahaha####[['small signal analysis', 'Mathematical_Related_Concept', 'NEU']]
thank you Mr Strang for your lecture!!! i don't understand yet the fact that with 2 millions subscribers, only 4000 folow your lecture!! Your chain is one of the best i found regarding basical science, congratulations!!!####[['Mr Strang', 'Instructor', 'POS'], ['lecture', 'Course_General_Feedback', 'POS']]
Felt like climax of the movie####[['NULL', 'Other', 'POS']]
18.06 was a very important stepping stone in my career.####[]
@[USERNAME]I meant (>)This was just an example.I wanted to ask if it was possible to differentiatethings like f(x)>g(x) and have still the  >But after some thinking i understanded that this canNOT happen no way because the fact that f(x) > g(x) for every real x means that the graph of f(x) is higher from g(x) for every real x.But f derivative represents the slope of the tangent of f at x, giving us the monotony of f.Hope you understanded what i mean.Also thanks for the reply####[['reply', 'Other', 'POS']]
What's a long word for a bowl?  lol####[]
love the tranquil waterfall in these MIT classrooms####[['tranquil waterfall', 'Other', 'POS']]
Can I find some slides for these lesson?####[]
For those confused like me regarding the fishing example:for part d): The number of fish caught can be found in 2 waysConsider 3 Random Variables:F: No. of fish caughtT: Time (The values that time can take)FishTime: FishingTime (The values that fishing time takes, note that this is different from Time r.v.)1) E[F] = E[F|0<T<2] * P(0<T<2) + E[F|T>2] * P(T>2)                (0.6*2)       * 1               + 1              * P(0,2) 2) E[F] = E[F|FishTime=2] * P(FishTime = 2) + E[F|FishTime>2] * P(FishTime>2)                E       * (1-P(0,2))               + 1              * P(0,2)Here E will not be = lambda * tauThis is because if he fishes for exactly 2 hours it means he will definitely not catch 0 fish.So we need to calculate the conditional pmf. That is P(catches k fish|catches atleast 1 fish)Then use this to find the new Expected value by multiplying with k and summing for k = 1, 2....Then put this for E and calculate.Gives the same answer.####[]
if you are a random person like i am, which has nothing to do with anything of the information given in this video, like i am (i am a chef in a restaurant) you think to yourself, WTF IS HE TALKING ABOUT!!? and i watched this 10 fucking minutes ....####[['HE', 'Instructor', 'NEG']]
these statistics do not suit for psychology####[]
@[USERNAME]I read it in the comments of another one of these videos. I don't remember the exact comment though.####[]
His book seams very good as well.####[['book', 'Teaching_Setup', 'POS']]
+Osman ÇALIŞIR All the lecture notes, exams with solutions and assignments are available on the MIT OpenCourseWare site at: http://ocw.mit.edu/18-01F06####[]
his english is absolutely flawless. just has a thick accent which makes him seem even more intelligent, almost as if he mastered english overnight####[['english', 'Other', 'POS'], ['accent', 'Other', 'POS']]
"don't all speak at once" is he joking, or trying to hide the fact that the class is empty? not sure yet :)####[['NULL', 'Instructor', 'NEG']]
Wow! The way he teaches is amazing...Thanks a lot..####[['NULL', 'Instructor', 'POS']]
I believe that Mr. Strang is really amazing and incredible, but I got stuck when he said of "the pivot and free variables" , I mean he told us about the algorithm very well, but I am not able to connect these with that what does it mean to?? Why does non pivot columns can be considered anything?? And what are its effect on my graph if I wish to plot it on?? And what's the concept behind these pivot and free variables, how did it occur from anywhere??So , if you guys could help me out with this , it would really be appreciated!!####[]
I think that's because he's calculating how many blocks you need to have hanging over the edge of the first one. That would let him not count it in the calculation.####[]
Nice hair cut ;) And great lecture of course!####[['hair cut', 'Other', 'POS'], ['lecture', 'Course_General_Feedback', 'POS']]
Just finished the whole Single Variable Calculus course.Thank you MIT OCW for making this possible.Brazil, 2015.####[['MIT OCW', 'Other', 'POS'], ['Single Variable Calculus course', 'Course_General_Feedback', 'NEU']]
This teacher is not vesy good even for secondarry school!  His demonstration is very poor, I couldndt  understand how it is possible, that hy is MIT teacher ???!!! His geometric demonstration and explanation is really bad !!!!####[['teacher', 'Instructor', 'NEG'], ['demonstration', 'Teaching_Setup', 'NEG'], ['geometric demonstration', 'Teaching_Setup', 'NEG'], ['explanation', 'Course_General_Feedback', 'NEG']]
@[USERNAME]im in victoria, school started last monday####[]
"forgive me for doing such a thing" (looks at book)####[]
Is it better to take this course straight away or finish 18.06 first? Thanks!####[]
I think the 1st problem set of this course is not in the website. The website shows the ps1 of 18.01.####[]
calls the first row a 'HE'the second row a 'SHE'18:35####[]
anyone know how you would calculate the probability of x being greater than or equal to 1/2?####[['probability of x', 'Mathematical_Related_Concept', 'NEU']]
I am happy to see this person alive in 2019. May God gave him a long life####[['person', 'Instructor', 'POS']]
I'm really happy that great lectures are available for free. Young people should appreciate it that they have internet and they can learn from materials from other universities especially from other countries from another part of the globe.####[['lectures', 'Course_General_Feedback', 'POS']]
Sur how to find out volumme of tetrahedron using triple integral.what is procedure for limits>?####[['volumme of tetrahedron', 'Mathematical_Related_Concept', 'NEU']]