I'm still amazed that I get to sit in, for free, on this interesting class taught by someone who obviously knows the stuff cold AND is a good teacher. For this opportunity you used to have to apply and get admitted to college somewhere, and when you got there, maybe you would get a good teacher, and maybe not. Now, instead of all that hassle, I can just choose the best courses from anywhere in the world, without even having to get out of bed. That is stunning. Of course if I were a young person, it would be better all around for me to go to an actual college, and meet lots of students and teachers and make friends there. But I am not a young person anymore, and this is pretty much the best way for me to learn almost anything
+Ralph Dratman Dear Ralph, since you're a lifelong learner (which is super cool) you can also check out websites as Coursera, EdX, Udacity for free courses given by universities around the world. All the best !
+Ralph Dratman Just so you know; this video was recommended by my Mathematical Methods professor for homework. So you chose a good vid to watch and learn from.
For everyone complaining about the guy eating, it's super common to eat during lectures in grad school. Between going to lab, teaching, and your own coursework, you don't have much time especially if you work in a wet lab where it is a safety violation to eat while in lab. I have had days where I was doing an experiment from 7 am to 1 pm and had to go to class immediately after that without a break for lunch. Also, departments frequently hold seminars where they bring in high profile speakers from around the world, and to encourage attendance, they actually provide free lunch/dinner (typically pizza) or drinks (beer, wine, etc...). I have gone to lectures for the explicit reason of eating a free lunch that was provided there. It's so common that they some times call these "Lunch and Learns" or "Brown Bag Seminars". As long as you're being quiet and not eating some obnoxiously smelly food, literally no one cares.
I keep coming back to this lecture series in awe. There is simply nothing like it. I am binge watching it as if it were a netflix series, this is not a joke!
I now have to add Carl Bender to my list of Best Teachers Ever. The all have in common the obvious stuff -- totally grokking the subject, being able to explain it very clearly, completely understanding where a student's question is coming from and how to answer it, etc. But they also have something really special -- a great sense of humor. And I don't just mean telling jokes, which they all do with more or less success (sometimes less). I mean being greatly amused by, and making the students be greatly amused by, *the actual subject itself*! A sense of "Isn't this wonderful? Doesn't this make you practically laugh out loud by how wonderful it is?" P.S. I'm 73.
Having watched this lecture four or five times over the past few years (not always all the way through), I now enjoy watching it even more each successive time. Prof Bender has a pleasant impish quality that I like, and each time through I understand more of what he is doing. That is the kind of activity I call fun, but which most of the world would run away from, fast.
Prof. Bender is a star lecturer. A sheer pleasure listening to his way of teaching. Another excellent lecturer that I happened to come across while looking for some material for someone in my family is Denis Auroux when he was at MIT (MIT 18.02 Multivariable Calculus, Fall 2007).
THIS is what TH-cam was made for. Just looking at this fills my soul with joy and happiness, while it covertly fills my mind with knowledge and understanding.
That's just not the thing you do in the middle of a lecture. So many people want to stand out in so many ways, but this is plain unethical. I wouldn't want to sit next to him.
Excellent lecture focusing on Perturbation Theory and Asymptotic Methods. Much of the lecture may be supported with his now classic 1978 text Advanced Mathematical Methods for Scientists and Engineers. Prof. Bender is a master lecturer and explainer.
Because he didn't explain anything perhaps? He taught you how to compute and some bs about math that actively harms your notion of mathematical concepts. Funny thing, the computation methods he teaches is derived from "less powerful" rigorous math.
@@passerby4507 This video made it much easier for me to understand stuff about Perturbation Theory that I am currently studying in my own course. And I would say that "the ability to clarify a topic and make it easier to understand" is pretty much the definition of "explaining" something. By the way, are you very bitter about something? Because your post comes off as overly bitter, even if we take into account that you criticise this video.
@@Peter_1986 I have no idea, it's been two years. I do have a pet peeve against people teaching things that are so wrong that students get screwed over.
"But nevermind. That's just words." - ...and an attempt to draw parallels to something some students might recognize. For others it's something they need to hear. Beautifully done! :)
Thanks for pointing that out. I often read comments before I get far into a video, so I came back to this comment when I heard him say it.... Yes .. he's anchoring the concept for them. Outside of that, it's fairly meaningless, but within the scope of the classroom, it's powerful. He's a great teacher. I miss being in classrooms like this.
Thank you. This is an awesome series of lectures. I’m just jotting down a few notes here that I think are helpful. 17:43 The 𝜀^3 term should have an extra 10 a^3 from the 10 S^3 term. 23:17 The terms do not form a geometric progression. If they did, the solution would be rational - in this case, ⅘. He explains this later. 50:29 The symbol ≅ means “is isomorphic to” and is very precise. It does not mean “is approximately”.
I remember finding this in 2018 and just being awestruck. I'm glad to see this is gaining appreciation, if I remember correctly there were only 30k views or so in 2018.
Wonderful lecture series; high quality stuff, unhurried, with deep insights and perspective. Watching these videos is probably better than sitting in the classroom since the professor's writing turns into microfiche at times.
A small mathematical quibble. It's true from number theory that the general quintic can't be solved exactly by radicals. However, the particular example used in this lecture, X^5+X=1, _can_ be solved exactly. I can't figure out how to enter the exact solution here, but you can see it by going over to Wolfram Alpha and entering X^5+X=1.
Here I am a college dropout who lost the passion for learning in middle school watching advanced mathematics at 2:00 a.m. because I can't sleep and I do find this type of stuff generally interesting but I don't have the passion or the drive to really get into it
What i like about this lesson is that he explained very well how You start from what you know about the solutions to how the unperturbated problem can be solved..............., but making small corrections that approximate the effects of the perturbation under consideration......OMG>.i found this course truly inspiring...
For me this is a good class.. The basic concept of this idea is that, to make a complicated statements ("hard problems") in which it can exist in a "true" or "false" statements (i.e one or zero) isn't going to be easy. Its like, imagine on your right hand is the language spoken in between human beings in which we can understand each other well and execute the task given accordingly. For example, if you are reading this comment, and you have the consciousness and awareness that if i told you to get some drink you are able to take some drink that you like before asking me what drink that I like. On the other hand (which is in your left hand), lies the "hard problems" which is converting what is inside in your right hand (the language that human can understand) into only "one and zero information". Then, you move your left hand a bit to the right then, you get a statement like "yes or no" or "true or false". If then, you can think if true= 1; so 0 must be equals to false. Then you work your way from your left hand to the right hand until it maps. At least this is from my perception only.
Its like trying to teach a computer to do certain task in the form of "1 and 0s informations". For example, take the first example that i mentioned before , that if you want to teach the computer to take a drink, it wouldnt know how to execute it or do it. It will constantly ask you questions until it gets into one and zero information. This is called definition. Imagine if a computer exist as a human being , with eyes, hands and legs, but with the brain of a computer. So when you tell him to take the drink. Then you need to define to him what is "take" and what is "drink". Then you tell him take means move your hands towards something on the table which has a cylinder shape (presumably the drink is in the form of canned soda and it is the only drink that are available on the table). Then, the computer will keep asking questions, what is "hand" ? Then you can define it the way you want until you define it into numbers for example the coordinate of hand is (-5,4,0) based on (x,y,z) axis, in relative from your navel position. Then you define fingers, coordinates of it, etc,etc. Then, finally hopefully, when you want it to execute the action of taking the drink can on the table you can say something like your thumb x+3 , the other fingers x-5, or something like that. Every small definitions in the end will execute as a function the finger function and so on.
I am amazed, I just ran into this video by pure chance, I can’t believe Prof. Bender is still teaching at Wash U . I graduated as undergrad in 1985 and I was in his class! He looks good!What a brilliant mind....
This lecture is at the Perimeter Institute in Canada, not at your almamater Washington U. Bender used slides made for his courses at Washington U. pitp.ca/training/perimeter-scholars-international/lectures/2011/2012-psi-lectures I'm still not sure what Perimeter is about except that it's funded by Blackberry's founder. There's usually a -point- to privately funded research.
@@iroulis first of all thankyou so much for informing us about the name of the institute. can you please tell me how to find other parts of this series or other lectures by prof bender. I went to the site through the link provided by you but it showed page missing. Is there any other place where i can find these lectures??? THANKYOU SO MUCH IN ADVANCE.
I love his lessons sooo much! Clear, straightforward, no nonsense, interesting and engaging. But, there's an unsolved problem in this class.. Why is the hockey stick there!?
@@kingfrozen4257 They aren't working on string theory noob. Quantum mechanics is as real as it can get. Unless of course you want to say that physical evidence is bullshit. But yeah string theory and such are just fantasies of the physicists.
When I first watched this video, I thought this guy's name sounded familiar. It took me a bit to realize that he wrote a paper that I cited for my undergrad honors thesis. Small world.
I also had a mathematical physics teacher who used the word trivial a lot. What he meant was that the solution was already known, and could be looked up.
I am in covid19 quarantine, it's midnight, I was not looking for this topic and now I am enjoying this introduction to perturbation methods, and moreover, my mother tongue is Spanish.
H bar is not negligible as you and I know that h bar is equal to 1. Pure gold, one of the best jokes I have ever heard. Now to find someone to tell it too :(
Pan Raphael, you're very correct, I'm 12 and thus only have a brief introduction in calculus, and yet I was able to grasp and apply the material in this course. Honestly, I wished all classes could have teachers this devoted. I have been interested in mathematics since I was young, and it's classes like this that make me want to learn more, thank you.
Operators are at the heart of mathematical physics. Understand the actions and the inherent meanings of the operators and you’ll understand mathematical physics.
I downloaded them directly from the PSI webpage. To be honest, the resolution of these videos are far from being HD, which technically refer to no less than 720p, and which perhaps they could have provided. However, it would then take me too much time to upload them onto TH-cam, since each HD would be too large in size. So I guess these 360p lectures are just proper for web use.
Consider that gravity overall is a parabolic curve from lambda (cosmological constant, the lowest energy density apparently possible) to event horizon. This is the net universal flow. Neutron decay cosmology closes those points in the catastrophe of the event horizon. Neutrons which contact event horizon become the vacuum energy for one Planck second then reemerge in lowest energy density points of space, deep voids. There they decay into amorphous atomic hydrogen. This decay process includes a volume increase, energy density decrease, of 10^54 times. Expansion. Dark energy. Lambda. Fine tuning also since a gas fills available space. The universe has shock absorbers. LoL The decay product of neutrons is hydrogen. But initially it doesn't have stable orbital electron so can't emit our absorb photons. Dark matter. In time it stabilizes and followed usual evolution pathway from has to nebula to proto star to star until in distant future it is again at edge of event horizon. Event horizons act like energy pressure release valves. Venting energy pressure from highest energy density conditions to lowest.
I have had a long fascination with & personal mathematical struggle with the Lagrange Inversion Formula (LIF) and its numerous incarnations, combinatorial interpretations, generalizations to multiple variables & equations, since 1988. For one thing, the LIF gives one only ONE root of inverting y=g(x), where g(0)=0 and g'(0)!=0 to x=f(y) where f(0)=0. But, I want to find ALL the roots, which, in general, is countably infinitely many.
Nice idea with the unsolvable quintic, but that polynomial is not irreducible...the solution can be written as a combination of radicals - no need for perturbation, I can write down the exact solution.
i could hang with 80% of this, but was completely lost for the first 5 minutes of the 2nd lecture. What mathematics should I study in order to get up to speed for this?
he explained that at 14:20, the solution for the inperturbed problem is the first term of the series. That's the whole idea of the theory, you start with the unperturbed term a0 and add to it the infinite perturbations. did you understand?
i really dont know why im watching this. i dont understand a word and i have no interest in mathematics nor physics.. yet im here, watching... and commenting!
Actually its because maybe you find all of this mathematical brain talking and the chalk writing on the blackboards is satisfying, Knowledge is Our Treasure and we're an advanced species of the human race that feeds on Knowledge like this
Your perturbation series is correct and if the result is convergent.but in quantum mechanics if the series is divergent it can still be convergent for the epsilon has become a série of quantum epsilon variable with an sum gravitational constant index for a finite E solution convergence. Mr bender you are at least someone with an open mind in maths not the old school collar out of date. Why cause in quantum mechanics if the maths do not serve the right study phenomena you have to invent a new way to ascertain the end search results. Thank you with those new at least open end teachings.
tbh I do. When I studied chemistry there were days (especially fridays) where I had 8hours with out any kind of break to eat anything. Just enough to the next class. Friday was especially bad, however on Frida we had physics and our physics teacher would always be about five minutes late. and it was about 12:30 lunch time and right next to the room we had physics in (don´t know what university classrooms are called correctly in english, sorry) was a cafeteria where you could salads with plastic forks. Of course I bought a salad and there was no way, i could finish that before class started. I´d be crazy to not eat in class. I´m in university since 7:30 bolting from class to class. Haven´t eaten anything and i have to rush to the lab, where eating is absolutely prohibited right after? plus there is an opportunity to get something to eat next to the classroom. tell me yo uwould not get something to eat and just eat in class. and yes I ate directly in the front row too. Because I was paying attention. and it´s not hard to ask questions between bites. (that´s probably why the professor didn´t mind that. I still asked questions)
@Wemple this was a 7yr old comment, and no. They don't schedule classes at 12pm. Or qt least any colleges I know of, or if so it's out at 1pm... but whatever.
+Karl Davis He uses that example because it makes his explanations much easier to follow. It is a pretty bad idea to immediately start with sophisticated equations that "require" a new method, you should always use as simple examples as possible in the beginning (but still hard enough so that you can see what happens when you use the new method) so that the students get a chance to absorb the concepts that are actually important. The important thing in that first equation isn't "look how tricky and messy this is, we MUST use Perturbation Theory!", but rather "here is a simple equation that demonstrates how Perturbation Theory works".
Newton's method converges really quickly, but I totally understand Laurelindo's explanation that it's just an example. I guess perturbations aren't my thing, I had it in college and just couldn't connect to it. Other areas of math do work for me - 15% of my time at work is spent doing NP hard optimization with multiple weighted goals. I do love math overall, but like many people I like some areas much more than others.
MrDpsc How Mathematica works is a different story entirely. I am just showing that it is exactly solvable. If not to you then to people who might be interested.
I don’t think the part around 1:02 when he moved from f(x)+g(x)=h(x) (1) to analyzing the asymptotic behavior of ex^5+x=1 as e ->0 is very rigorous. If we take e -> 0 then we have to assume that ex^5 and x are functions of e. Thus, it seems that we need to fix x as constant so that ex^5 is only a function of e. But with each e in the real number, there’re only 5 x’s (precisely the roots of the eqn) that satisfying that ex^5+x=1. But a function must uniquely maps each e to one y=ex^5, so how do we choose the mapping between 5 possible choices for x’s?
Depends on the place, my friend and I used to eat dinner in our real analysis class. It was okay because we didn't leave a mess and the professor knew we were up-to-date. I would say it usually depends on the professor. Even if you're *not supposed to* eat in a facility, most don't care as long as you aren't a distraction. Just my experience with food in class :P Note: There's a dude with a laptop out, too. That's arguably more egregious, since it's a distraction.
These are really excellent. Bender's an incredible communicator. Also, I'm really interested in this material. What are some books in which I can read more about this stuff?
+Ryan Tamburrino Mathematical Methods for Physics and Engineering by Riley and there's a student solutions manual that you can get a long with it which is pretty cool. That's what I got because of the solutions manual. The more popular book based on the reviews I read on Amazon was Mathematical Methods in the Physical Sciences by Boas.
Mathematical Methods in the Physical Sciences by Boas has been my go-to book for my course, you can get the economic version on Amazon for about $25 usd. Another great one, really, is Mathematical Methods for Physicists, by Arfken.
There is a book authored by Bender and Orszag called Advanced Mathematical Methods for Scientists and Engineers. You can take a look at it if you are still interested in the material. www.amazon.com/Advanced-Mathematical-Methods-Scientists-Engineers/dp/0387989315
Mathematical physics. Existence is mental and mathematical Existence is both mental and mathematical. In platonic physics, the mental is the domain of causal sets. One aspect of Leibniz's Principle of Sufficient Reason that once puzzled me is that according to the principle, things are as they are only because of a sufficient reason. This caused me to ask, "But isn't a Cause Agent required to bring things about ?" Now, I see that a separate Cause Agent is not required, or that Mind itself (the One) is its own cause agent (is self-causing), following a) Having discovered causal set theory en.wikipedia.org/wiki/Causal_sets now used as the basis of a new theory of gravity. b) Having discovered a suggestion that a set owns or "controls" its objects, c) That in Plato-Leibniz, causation is mental , topdown from Plato's One (Mind) d) That there is no separate Cause Agent in Leibniz, not even God, a belief which is backed by Leibniz's denial of God's intervening in the operations of the universe (denying interventionism). e) That the mental, being subjective, in a sense implies that the mental, being First Person Singular, is its own Cause Agent. It is self-causing amd self-organizing. f) Having found that causal set theory, being set theory, has discrete objects as its subjects. This agrees with my discovery that since Plato's One or Mind is timeless and spaceless, time and space and the objects therein must be discrete points (mathematical points). This agrees with the account of causal sets given in en.wikipedia.org/wiki/Causal_sets "The causal sets programme is an approach to quantum gravity. Its founding principle is that spacetime is fundamentally discrete and that the spacetime events are related by a partial order. This partial order has the physical meaning of the causality relations between spacetime events. The programme is based on a theorem[1] by David Malament that states that if there is a bijective map between two past and future distinguishing spacetimes that preserves their causal structure then the map is a conformal isomorphism. The conformal factor that is left undetermined is related to the volume of regions in the spacetime. This volume factor can be recovered by specifying a volume element for each spacetime point. The volume of a spacetime region could then be found by counting the number of points in that region. Causal sets was initiated by Rafael Sorkin who continues to be the main proponent of the programme. He has coined the slogan "Order + Number = Geometry" to characterise the above argument. The programme provides a theory in which spacetime is fundamentally discrete while retaining local Lorentz invariance." Dr. Roger B Clough NIST (retired, 2000). See my Leibniz site: rclough@verizon.academia.edu/RogerClough For personal messages use rclough@verizon.net
Looks like a great lecture. Maybe there is a cultural difference, but here this would be called 'mathematical physics' more like 'mathematical methods of physics'. Mathematical physics is more concerned with proofs (like math). I mean look at the books eg by Thirring.
..his attitude of teaching techniques in educational psychology point of view seems like he is eagerly intends to make the matter harder than it is, and asks questions in exams that he didn't cover in class, at all
@@znero6975 ...."ship motions" is a challenging subject and people likes the class and lecturing professors regardless of its complex exam questions..... as.a conclusion, i do not have the satisfying answer for your question.
I'm still amazed that I get to sit in, for free, on this interesting class taught by someone who obviously knows the stuff cold AND is a good teacher. For this opportunity you used to have to apply and get admitted to college somewhere, and when you got there, maybe you would get a good teacher, and maybe not. Now, instead of all that hassle, I can just choose the best courses from anywhere in the world, without even having to get out of bed. That is stunning. Of course if I were a young person, it would be better all around for me to go to an actual college, and meet lots of students and teachers and make friends there. But I am not a young person anymore, and this is pretty much the best way for me to learn almost anything
Happy for you. Wish you luck. It's nice to see people like you. Many people don't wanna learn anymore especially at your age. Keep it up.
+Ralph Dratman Dear Ralph, since you're a lifelong learner (which is super cool) you can also check out websites as Coursera, EdX, Udacity for free courses given by universities around the world. All the best !
+Vault Von Wow. Are you sure that many people his age don't wanna learn any more? Are you sure that many people your age do?
+Ralph Dratman Just so you know; this video was recommended by my Mathematical Methods professor for homework. So you chose a good vid to watch and learn from.
i really feal the same and i am young , this is one of the few reasons i love modern world and technology
For everyone complaining about the guy eating, it's super common to eat during lectures in grad school. Between going to lab, teaching, and your own coursework, you don't have much time especially if you work in a wet lab where it is a safety violation to eat while in lab. I have had days where I was doing an experiment from 7 am to 1 pm and had to go to class immediately after that without a break for lunch. Also, departments frequently hold seminars where they bring in high profile speakers from around the world, and to encourage attendance, they actually provide free lunch/dinner (typically pizza) or drinks (beer, wine, etc...). I have gone to lectures for the explicit reason of eating a free lunch that was provided there. It's so common that they some times call these "Lunch and Learns" or "Brown Bag Seminars". As long as you're being quiet and not eating some obnoxiously smelly food, literally no one cares.
Still rubbish behaviour. Very disrespectful
@@matteogirelli1023 you know nothing
I keep coming back to this lecture series in awe. There is simply nothing like it. I am binge watching it as if it were a netflix series, this is not a joke!
I now have to add Carl Bender to my list of Best Teachers Ever. The all have in common the obvious stuff -- totally grokking the subject, being able to explain it very clearly, completely understanding where a student's question is coming from and how to answer it, etc. But they also have something really special -- a great sense of humor. And I don't just mean telling jokes, which they all do with more or less success (sometimes less). I mean being greatly amused by, and making the students be greatly amused by, *the actual subject itself*! A sense of "Isn't this wonderful? Doesn't this make you practically laugh out loud by how wonderful it is?"
P.S. I'm 73.
Having watched this lecture four or five times over the past few years (not always all the way through), I now enjoy watching it even more each successive time. Prof Bender has a pleasant impish quality that I like, and each time through I understand more of what he is doing. That is the kind of activity I call fun, but which most of the world would run away from, fast.
It’s cool to see you coming back to it, after ur initial comment u left 6 years ago!
Prof. Bender is a star lecturer. A sheer pleasure listening to his way of teaching.
Another excellent lecturer that I happened to come across while looking for some material for someone in my family is Denis Auroux when he was at MIT (MIT 18.02 Multivariable Calculus, Fall 2007).
Fine. Hope you like them. And please let me know if you happen to find the same series with better resolution or quality. Cheers.
Fine what? Who are you responding to?
@@zada4a 8 years ago, youtube comment section worked differently.
THIS is what TH-cam was made for. Just looking at this fills my soul with joy and happiness, while it covertly fills my mind with knowledge and understanding.
Wow, a really gifted teacher, for the first time I really understand perturbation theory.
Right on Professor!
1:24 This man is eating a fine course meal
Wtf
lol wtf
what he doin ????
bro? xd just noticed
That's just not the thing you do in the middle of a lecture. So many people want to stand out in so many ways, but this is plain unethical. I wouldn't want to sit next to him.
Excellent lecture focusing on Perturbation Theory and Asymptotic Methods. Much of the lecture may be supported with his now classic 1978 text Advanced Mathematical Methods for Scientists and Engineers. Prof. Bender is a master lecturer and explainer.
DUDE.. is that a guy eating with a KNIFE and FORK in the front row? WHAT?
MoTheDeliciousPeach Communist with knife and fork meets capitalist with steak and kidney pudding.
ahahhahahahahahahhahhahahahhahhahahaahahaahahahahha )))
MoTheDeliciousPeach he was eating the lesson. an easier way to get the material inside
eating the lesson is absorption of the information is what I mean
MoTheDeliciousPeach
I think this is in Canada.
Ahh, the man himself! When I was young, the "Bender and Orszag" book gave me many hours of both pleasure and frustration.
K Dub a sexual ideal
(One of) his is grad student(s), William Paulsen, also went on to write a fantabulous book on Asymptotic and Perturbative Analysis.
mathematician: enter the video
mathematician two seconds later: leaves immediately
@Call me Joe It was actually a great lecture
The sad part of the intro was that power expansions *are* a numerical technique.
@@Wtahc no, because Mathematician aren't interested in non rigourous theories
@@armycin aka, ya'll nerds
@@Wtahc I would add that at least physicists comprehend what they study
I love his sense of humour. It makes the lecture much easier to digest.
It's been about 10 years since the last time I saw someone explain such a deep concept with such simplicity and elegance.
Because he didn't explain anything perhaps? He taught you how to compute and some bs about math that actively harms your notion of mathematical concepts. Funny thing, the computation methods he teaches is derived from "less powerful" rigorous math.
@@passerby4507 This video made it much easier for me to understand stuff about Perturbation Theory that I am currently studying in my own course.
And I would say that "the ability to clarify a topic and make it easier to understand" is pretty much the definition of "explaining" something.
By the way, are you very bitter about something?
Because your post comes off as overly bitter, even if we take into account that you criticise this video.
@@Peter_1986 I have no idea, it's been two years. I do have a pet peeve against people teaching things that are so wrong that students get screwed over.
I like this guy's teaching approach. It is a very natural and reveals a free thinking attitude. This is contagious !
"But nevermind. That's just words." - ...and an attempt to draw parallels to something some students might recognize. For others it's something they need to hear. Beautifully done! :)
Thanks for pointing that out. I often read comments before I get far into a video, so I came back to this comment when I heard him say it.... Yes .. he's anchoring the concept for them. Outside of that, it's fairly meaningless, but within the scope of the classroom, it's powerful. He's a great teacher. I miss being in classrooms like this.
Thank you. This is an awesome series of lectures.
I’m just jotting down a few notes here that I think are helpful.
17:43 The 𝜀^3 term should have an extra 10 a^3 from the 10 S^3 term.
23:17 The terms do not form a geometric progression. If they did, the solution would be rational - in this case, ⅘. He explains this later.
50:29 The symbol ≅ means “is isomorphic to” and is very precise. It does not mean “is approximately”.
"It does not mean “is approximately”."
I have been in courses where the lecturer used it to mean the above.
I remember finding this in 2018 and just being awestruck. I'm glad to see this is gaining appreciation, if I remember correctly there were only 30k views or so in 2018.
1:22 is that guy eating dinner from a plate with a fork and a knife? What a legend.
I love this man, he makes everyone be addicted to the subject, can't stop watching these lectures!
Wonderful lecture series; high quality stuff, unhurried, with deep insights and perspective. Watching these videos is probably better than sitting in the classroom since the professor's writing turns into microfiche at times.
LOL the hockey stick for pointing on the slides board.
1:23 my man having his breakfast in the class wtf
LOOOOOOOOOOOL
OMG, that kinda cracked me up tho but wtf
WTF
He's "digesting" the knowledge...
A small mathematical quibble. It's true from number theory that the general quintic can't be solved exactly by radicals. However, the particular example used in this lecture, X^5+X=1, _can_ be solved exactly. I can't figure out how to enter the exact solution here, but you can see it by going over to Wolfram Alpha and entering X^5+X=1.
Here I am a college dropout who lost the passion for learning in middle school watching advanced mathematics at 2:00 a.m. because I can't sleep and I do find this type of stuff generally interesting but I don't have the passion or the drive to really get into it
What i like about this lesson is that he explained very well how You start from what you know about the solutions to how the unperturbated problem can be solved..............., but making small corrections that approximate the effects of the perturbation under consideration......OMG>.i found this course truly inspiring...
For me this is a good class..
The basic concept of this idea is that, to make a complicated statements ("hard problems") in which it can exist in a "true" or "false"
statements (i.e one or zero) isn't going to be easy.
Its like, imagine on your right hand is the language spoken in between human beings in which we can understand each other well and execute the task given accordingly. For example, if you are reading this comment, and you have the consciousness and awareness that if i told you to get some drink you are able to take some drink that you like before asking me what drink that
I like. On the other hand (which is in your left hand), lies the "hard problems" which is converting what is inside in your right hand (the language that human can understand) into only "one and zero information". Then, you move your left hand a bit to the right then, you get a statement like "yes or no" or "true or false". If then, you can think if true= 1; so 0 must be equals to false.
Then you work your way from your left hand to the right hand until it maps.
At least this is from my perception only.
Its like trying to teach a computer to do certain task in the form of "1 and 0s informations". For example, take the first example that i mentioned before , that if you want to teach the computer to take a drink, it wouldnt know how to execute it or do it. It will constantly ask you questions until it gets into one and zero information. This is called definition. Imagine if a computer exist as a human being , with eyes, hands and legs, but with the brain of a computer. So when you tell him to take the drink. Then you need to define to him what is "take" and what is "drink".
Then you tell him take means move your hands towards something on the table which has a cylinder shape (presumably the drink is in the form of canned soda and it is the only drink that are available on the table). Then, the computer will keep asking questions, what is "hand" ? Then you can define it the way you want until you define it into numbers for example the coordinate of hand is (-5,4,0) based on (x,y,z) axis, in relative from your navel position. Then you define fingers, coordinates of it, etc,etc. Then, finally hopefully, when you want it to execute the action of taking the drink can on the table you can say something like your thumb x+3 , the other fingers x-5, or something like that. Every small definitions in the end will execute as a function the finger function and so on.
I am amazed, I just ran into this video by pure chance, I can’t believe Prof. Bender is still teaching at Wash U . I graduated as undergrad in 1985 and I was in his class! He looks good!What a brilliant mind....
This lecture is at the Perimeter Institute in Canada, not at your almamater Washington U. Bender used slides made for his courses at Washington U.
pitp.ca/training/perimeter-scholars-international/lectures/2011/2012-psi-lectures
I'm still not sure what Perimeter is about except that it's funded by Blackberry's founder. There's usually a -point- to privately funded research.
@@iroulis first of all thankyou so much for informing us about the name of the institute. can you please tell me how to find other parts of this series or other lectures by prof bender. I went to the site through the link provided by you but it showed page missing. Is there any other place where i can find these lectures??? THANKYOU SO MUCH IN ADVANCE.
@@sharatpandey8067 This video is part of a Series: th-cam.com/play/PLOFVFbzrQ49TNlDOxxCAjC7kbnorAR1MU.html
@@iroulis thankyou so much again for the reply. Can I find other lectures by prof bender anywhere??
@@sharatpandey8067 Wow. You're done with that 25 hr lecture series already?
This guy made the subject matter very palatable.
18:58 “You can do this in Jr. High School, this is not hard.”
_takes one look at board in deep confusion_
Carl Bender is a good lecturer, and explains the concepts and methodology of perturbation theory exceedingly well.
I love his lessons sooo much! Clear, straightforward, no nonsense, interesting and engaging. But, there's an unsolved problem in this class.. Why is the hockey stick there!?
I'm not that interested in math (never have been), but I found this lecture fascinating, i couldn't stop watching it hah.
Cuz its not math its bullshit
@@kingfrozen4257 true, hate all this like comments
Cool do something with it
@@kingfrozen4257 how so?
@@kingfrozen4257 They aren't working on string theory noob. Quantum mechanics is as real as it can get. Unless of course you want to say that physical evidence is bullshit. But yeah string theory and such are just fantasies of the physicists.
When I first watched this video, I thought this guy's name sounded familiar. It took me a bit to realize that he wrote a paper that I cited for my undergrad honors thesis. Small world.
I also had a mathematical physics teacher who used the word trivial a lot. What he meant was that the solution was already known, and could be looked up.
Being rigorous is not about being powerful or not, it’s about being right. Hand waving is useful for starting out but won’t get you far.
I can't believe that they still teach it like this. I watched a documentary online about this. Totally disproves it all. So crazy!!!
please name that documentary.
27:52 The exact answer is calculated by the computer using Numerical Methods: Sausage.
I am in covid19 quarantine, it's midnight, I was not looking for this topic and now I am enjoying this introduction to perturbation methods, and moreover, my mother tongue is Spanish.
H bar is not negligible as you and I know that h bar is equal to 1. Pure gold, one of the best jokes I have ever heard. Now to find someone to tell it too :(
i loved when he said, its like sausage you never trust until you know what they go through lol
Ya
Thank you for posting these. They're amazing lectures.
Pan Raphael, you're very correct, I'm 12 and thus only have a brief introduction in calculus, and yet I was able to grasp and apply the material in this course. Honestly, I wished all classes could have teachers this devoted. I have been interested in mathematics since I was young, and it's classes like this that make me want to learn more, thank you.
Operators are at the heart of mathematical physics. Understand the actions and the inherent meanings of the operators and you’ll understand mathematical physics.
amazing professor....loved the way he teaches and makes us understand the whole in a very simple way....truly awesome
Thankyou Mr bender a great series of lectures.
what a good teacher to make it easy to understand for a lay person!
I really did a good job teaching math. If the students have learned with the teacher, they will understand the offer.
I downloaded them directly from the PSI webpage. To be honest, the resolution of these videos are far from being HD, which technically refer to no less than 720p, and which perhaps they could have provided. However, it would then take me too much time to upload them onto TH-cam, since each HD would be too large in size. So I guess these 360p lectures are just proper for web use.
can you please provide the link to the site or at least some other lead??? thank you so much
Words fail me to express how wonderful this is. Thank you Carl Bender!
Wow, wish I had found this guy's lectures years ago.
17:49 the ε cubed term is not complete (correct). It lacks 10*s^3 part, which turns out to be 10a^3ε^3, thus:
...+ε^3(5c+20ab+10a^3)+...
Without the 10a^3, c wouldn't be -1/125. The prof probably already knew the answer
Consider that gravity overall is a parabolic curve from lambda (cosmological constant, the lowest energy density apparently possible) to event horizon. This is the net universal flow.
Neutron decay cosmology closes those points in the catastrophe of the event horizon.
Neutrons which contact event horizon become the vacuum energy for one Planck second then reemerge in lowest energy density points of space, deep voids. There they decay into amorphous atomic hydrogen. This decay process includes a volume increase, energy density decrease, of 10^54 times. Expansion. Dark energy. Lambda. Fine tuning also since a gas fills available space. The universe has shock absorbers. LoL
The decay product of neutrons is hydrogen. But initially it doesn't have stable orbital electron so can't emit our absorb photons. Dark matter.
In time it stabilizes and followed usual evolution pathway from has to nebula to proto star to star until in distant future it is again at edge of event horizon.
Event horizons act like energy pressure release valves. Venting energy pressure from highest energy density conditions to lowest.
Each coefficient of epsilon goes to zero because epsilon, epsilon^2... are linearly independent.
+AnkhArcRod This is more important a point than was made in the lecture. Good catch.
Amazing. Thank you Professor Bender. You are an incredibly awesome teacher.
his remarks re: divergent series are reminiscent of Oliver Heaviside's comments"aha! the series diverges! now we can do something useful with it!
I have had a long fascination with & personal mathematical struggle with the Lagrange Inversion Formula (LIF) and its numerous incarnations, combinatorial interpretations, generalizations to multiple variables & equations, since 1988.
For one thing, the LIF gives one only ONE root of inverting y=g(x), where g(0)=0 and g'(0)!=0 to x=f(y) where f(0)=0.
But, I want to find ALL the roots, which, in general, is countably infinitely many.
brilliant lecturer explaining perturbation theory as simple as teaching high school algebra
He did the 0.755 = 1 engineering thing
When I saw the thumbnail, I thought he was smoking in class😂
lol same
Lol
Lol 😂
This is a gem of a course..thanks a ton for making it available!
Nice idea with the unsolvable quintic, but that polynomial is not irreducible...the solution can be written as a combination of radicals - no need for perturbation, I can write down the exact solution.
he got me so pumped with that pade summation! can't wait to get there
You need the 10s^3 term as well in the expansion of (1+S)^5 in order to get 10a^3e^3
Is the camera guy eating chips or something? Christ.
i could hang with 80% of this, but was completely lost for the first 5 minutes of the 2nd lecture. What mathematics should I study in order to get up to speed for this?
Ok, I studied with this video. Now I am going to watch best Benteke's goals...
he explained that at 14:20, the solution for the inperturbed problem is the first term of the series.
That's the whole idea of the theory, you start with the unperturbed term a0 and add to it the infinite perturbations.
did you understand?
Very knowledgeable lecture for me👍🏻👍🏻🙏🏻🙏🏻🙏🏻
i really dont know why im watching this. i dont understand a word and i have no interest in mathematics nor physics.. yet im here, watching... and commenting!
I also don't know why I am here. It's destiny.
Destiny? She broke my heart once, 3 years ago, i still havent got over it :(
Trip Tamine It's been 6 years now, are you over it yet?
Actually its because maybe you find all of this mathematical brain talking and the chalk writing on the blackboards is satisfying, Knowledge is Our Treasure and we're an advanced species of the human race that feeds on Knowledge like this
Your perturbation series is correct and if the result is convergent.but in quantum mechanics if the series is divergent it can still be convergent for the epsilon has become a série of quantum epsilon variable with an sum gravitational constant index for a finite E solution convergence. Mr bender you are at least someone with an open mind in maths not the old school collar out of date. Why cause in quantum mechanics if the maths do not serve the right study phenomena you have to invent a new way to ascertain the end search results. Thank you with those new at least open end teachings.
crunch munch munch munch .... cruuuuunch munch munch munch... never understood eating in class...
😂😂
tbh I do. When I studied chemistry there were days (especially fridays) where I had 8hours with out any kind of break to eat anything. Just enough to the next class. Friday was especially bad, however on Frida we had physics and our physics teacher would always be about five minutes late. and it was about 12:30 lunch time and right next to the room we had physics in (don´t know what university classrooms are called correctly in english, sorry) was a cafeteria where you could salads with plastic forks. Of course I bought a salad and there was no way, i could finish that before class started. I´d be crazy to not eat in class. I´m in university since 7:30 bolting from class to class. Haven´t eaten anything and i have to rush to the lab, where eating is absolutely prohibited right after? plus there is an opportunity to get something to eat next to the classroom. tell me yo uwould not get something to eat and just eat in class. and yes I ate directly in the front row too. Because I was paying attention. and it´s not hard to ask questions between bites. (that´s probably why the professor didn´t mind that. I still asked questions)
it combines two most basic human hungers - for food and knowledge
@Wemple this was a 7yr old comment, and no. They don't schedule classes at 12pm. Or qt least any colleges I know of, or if so it's out at 1pm... but whatever.
what do i missed in my education, as we got a second-rated Prof. who was not interested to teach, we all passed, without learning anything
Faced with x^5+x=1, I would use Newton's method.
+Karl Davis
He uses that example because it makes his explanations much easier to follow.
It is a pretty bad idea to immediately start with sophisticated equations that "require" a new method, you should always use as simple examples as possible in the beginning (but still hard enough so that you can see what happens when you use the new method) so that the students get a chance to absorb the concepts that are actually important.
The important thing in that first equation isn't "look how tricky and messy this is, we MUST use Perturbation Theory!", but rather "here is a simple equation that demonstrates how Perturbation Theory works".
+Karl Davis Yes, that occured to me as well. When I tried it by hand, it was closer to the answer than the perturbation based result.
Newton's method converges really quickly, but I totally understand Laurelindo's explanation that it's just an example. I guess perturbations aren't my thing, I had it in college and just couldn't connect to it. Other areas of math do work for me - 15% of my time at work is spent doing NP hard optimization with multiple weighted goals. I do love math overall, but like many people I like some areas much more than others.
+Karl Davis Pretty much all of applied physics involves doing some perturbations.
Oh my god, I learned some new mathematics.
the perfect white noise for sleep
Whenever I watch these videos I just think traditional mathematics is a primitive form of code.
that's a kickass pointer, eh?
If you use Mathematica to solve x^5 + x = 1, you will get the exact answer as one of the five roots. the other roots are all complex number.
ah, but do you? how do you know it's exact and not numerical?
MrDpsc
-1+x+x^5 is a quintic in Bring-Jerrard form and is solvable exactly by radicals: (1-x+x^2) (-1+x^2+x^3)
Agustinus Law I'm pretty sure that's not how mathematica got it's result
Agustinus Law , exactly! Thanks for the comment.
MrDpsc How Mathematica works is a different story entirely. I am just showing that it is exactly solvable. If not to you then to people who might be interested.
I don’t think the part around 1:02 when he moved from f(x)+g(x)=h(x) (1) to analyzing the asymptotic behavior of ex^5+x=1 as e ->0 is very rigorous. If we take e -> 0 then we have to assume that ex^5 and x are functions of e. Thus, it seems that we need to fix x as constant so that ex^5 is only a function of e. But with each e in the real number, there’re only 5 x’s (precisely the roots of the eqn) that satisfying that ex^5+x=1. But a function must uniquely maps each e to one y=ex^5, so how do we choose the mapping between 5 possible choices for x’s?
This is so cool! Easy to follow, and very powerful techniques!
Depends on the place, my friend and I used to eat dinner in our real analysis class. It was okay because we didn't leave a mess and the professor knew we were up-to-date.
I would say it usually depends on the professor. Even if you're *not supposed to* eat in a facility, most don't care as long as you aren't a distraction.
Just my experience with food in class :P
Note: There's a dude with a laptop out, too. That's arguably more egregious, since it's a distraction.
Amazing teacher!
These are really excellent. Bender's an incredible communicator. Also, I'm really interested in this material. What are some books in which I can read more about this stuff?
+Ryan Tamburrino Mathematical Methods for Physics and Engineering by Riley and there's a student solutions manual that you can get a long with it which is pretty cool. That's what I got because of the solutions manual. The more popular book based on the reviews I read on Amazon was Mathematical Methods in the Physical Sciences by Boas.
+Michael Sayad Thanks man!
Mathematical Methods in the Physical Sciences by Boas has been my go-to book for my course, you can get the economic version on Amazon for about $25 usd.
Another great one, really, is Mathematical Methods for Physicists, by Arfken.
There is a book authored by Bender and Orszag called Advanced Mathematical Methods for Scientists and Engineers. You can take a look at it if you are still interested in the material.
www.amazon.com/Advanced-Mathematical-Methods-Scientists-Engineers/dp/0387989315
Very successful. I felt like appluading several times.
Mathematical physics. Existence is mental and mathematical
Existence is both mental and mathematical. In platonic physics, the mental is the domain of causal sets.
One aspect of Leibniz's Principle of Sufficient Reason that once puzzled me is that according to the principle, things are as they are only because of a sufficient reason. This caused me to ask, "But isn't a Cause Agent required to bring things about ?"
Now, I see that a separate Cause Agent is not required, or that Mind itself (the One) is its own cause agent (is self-causing), following
a) Having discovered causal set theory en.wikipedia.org/wiki/Causal_sets now used as the basis of a new theory of gravity.
b) Having discovered a suggestion that a set owns or "controls" its objects,
c) That in Plato-Leibniz, causation is mental , topdown from Plato's One (Mind)
d) That there is no separate Cause Agent in Leibniz, not even God, a belief which is backed by Leibniz's denial of God's intervening in the operations of the universe (denying interventionism).
e) That the mental, being subjective, in a sense implies that the mental, being First Person Singular,
is its own Cause Agent. It is self-causing amd self-organizing.
f) Having found that causal set theory, being set theory, has discrete objects as its subjects. This agrees with my discovery that since Plato's One or Mind is timeless and spaceless, time and space and the objects therein must be discrete points (mathematical points).
This agrees with the account of causal sets given in
en.wikipedia.org/wiki/Causal_sets
"The causal sets programme is an approach to quantum gravity. Its founding principle is that
spacetime is fundamentally discrete and that the spacetime events are related by a partial order.
This partial order has the physical meaning of the causality relations between spacetime events.
The programme is based on a theorem[1] by David Malament that states that if there is a bijective
map between two past and future distinguishing spacetimes that preserves their causal structure
then the map is a conformal isomorphism. The conformal factor that is left undetermined is related to the volume of regions in the spacetime. This volume factor can be recovered by specifying a volume element for each spacetime point. The volume of a spacetime region could then be found by counting the number of points in that region.
Causal sets was initiated by Rafael Sorkin who continues to be the main proponent of the programme.
He has coined the slogan "Order + Number = Geometry" to characterise the above argument. The
programme provides a theory in which spacetime is fundamentally discrete while retaining local
Lorentz invariance."
Dr. Roger B Clough NIST (retired, 2000).
See my Leibniz site: rclough@verizon.academia.edu/RogerClough
For personal messages use rclough@verizon.net
Looks like a great lecture. Maybe there is a cultural difference, but here this would be called 'mathematical physics' more like 'mathematical methods of physics'. Mathematical physics is more concerned with proofs (like math). I mean look at the books eg by Thirring.
Awesome, I've been looking for a lecture like this on youtube for awhile now.
I remember math. Just for a while while I’m trying on break.
Add up the series, make your calculation. Simple. Thanks for the upload, Zicheng!
This is good to learn... I want to learn more..
I like it..
x^3 is ~ to x^2 as x approaches 1
Great teacher....and notice, no notes in his hands. Wow...
Absolutely outstanding lecture.
Interesting the Prof is Left Handed
Five roots! Forget not the missing four roots, because they are, in fact, not missing at all.
Wow, I took his course! And his exams are super hard... Many students only got 0 in the midterm...
At Berkeley Physics, 10 out of 100 was a "A".
..his attitude of teaching techniques in educational psychology point of view seems like he is eagerly intends to make the matter harder than it is, and asks questions in exams that he didn't cover in class, at all
@@aliyardimoglu5629 Then why he still attracted so many students including a lot of undergrads? And many still liked his course.
@@znero6975 ...."ship motions" is a challenging subject and people likes the class and lecturing professors regardless of its complex exam questions..... as.a conclusion, i do not have the satisfying answer for your question.
Im so lucky to have found this wow!
Well, Hi there!