The difference between most universities and places like MIT isn't the curriculum, it's the instructors. And by some happy miracle, we've ended up in a world where these lectures are free to watch!
@@juliusolaifa5111 there are so many different fields within AI! I would say study all the basic Math needed for ML first like Calculus, Linear Algebra, maybe Optimization Theory, then studying some foundational Machine Learning ( you can try out Andrew Ng's Machine Learning course on Coursera for a non-math heavy introductoon, or go straight to books like Elements of Statistical Learning, and Learning from Data for more math-y theory). If you want a more hands-on coding introduction, I would suggest the Hands-on Machine Learning with Scikit-learn, Keras, and Tensorflow book. Once, you have some intuition of foundational ML, you can explore other subfields like Computer Vision, NLP, Reinforcement Learning, Robotics, and so many more. Personally, I have been studying a lot of Reinforcement Learning + Robotics this past year. I'm looking toward learning more NLP soon to work on some social robots 🤖 that can intelligently communicate with people! Good luck on your journey in AI/ML!
@@khailai5204 Can you suggest materials on Robotics and Reinforcement Learning? I have gone through Andrew Ng course both ML and DL specialization. I bought ESL but haven't read much.
I am also self-studying ML (also taking a professional certificate class from Columbia). These videos are excellent. But I wish there was more programming in them.
These lectures are awesome! I dont know how integration and these transformations work, but I like the way Mr. Winston is teaching. Its all very clear, simple and structured that makes it easy to follow and its also very interesting how he is solving problems. Another fact is that other instructors get lost even with notes, presentations and materials and hes just doing it out of mind and that show that he unterstood what hes talking about!
Damn this course is good. My AI course began with "this is a node, this is a breadth first search, this is a..., you memorize this to pass the exam", this deals with the core concepts which I find more beneficial.
The calculus problem is much more interesting (and far less patronizing) than the typical "A traveler wants to get from city A to city C..." and I appreciate that about it.
Prof - "So this then, forms the core of an integration program, that will integrate almost nothing. But actually, almost nothing is integrable anyways, so it's a good head start." - 8:54
Thanks a lot for the free content. Im one of those cases that cant go to college because of cronic illness, so this is the best type of content for self teaching. :D
I'm literally sat here, open mouthed, trying to understand why nobody tried to teach calculus this way. Splitting into safe and heuristic operations, and formalising the approach to solving problems would have really helped back when I was studying mathematics.
To some extent that is because the purpose of a mathematics class is not to simply teach you how to solve mathematical problems via heuristic steps, but rather to give you an understanding of the underlying mathematical theory. Perhaps one lesson or so of this could have been useful at some point to help bolster grades though...
So impressed. This robot professor is the best example of artificial intelligence I have ever seen! Hopefully in the next version MIT will be able to create artificial emotions as well.
Hahaha You know what? That is why he sat in this lecture in MIT, because ordain people just say " Hi" to you even you ever told him your name last time not long ago. And that is why there are countless the average dumb Joes around your daily life even now you have already out of campus into working life. And guess you couldn't agree me more about my remarks....................... Merry Xmas from Melbourne..........STF....................
Well this explains why there seem to be so many in AI that come from mathematics. As for the program, it simply automates a process that was derived from human thought.
Jim Slagle's PhD thesis is here: dspace.mit.edu/bitstream/handle/1721.1/11997/31225400-MIT.pdf?sequence=2 For symbolic integration the paper by Ritt on Liouville's theory is pretty important
For those having their Math rusty like me here is why he substitute with sinx or cosx, it is simply because the function is defined in the domain [0,1[ that is because of (1-x2)^5/2=(sqrt(1-x2))^5 and anything under the sqrt should be positive so 1-x2 needs to be >=0 then 1>X2.....
I see a some comments about being lost in the integrals. Well, as he said, he wanted us to witness the detailed process so we could understand how the "intelligence" works. The point of the lecture is that the computation is done with a set of rules and leads to a set of possible outcomes, as represented by the tree. Honestly, however, the calculus problem is quite basic. If you want to understand how to solve such problems I'd recommend watching a couple Khan Academy videos on simple integral calculus.
The point of the lecture was to take a hard problem that most of the students couldn't solve and show how a computer could solve those problems, in order to pose the question "Is this intelligence?"
Im so mad that I had a terrible math teacher at my university! Teaching is a skill and I guess some profs just haven’t witnessed what it means to be good at teaching. I’m truly thankful for this resource
Tarun We're given y=tan(z) -> dy/dz = sec^2(z) -> dy = dz sec^2(z) = dz/cos^2(z) . Use this result to replace dy back in the problem qn. To get dz like what u hv asked, we just need to verify that 1/1+y^2 is indeed eql to cos^2(z). 1+y^2 = 1 + tan^2(z) = 1+sin^2(z)/cos^2(z) =(cos^2(z)+sin^2(z))/cos^2(z) = 1/cos^2(z). This 1/1+y^2 = cos^2(z).
Summary: - Key Insights for [2. Reasoning: Goal Trees and Problem Solving](ruclips.net/video/PNKj529yY5c/видео.html) by [Merlin AI](merlin.foyer.work/) **Understanding Problem Solving in Integration** - The lecture presents a model of human problem-solving techniques, particularly in symbolic integration, contrasting human capabilities with those of computational programs. - A foundational aspect of problem-solving is recognizing the nature of the problem and determining whether it can be solved using known methods or transformations. - The approach to problem-solving is likened to a skill that can be mastered through practice and understanding, leading to instinctive application in various scenarios. **Problem Reduction Techniques** - The concept of "problem reduction" is introduced, which involves transforming a complex problem into a simpler one that can be solved more easily. - Simple transformations are highlighted as essential tools in calculus, enabling the solver to manipulate integrals into more manageable forms. - A list of "safe transformations" is provided, such as taking constants out of integrals and using algebraic identities to simplify functions before integration. **Knowledge Representation in Problem Solving** - The lecture emphasizes the types of knowledge necessary for effective problem-solving, including procedural knowledge and conceptual understanding of integration techniques. - Knowledge is represented through tables of integrals and transformation rules, which guide the solver in choosing appropriate methods. - The educational philosophy suggests that understanding the underlying principles is crucial for developing effective problem-solving skills, which can then be applied instinctively. **The Role of Goal Trees in Problem Solving** - The discussion introduces "goal trees" as a visual representation of how different problems and transformations relate, sometimes referred to as "And/Or trees." - Goal trees help to visualize the pathways through which various transformations can lead to solutions, allowing for strategic decision-making in problem-solving. - By employing goal trees, solvers can identify which transformations to apply based on their familiarity and the complexity of the resulting expressions. **Evaluating the Effectiveness of Integration Programs** - The effectiveness of early integration programs, such as those developed at MIT, is assessed based on their ability to solve complex calculus problems with limited computational resources. - Performance metrics are discussed, revealing that even with minimal knowledge (e.g., a small table of integrals), these programs could achieve high success rates in solving integration problems. - The lecture concludes with a reflection on the perceived intelligence of computational programs, suggesting that understanding the mechanisms behind their operation can diminish the perceived complexity of their problem-solving capabilities.
Out of curiosity: What level of mathematics should I have before watching these videos. I have never taken a calculus course, so I don't know why those transformations work. Do I need calculus, or can I get by without it? Or can I learn a certain calculus subjects without having to go into calculus in depth?
+Soulsphere001 The 6.034 MIT course page does list 18.02 as a prerequisite (as well as 6.01): 6.01-This is the only formal pre-requisite but we will depend on it strongly. In particular, we assume that you can programs in Python, that you understand search algorithms (depth-first, breadth-first, uniform-cost, A*) and basic probability and state estimation to the level covered in 6.01 18.02-We will assume that you know what the chain rule is and partial derivatives and dot products. If you have not taken 18.02 (or are not taking it concurrently), you should really wait to take 6.034 until you have.
***** For some reason I cannot find the prerequisites anywhere on the course's webpages, so I really appreciate the reply. Thank you very much. I did notice the Python prerequisite, and I started learning it two days ago. One of my cousins knows it and has been recommending, for years, that I learn it. Fortunately, programming isn't a new topic for me.
Bob Jones, I've been meaning to learn some calculus at some point, but I should go through my old precalculus book first. But, yes, I could probably just learn the specific calculus required for those equations.
"Bring the number down and lower the power" is a quote that my brother used to used a lot, and now I finally understand what it means. Thanks for the information. I'll do as you suggest.
Add 1 and subtract 1 on the numerator. Then split (y^4 - 1) into (y^2 - 1) * (y^2 + 1). Cancel out the common terms and that should be it. Writing on paper should make it more obvious if it is confusing.
@@muraliavarma That is one way to do it, but you could also go for polynomial long division, and for anybody reading this wanting to know how it works, take a look at this link: www.emathhelp.net/calculators/algebra-1/polynomial-long-division-calculator/?numer=y%5E4&denom=1+%2B+y%5E2&steps=on
Hey could someone explain me why dx = cos y at about 19:25? that would be very nice. I cant finde an explanation online. A good link would help me too. Thanks
I don't understand any of this, but I'm watching lol. Would love to learn more calc and trig to understand all this better. Someone let me know if you have any suggestions on how I can teach my self!
We suggest you watch this playlist to get an overview of calculus: ruclips.net/p/PLBE9407EA64E2C318. There are a lot of channels on RUclips for calculus and trigonometry like Khan Academy or 3Blue1Brown. We recommend you look at those as well. Best wishes on your studies!
I don't understand the explanation why the denominator became Cos^4 y as opposed to cos^5 y. How does the derivative of sin being equal to cos explain this? If anyone can assist in my understanding I would appreciate it very much.
MrX5tech Got it, he's moving dx into the numerator in order to make the integral with respect to y... so the numerator becomes sin^4 y cos y and the cos y cancels one of cos's in the denominator DUUH ! sometimes the most obvious things get ya. Hey man Thanks !
Ma Yo Fluid theory (Reproduction/Feed/Reasoning) decanted selfmultidimentionalover... The polydynamics of the movement generates pseudo-autonomy as material property, of the autogenous phenomenon; existing.(...) Simultaneous as my unidimensional variability... unidimensional variability = live-beings
We recommend checking out the EECS undergraduate curriculum to see how this course fits within all the other courses: www.eecs.mit.edu/academics-admissions/undergraduate-programs/course-6-2-electrical-eng-computer-science
There is one question, that when they apply x=sin(y), there is a subtle constraint of the range of x applied, which means abs(x) cannot be bigger than 1. But the original formula does not have the constraint of x value range. Are we losing something here?!
I noticed there has been a mistake on the integral ''\int sin^4 y/ cos^4 y dy''...it should be ...'' \int sin^4 y/ cos^3 y'' as long x=siny so dx= cos y dy...
Angelos Manglis Incorrect. The integral transformation he applied gave the integral of ((sin^4 y * cos y) / (cos^5 y))dy, which is the integral of (sin^4 y / cos^4 y)dy.
@@mayo7199 I suppose, as i expect, than you had solved your problem, but in case than a new visitor has the same question, then: x = sen(y) --> dx = cos(y) dy; int( sen4(y) * cos(y) dy / ( cos5(y) ) ) // Just is a replace. That's the cause of why there are a cos(y) in the enumerator; int( sen4(y) dy / cos4(y) );
Where can I find readings for the transformations mentioned at 14:30 ? I have taken calculus classes but I have never seen anything similar to that before and would like to learn.
these transformations and stuff are human ideas. I wonder if we can make a machine with elementary ideas of what integration is and then can do any problem ( Alpha Zero in chess world is an example)
Sanket Patole Fluid theory (Reproduction/Feed/Reasoning) decanted selfmultidimentionalover... The polydynamics of the movement generates pseudo-autonomy as material property, of the autogenous phenomenon; existing.(...) Simultaneous as my unidimensional variability... unidimensional variability = live-beings
+Attreya Bhatt It's because tan4 is a less complex composition of functions. You can think of tan4 (x) as a composition of 2 functions: tan x and x^4. Similarly, 1/cot4 (x) is a composition of 3 functions: cot x, x^4, and 1/x. Since it is generally simpler to integrate a composition of 2 functions than a composition of 3 functions, tan4 x was chosen
using x=siny,x^4 becomes sin^4(x),1-x^2 becomes cos^2(x),so cos^(2*5/2)(x) becomes cos^5(x) and then dx = cosy dy,so use all these transformations and you'll get it. Hope it helps :)
I’m only on the second lecture as well, but I have heard that AI theory requires calculus and linear algebra so it might take some of that knowledge for the rest of the course, but this stuff actually isn’t too bad. If you want to learn it quickly, I’d just watch some videos on integration and then learn integration techniques. Being very good at it is pretty difficult, but understanding the basics is actually quite simple because it’s really algorithmic.
The only thing about this program that seems strange to me is how it’s classified as artificially intelligent. I don’t see how it’s different from any other program. I do see how it “thinks” in the same way as I do while doing integration, but that “thinking” seems like pretty much the same control flow as any other program.
It would be actually interesting if you can detect all the yawning persons in the audience. Hold the footage, look for someone who opens his mouth, if so he's yawning or speaking. People also sometimes hold the hand in front of the mouth. The difference can only tell a human. Not a simple task for a computer.
+imalive I believe he means, how many steps do I need to take before I reach the answer? For instance, take the problem Derivative(5x^2). 1) Factor out five. 5*Derivative(x^2) 2) Reference table of derivatives to find answer: 5*2*x. As I understand, this problem has a depth of 2.
AI was a hot topic in the 1980's. I did neural nets and troubleshooting and configuration expert systems. Some of those programs scared people. Now it's hot again. I'm somewhat surprised that so little progress has been made. I ultimately came around to the view the AI should be used to augment humans, not replace them. Doctors should be open to programs that help them make accurate diagnoses so they can spend their time caring for the person. How will we program non-local consciousness?
AI is incredibly mathy as you go down this series, he makes several references to partial differentiations, Lagrange multipliers and similar that are required for the algorithms. Not to mention the. Point of most AI is to minimize or maximize some unknown measure, that always leads you to Calculus especially Multivariable calculus
The amount of people who want to work with a machine that only thinks in number at an intimate level that do not like math is concerning and explanatory of why the field is oversaturated
![I.N "HALLUCINATION" | [Stray Kids : SKZ-PLAYER]](http://i.ytimg.com/vi/n5B5q1Hwt_U/mqdefault.jpg)
The difference between most universities and places like MIT isn't the curriculum, it's the instructors. And by some happy miracle, we've ended up in a world where these lectures are free to watch!
I wish those classes could be given in poor neighborhoods, so our youth could have a good education
From a person self-studying Artificial Intelligence, thank you so much for publishing this playlist! It is truly a great resource for me.
As someone who started self studying AI before me, what do you suggest? Books and courses
@@juliusolaifa5111 there are so many different fields within AI! I would say study all the basic Math needed for ML first like Calculus, Linear Algebra, maybe Optimization Theory, then studying some foundational Machine Learning ( you can try out Andrew Ng's Machine Learning course on Coursera for a non-math heavy introductoon, or go straight to books like Elements of Statistical Learning, and Learning from Data for more math-y theory). If you want a more hands-on coding introduction, I would suggest the Hands-on Machine Learning with Scikit-learn, Keras, and Tensorflow book.
Once, you have some intuition of foundational ML, you can explore other subfields like Computer Vision, NLP, Reinforcement Learning, Robotics, and so many more.
Personally, I have been studying a lot of Reinforcement Learning + Robotics this past year. I'm looking toward learning more NLP soon to work on some social robots 🤖 that can intelligently communicate with people!
Good luck on your journey in AI/ML!
@@khailai5204 Can you suggest materials on Robotics and Reinforcement Learning? I have gone through Andrew Ng course both ML and DL specialization. I bought ESL but haven't read much.
I am also self-studying ML (also taking a professional certificate class from Columbia). These videos are excellent. But I wish there was more programming in them.
Who else in quarantine and chilling with these lectures?
Learning never ends!
@@ericfitzgerald9214 aaye!!!
Yes broo
hell yea
Me🙋🏻♂️
These lectures are awesome!
I dont know how integration and these transformations work, but I like the way Mr. Winston is teaching. Its all very clear, simple and structured that makes it easy to follow and its also very interesting how he is solving problems.
Another fact is that other instructors get lost even with notes, presentations and materials and hes just doing it out of mind and that show that he unterstood what hes talking about!
Damn this course is good. My AI course began with "this is a node, this is a breadth first search, this is a..., you memorize this to pass the exam", this deals with the core concepts which I find more beneficial.
I can relate to this. Our course follows the same nonsense.
The calculus problem is much more interesting (and far less patronizing) than the typical "A traveler wants to get from city A to city C..." and I appreciate that about it.
I wish I could be a student at MIT. Awesome education,thanks for sharing as we believe knowledge is freedom.
Thanks to OCW, we *all* are :-)
(Thanks MIT!)
@@RogerBarraud it doesnt give the vibes of getting a coffee attending to class and then chilling at the campus.. But its something
Prof - "So this then, forms the core of an integration program, that will integrate almost nothing. But actually, almost nothing is integrable anyways, so it's a good head start." - 8:54
Yeah he got me good there :))
Thanks a lot for the free content. Im one of those cases that cant go to college because of cronic illness, so this is the best type of content for self teaching. :D
I'm literally sat here, open mouthed, trying to understand why nobody tried to teach calculus this way. Splitting into safe and heuristic operations, and formalising the approach to solving problems would have really helped back when I was studying mathematics.
To some extent that is because the purpose of a mathematics class is not to simply teach you how to solve mathematical problems via heuristic steps, but rather to give you an understanding of the underlying mathematical theory.
Perhaps one lesson or so of this could have been useful at some point to help bolster grades though...
This professor is a LEGEND.
Love the ending. Well said by the instructor.
I would like to add: "AI is whatever hasn't been done yet." - Douglas Hofstadter
Not quite agreeing here.
Knowlegde about knowledge is power! -Professor
So impressed. This robot professor is the best example of artificial intelligence I have ever seen!
Hopefully in the next version MIT will be able to create artificial emotions as well.
On the most fundamental level, you could kinda ask the same thing about us. I suppose.
you have no idea.
RIP Prof Patrick Winston :'(
" i take it back, it's not intelligent after all. It does integration the same way i do " best part of this video.
Second lecture and he knows everyone's name? Damn!
Read his post on why he decided to memorize all of his students' names. slice.mit.edu/2009/08/16/the-rumpelstiltskin-principle/
He knew everyone by name in the first lecture.
He actually knew their names by the first lecture.
the post's amzingly cool
Hahaha You know what? That is why he sat in this lecture in MIT, because ordain people just say " Hi" to you even you ever told him your name last time not long ago. And that is why there are countless the average dumb Joes around your daily life even now you have already out of campus into working life. And guess you couldn't agree me more about my remarks....................... Merry Xmas from Melbourne..........STF....................
So intelligence is doing something someone else does't know how to do?
Fair point
43:33 This... professor.. knows what's up.
Well this explains why there seem to be so many in AI that come from mathematics. As for the program, it simply automates a process that was derived from human thought.
Jim Slagle's PhD thesis is here: dspace.mit.edu/bitstream/handle/1721.1/11997/31225400-MIT.pdf?sequence=2
For symbolic integration the paper by Ritt on Liouville's theory is pretty important
Thanks!
Thank you! I was looking for this.
19:08 pretty cool how he preempted their thoughts
For those having their Math rusty like me here is why he substitute with sinx or cosx, it is simply because the function is defined in the domain [0,1[ that is because of (1-x2)^5/2=(sqrt(1-x2))^5 and anything under the sqrt should be positive so 1-x2 needs to be >=0 then 1>X2.....
What a good lecturer!
Wow ,great fun lectures. It's really changed my mind about what actually learning is about
I love this guy's stuff TOTALLY... Must watch his vids on teaching...
I see a some comments about being lost in the integrals. Well, as he said, he wanted us to witness the detailed process so we could understand how the "intelligence" works. The point of the lecture is that the computation is done with a set of rules and leads to a set of possible outcomes, as represented by the tree. Honestly, however, the calculus problem is quite basic. If you want to understand how to solve such problems I'd recommend watching a couple Khan Academy videos on simple integral calculus.
The point of the lecture was to take a hard problem that most of the students couldn't solve and show how a computer could solve those problems, in order to pose the question "Is this intelligence?"
Im so mad that I had a terrible math teacher at my university! Teaching is a skill and I guess some profs just haven’t witnessed what it means to be good at teaching. I’m truly thankful for this resource
is there any text book accompanied the lecture???
44:44 they solve some problem, they seem super smart. They tell you how they did it, and they don't seem so smart anymore! - words of wisdom
Thanks for such an insightful presentation/Lecture. By the way, I am from Tanzania, East Africa
I wish I could like this 100 times.
R.I.P. Professor Winston
How did he get to dz from 1/(1+y^2) dy at 31:07 ?
Tarun We're given y=tan(z) -> dy/dz = sec^2(z) -> dy = dz sec^2(z) = dz/cos^2(z) . Use this result to replace dy back in the problem qn. To get dz like what u hv asked, we just need to verify that 1/1+y^2 is indeed eql to cos^2(z). 1+y^2 = 1 + tan^2(z) = 1+sin^2(z)/cos^2(z) =(cos^2(z)+sin^2(z))/cos^2(z) = 1/cos^2(z). This 1/1+y^2 = cos^2(z).
@@jackedelic9188 thank you
Summary: -
Key Insights for [2. Reasoning: Goal Trees and Problem Solving](ruclips.net/video/PNKj529yY5c/видео.html) by [Merlin AI](merlin.foyer.work/)
**Understanding Problem Solving in Integration**
- The lecture presents a model of human problem-solving techniques, particularly in symbolic integration, contrasting human capabilities with those of computational programs.
- A foundational aspect of problem-solving is recognizing the nature of the problem and determining whether it can be solved using known methods or transformations.
- The approach to problem-solving is likened to a skill that can be mastered through practice and understanding, leading to instinctive application in various scenarios.
**Problem Reduction Techniques**
- The concept of "problem reduction" is introduced, which involves transforming a complex problem into a simpler one that can be solved more easily.
- Simple transformations are highlighted as essential tools in calculus, enabling the solver to manipulate integrals into more manageable forms.
- A list of "safe transformations" is provided, such as taking constants out of integrals and using algebraic identities to simplify functions before integration.
**Knowledge Representation in Problem Solving**
- The lecture emphasizes the types of knowledge necessary for effective problem-solving, including procedural knowledge and conceptual understanding of integration techniques.
- Knowledge is represented through tables of integrals and transformation rules, which guide the solver in choosing appropriate methods.
- The educational philosophy suggests that understanding the underlying principles is crucial for developing effective problem-solving skills, which can then be applied instinctively.
**The Role of Goal Trees in Problem Solving**
- The discussion introduces "goal trees" as a visual representation of how different problems and transformations relate, sometimes referred to as "And/Or trees."
- Goal trees help to visualize the pathways through which various transformations can lead to solutions, allowing for strategic decision-making in problem-solving.
- By employing goal trees, solvers can identify which transformations to apply based on their familiarity and the complexity of the resulting expressions.
**Evaluating the Effectiveness of Integration Programs**
- The effectiveness of early integration programs, such as those developed at MIT, is assessed based on their ability to solve complex calculus problems with limited computational resources.
- Performance metrics are discussed, revealing that even with minimal knowledge (e.g., a small table of integrals), these programs could achieve high success rates in solving integration problems.
- The lecture concludes with a reflection on the perceived intelligence of computational programs, suggesting that understanding the mechanisms behind their operation can diminish the perceived complexity of their problem-solving capabilities.
Out of curiosity: What level of mathematics should I have before watching these videos. I have never taken a calculus course, so I don't know why those transformations work. Do I need calculus, or can I get by without it? Or can I learn a certain calculus subjects without having to go into calculus in depth?
+Soulsphere001 The 6.034 MIT course page does list 18.02 as a prerequisite (as well as 6.01):
6.01-This is the only formal pre-requisite but we will depend on it strongly. In particular, we assume that you can programs in Python, that you understand search algorithms (depth-first, breadth-first, uniform-cost, A*) and basic probability and state estimation to the level covered in 6.01
18.02-We will assume that you know what the chain rule is and partial derivatives and dot products. If you have not taken 18.02 (or are not taking it concurrently), you should really wait to take 6.034 until you have.
*****
For some reason I cannot find the prerequisites anywhere on the course's webpages, so I really appreciate the reply. Thank you very much.
I did notice the Python prerequisite, and I started learning it two days ago. One of my cousins knows it and has been recommending, for years, that I learn it. Fortunately, programming isn't a new topic for me.
Bob Jones, I've been meaning to learn some calculus at some point, but I should go through my old precalculus book first. But, yes, I could probably just learn the specific calculus required for those equations.
"Bring the number down and lower the power" is a quote that my brother used to used a lot, and now I finally understand what it means.
Thanks for the information. I'll do as you suggest.
can anyone tell me at 28:50 how did he get that division result
its synthetic devision, just look it up, or go to high school, either would work
Add 1 and subtract 1 on the numerator. Then split (y^4 - 1) into (y^2 - 1) * (y^2 + 1). Cancel out the common terms and that should be it. Writing on paper should make it more obvious if it is confusing.
substitute y=tanx=> dy=1/cos^2x*dx=(1+tan^2x)dx. then tan^4dx=>tan^4y*dy/(tan^2+1). Hope this can help!!!
@@muraliavarma That is one way to do it, but you could also go for polynomial long division, and for anybody reading this wanting to know how it works, take a look at this link: www.emathhelp.net/calculators/algebra-1/polynomial-long-division-calculator/?numer=y%5E4&denom=1+%2B+y%5E2&steps=on
Hey could someone explain me why dx = cos y at about 19:25? that would be very nice. I cant finde an explanation online. A good link would help me too. Thanks
he just derived the x = sin y and he got dx = cos y dy
thank you! i wanst used to this nototation back then. :)
how i wish i got these methods of integration before my A-level exam
I now know that after 30 years not doing it, I've completely forgotten how to do integration 😟
I don't understand any of this, but I'm watching lol.
Would love to learn more calc and trig to understand all this better.
Someone let me know if you have any suggestions on how I can teach my self!
Going to keep watching
We suggest you watch this playlist to get an overview of calculus: ruclips.net/p/PLBE9407EA64E2C318. There are a lot of channels on RUclips for calculus and trigonometry like Khan Academy or 3Blue1Brown. We recommend you look at those as well. Best wishes on your studies!
Why why why did they install the electronic chalkboard movers? What was wrong with the old system?
How did he find functional composition depth at 34:45
Where the heuristic transformations after 15:30 come from, what is this?
Last quote was amazing!
his notation is amazing!
I don't understand the explanation why the denominator became Cos^4 y as opposed to cos^5 y. How does the derivative of sin being equal to cos explain this? If anyone can assist in my understanding I would appreciate it very much.
+Ma Yo x=siny => dx=cosydy as was said a second later
+MrX5tech I heard him say just that, but As I mentioned I didn't understand his explanation
MrX5tech Got it, he's moving dx into the numerator in order to make the integral with respect to y... so the numerator becomes sin^4 y cos y and the cos y cancels one of cos's in the denominator DUUH ! sometimes the most obvious things get ya. Hey man Thanks !
Ma Yo Fluid theory (Reproduction/Feed/Reasoning) decanted selfmultidimentionalover...
The polydynamics of the movement generates pseudo-autonomy as material property, of the autogenous phenomenon; existing.(...)
Simultaneous as my unidimensional variability...
unidimensional variability = live-beings
R.I.P Patrick Winston
This course if for Comp sci. engineers or electrical engineers? Does this course coincide with Machine Learning and data Science?
We recommend checking out the EECS undergraduate curriculum to see how this course fits within all the other courses: www.eecs.mit.edu/academics-admissions/undergraduate-programs/course-6-2-electrical-eng-computer-science
I’m dumb and all, but what happened to the ^5/2 before transform c happened?
There is one question, that when they apply x=sin(y), there is a subtle constraint of the range of x applied, which means abs(x) cannot be bigger than 1. But the original formula does not have the constraint of x value range. Are we losing something here?!
awwww...23:00
red sweater with the muffler
17:24 -> Her name is Sila :).
Her zaman bir önerisi mi varmış.
I noticed there has been a mistake on the integral ''\int sin^4 y/ cos^4 y dy''...it should be ...'' \int sin^4 y/ cos^3 y'' as long x=siny so dx= cos y dy...
Angelos Manglis Incorrect. The integral transformation he applied gave the integral of ((sin^4 y * cos y) / (cos^5 y))dy, which is the integral of (sin^4 y / cos^4 y)dy.
+James N How does the numerator become sin^4 y cos y, with direct substitution it shld be sin^4 y ?! Help !!
@@mayo7199 I suppose, as i expect, than you had solved your problem, but in case than a new visitor has the same question, then:
x = sen(y) --> dx = cos(y) dy;
int( sen4(y) * cos(y) dy / ( cos5(y) ) ) // Just is a replace. That's the cause of why there are a cos(y) in the enumerator;
int( sen4(y) dy / cos4(y) );
Impressed by the board.
8:53 Four Integrals
what's problem reduction? 03:35
Reducing the problem to the form that you are familiar with or have worked on before.
28:00 (tanx)^4 = y^4/(1 + y^2)^4 did he forget to put power 4 on the denominator
no, he was right, (tan(x))dx=1/cos(x)^2=1+tan(x)^2
Where can I find readings for the transformations mentioned at 14:30 ? I have taken calculus classes but I have never seen anything similar to that before and would like to learn.
+Erich Kramer See the course on MIT OpenCourseWare for the complete materials (including a list of readings) at ocw.mit.edu/6-034F10.
He's just pointing out that you can transform any of the trig functions into different trig functions using trig identities, demonstrated at 20:45
You don't realize the difference between an MIT professor and a non-MIT professor until you watch MIT OCW.
can anyone tell me the name of integration model;Is it sleighel or slaygal or something else. that solved 54/56 Integration problems
Why did he chose those specific transformations as safe transformations?
O the joy of being enlightened…
these transformations and stuff are human ideas. I wonder if we can make a machine with elementary ideas of what integration is and then can do any problem ( Alpha Zero in chess world is an example)
What this Professor teaches is not just AI, but how to teach a subject as well...RIP `(-_-)'
Spent whole time solving an integral problem to demonstrate a simple intuitive concept/approach.
Sanket Patole Fluid theory (Reproduction/Feed/Reasoning) decanted selfmultidimentionalover...
The polydynamics of the movement generates pseudo-autonomy as material property, of the autogenous phenomenon; existing.(...)
Simultaneous as my unidimensional variability...
unidimensional variability = live-beings
Great Teacher!! Thanks for the material!!
thanks for doing a calculus problem half the class. could easily made the point within 10 mins
I think you missed the point.
Why was tan4 chosen instead of cot4? I couldn't understand it.
+Attreya Bhatt It's because tan4 is a less complex composition of functions. You can think of tan4 (x) as a composition of 2 functions: tan x and x^4. Similarly, 1/cot4 (x) is a composition of 3 functions: cot x, x^4, and 1/x. Since it is generally simpler to integrate a composition of 2 functions than a composition of 3 functions, tan4 x was chosen
Oh thanks
this is such an insanely cool topic!!!!!!!!!
Thank you for great series
By the way very interesting lectures well taught and also atracts your interest to go through them!!
Really fun lecture. Thanks.
I got lost when he apply C and got to sin^4y/cos^4y. can someone explain it in detail for me? thanks...
using x=siny,x^4 becomes sin^4(x),1-x^2 becomes cos^2(x),so cos^(2*5/2)(x) becomes cos^5(x) and then dx = cosy dy,so use all these transformations and you'll get it.
Hope it helps :)
when do they start with the code ??
The joke in the end is so interesting¡
Finishing was awesome.. i loved it to the core
When he wrote knowledge is power, how many of you got the remembrance of badass little finger-cersei scence..
Power is power
exciting and excited
Great lecture, thank you
"feels?!"
hmm. This got advanced fast :(
I’m only on the second lecture as well, but I have heard that AI theory requires calculus and linear algebra so it might take some of that knowledge for the rest of the course, but this stuff actually isn’t too bad. If you want to learn it quickly, I’d just watch some videos on integration and then learn integration techniques. Being very good at it is pretty difficult, but understanding the basics is actually quite simple because it’s really algorithmic.
thank you for this interesting course
The only thing about this program that seems strange to me is how it’s classified as artificially intelligent. I don’t see how it’s different from any other program. I do see how it “thinks” in the same way as I do while doing integration, but that “thinking” seems like pretty much the same control flow as any other program.
is this how Wolfram Alpha works?
Cisco Ramon in the first row.
It would be actually interesting if you can detect all the yawning persons in the audience. Hold the footage, look for someone who opens his mouth, if so he's yawning or speaking. People also sometimes hold the hand in front of the mouth. The difference can only tell a human. Not a simple task for a computer.
I had these kind of problems in my university's Scheme course.
how is average depth of tree = 3
+imalive I believe he means, how many steps do I need to take before I reach the answer? For instance, take the problem Derivative(5x^2).
1) Factor out five. 5*Derivative(x^2)
2) Reference table of derivatives to find answer: 5*2*x.
As I understand, this problem has a depth of 2.
Thanks :-)
1 heuristic , 1 safe, 1 table lookup
we all will choose to ignore what was written on the board?
Damn the ending........ Concludes the question that the program can not in fact be called intelligent
How did a blind man write such a complex program?
funny coming from you, euler
Was calling a Turkish student "the young Turk" not weird in 2010? 😂
AI was a hot topic in the 1980's. I did neural nets and troubleshooting and configuration expert systems. Some of those programs scared people. Now it's hot again. I'm somewhat surprised that so little progress has been made. I ultimately came around to the view the AI should be used to augment humans, not replace them. Doctors should be open to programs that help them make accurate diagnoses so they can spend their time caring for the person. How will we program non-local consciousness?
***** What do you mean by "non-local consciousness"?
I wanna ask: Is this lecture for master or bachelor?
bachelors
18:00 33:00
I studied computer science but I never was a math guy. Can someone please explain me why this lectures of him matters for understanding ai?
AI is incredibly mathy as you go down this series, he makes several references to partial differentiations, Lagrange multipliers and similar that are required for the algorithms. Not to mention the. Point of most AI is to minimize or maximize some unknown measure, that always leads you to Calculus especially Multivariable calculus
Uhh...The program ??..
The amount of people who want to work with a machine that only thinks in number at an intimate level that do not like math is concerning and explanatory of why the field is oversaturated
I thought there's gonna be codes n stuffs 😅 but it's all Math, My worst enemy. 😢
I'm so lost
Thank you sir..