As a physics graduate student, I have benefited immensely from your excellent lectures and I thank you for uploading them. I am curious as to whether you will be delivering lectures on Conformal Field Theory and/or related topics sometime in the future?
That banging on the desk at the end seemed like the analogue of applause for education. What a wonderful teacher. The world is a better place because of you, we all thank you!
Side note this really needs to catch on in America, teachers are treated worthlessly 90% of the time, when they’re dedicating their time to helping the yputh
I think that greatest book on theoretical Mechanics (going deeply in its mathematical structure) is "Foundations of Mechanics" (Abraham, Marsden), but I understand this choise could be bad for a beginner, can be attracted and not get out of it . A light but dense book is "Géométrie différentielle et mécanique analytique" (Godbillon)
You don't need item (iii) at 49:00. It is optional. It makes the structure easier to use. But it makes it a tiny little bit harder to construct differentiable structures because you keep demonstrating the unnecessary item (iii). If you don't use it anywhere, you don't even need to write it on the definition. Thank you for the great lecture!
keeping a simple example in mind is good advice. it's easy to get lost in abstractions and terminology, but relating back to simple examples grounds you
Is this course a prerequisite for some other courses in physics/mathematics? Any example of such other course? For example, will this be needed in string theory/symplectic field theory?
This course is not a prerequisite for anything in physics. But I do cover such things as complex manifolds which can be very helpful in some parts of string theory. Sincerely, Tobias
hello prof, At 32:40 you mentioned U as connected. So U is connected with subspace topology. since U is arbitrary for each point i.e., the definition doesn't involve specific U, this can be stated as every point p in M has a neighborhood U which is connected. Is there any theorem that states If for every point p in M has U that is connected with subspace topology then M is connected with usual topology? Is this true or false? If true then M is Hausdorff connected. If false please provide a counter example or simply say why its not true.
Many thanks for your comment. Sadly I won't be able to teach anything about Calabi-Yau manifolds: this is just a bit too far away from my area of expertise (quantum information theory). Sincerely, Tobias Osborne
For people seeing this in the future: this is almost right, but it’s not that the number of open sets is countable but that we have a countable *basis* of open sets. A basis means every other open set can be written as a union of the ones in the basis (not uniquely). Equivalently, for any open U and a p in U, there’s an element of the basis V with p in V and V in U.
I hope that this excellent -- and important -- series of talks will be remade for the Internet. A few dozen people in the classroom may enjoy the medieval trappings of seeing the back of the fine teacher's head as he writes on the greenboard, but for the huge majority of us over time who will be seeing this electronically, more modern ways of presenting written material have been invented. The "canonical material" might be expanded beyond the written material on the boards. As the lecturer mentions, small parts of large expensive books are relevant to his aims. Perhaps these could be extracted and condensed? This might be a good place to re-publish is own doctoral work, perhaps? The lecturer himself will no doubt have more and better ideas about how his material can be presented electronically, just as he has shown himself capable of acting out the format of the Thomistic scholarly classroom -- itself a technological advance over the olde Greeks sitting around drawing in the sand.
Can someone explain why these videos are so huge? I tried to download one for offline viewing and it is already 5Gig and growing. Something must be wrong.
Dear Robert, The video is recorded at 4k, and the file I upload to youtube is about 20GB. RUclips then transcodes it to all the lower resolutions. Which version are you downloading? If it is 1080p then the file will still be large, e.g., somewhere around several GB (assuming a bitrate of 8Mbps). If it is 720p it should be more manageable. Another problem is that the video is so long and even low bitrates, e.g., 1Mbps, mean that a video which is 1.5 hours long already needs approx 0.5 GB. I hope that helps. Best wishes! Sincerely, Tobias
@@tobiasjosborne : In fact, a good reason to assume the space is second countable is that you don't want an n-dimensional space mapped onto (surjection) an (n+1)-dimensional space. I hope I can make it to the end of the course. Mathematicians should try to interact more with physicists. :-)
Here a supplement of this course : www.worldcat.org/title/structure-of-dynamical-systems-structure-des-systemes-dynamiques-a-symplectic-view-of-physics/oclc/909302372?referer=di&ht=edition
You da man, Tobias. You are the Samuel L Jackson of theoretical physics
The most impressive thing about this lecture is how fast those blackboards dry and how clean they are.
under the category of "oddly satisfying".
ruclips.net/video/XQIbn27dOjE/видео.html 💐
ASMR when he erases the board and symplectic geometry all in one place. Excellent service 10/10
As a physics graduate student, I have benefited immensely from your excellent lectures and I thank you for uploading them. I am curious as to whether you will be delivering lectures on Conformal Field Theory and/or related topics sometime in the future?
That banging on the desk at the end seemed like the analogue of applause for education. What a wonderful teacher. The world is a better place because of you, we all thank you!
Side note this really needs to catch on in America, teachers are treated worthlessly 90% of the time, when they’re dedicating their time to helping the yputh
It's a university thing. It is not done in schools. O don't know the reason for it just that this is what we do
I think that greatest book on theoretical Mechanics (going deeply in its mathematical structure) is "Foundations of Mechanics" (Abraham, Marsden), but I understand this choise could be bad for a beginner, can be attracted and not get out of it .
A light but dense book is "Géométrie différentielle et mécanique analytique" (Godbillon)
Tobias, thank you for taking the time to reply to my query below. I am looking forward to viewing your videos and learning from them.
You don't need item (iii) at 49:00. It is optional. It makes the structure easier to use. But it makes it a tiny little bit harder to construct differentiable structures because you keep demonstrating the unnecessary item (iii). If you don't use it anywhere, you don't even need to write it on the definition.
Thank you for the great lecture!
Thanks a lot, I stopped everything I was doing to watch this, and I'm eager to see the rest!
Best regards
keeping a simple example in mind is good advice. it's easy to get lost in abstractions and terminology, but relating back to simple examples grounds you
Thanks for these lectures. I think reading the book, foundations of mechanics by Abraham & marsden will supplement these lectures very well.
Walter Thiring, vol. 1.
Nope, Arnold Rocks
Thank you for publishing all this!!!
Can we speak about a differentiable function whithout the two notions of vector space and norm on it...
Was waiting for this series, very excited for it.
Really interesting stuff looking forward to more. And thanks for writing bigger this time :) much appreciated by your RUclips following
Thank you a lot for this interesting lecture series!
Do you already know how many lectures there will be in total?
The plan is to have 18 lectures, although I will possibly have a couple of extra lectures bringing the total to mayber 20. Sincerely,
Tobias
It is a classical optics problem to explain why the mirror image of people vanished after he brushed the board at 16:52.
Thank u sir. Was eagerly waiting for this!
Is this course a prerequisite for some other courses in physics/mathematics? Any example of such other course?
For example, will this be needed in string theory/symplectic field theory?
This course is not a prerequisite for anything in physics. But I do cover such things as complex manifolds which can be very helpful in some parts of string theory.
Sincerely,
Tobias
if symplectic geometry is not great for noisy systems, what approach should I use instead.
Peaceful Geometry. Sorry! 🤐😆
hello prof,
At 32:40 you mentioned U as connected. So U is connected with subspace topology. since U is arbitrary for each point i.e., the definition doesn't involve specific U, this can be stated as every point p in M has a neighborhood U which is connected. Is there any theorem that states If for every point p in M has U that is connected with subspace topology then M is connected with usual topology? Is this true or false? If true then M is Hausdorff connected. If false please provide a counter example or simply say why its not true.
ruclips.net/video/XQIbn27dOjE/видео.html 💐
When we map from the neighbourhood of a point on the manifold to R^d is it necessary that the mapping includes the origin?
no; this was just an accident of my drawings...
Sincerely,
Tobias Osborne
Hi Professor!!!I have a suggestion for you : next course . "Calabi Yau manifolds" :)...Yes!
Many thanks for your comment. Sadly I won't be able to teach anything about Calabi-Yau manifolds: this is just a bit too far away from my area of expertise (quantum information theory).
Sincerely,
Tobias Osborne
Hello.
I am wondering if you will also cover the mathematical foundations of QM, QFT, Statiscal Physics, General Relativity, and String theory?
Cheers
Thankyou for your comment. My teaching commitments for the next year do not include these subjects unfortunately.
Sincerely,
Tobias Osborne
I think that "second countable" means it has as many open sets as the natural numbers, which are enough open sets to work with
For people seeing this in the future: this is almost right, but it’s not that the number of open sets is countable but that we have a countable *basis* of open sets. A basis means every other open set can be written as a union of the ones in the basis (not uniquely). Equivalently, for any open U and a p in U, there’s an element of the basis V with p in V and V in U.
I also recommend Fredric Schuller Lectures:
ruclips.net/channel/UC6SaWe7xeOp31Vo8cQG1oXwplaylists
Euclidean space is a nice place to be
nice HD video and cool professor very interesting
I hope that this excellent -- and important -- series of talks will be remade for the Internet. A few dozen people in the classroom may enjoy the medieval trappings of seeing the back of the fine teacher's head as he writes on the greenboard, but for the huge majority of us over time who will be seeing this electronically, more modern ways of presenting written material have been invented.
The "canonical material" might be expanded beyond the written material on the boards. As the lecturer mentions, small parts of large expensive books are relevant to his aims. Perhaps these could be extracted and condensed? This might be a good place to re-publish is own doctoral work, perhaps?
The lecturer himself will no doubt have more and better ideas about how his material can be presented electronically, just as he has shown himself capable of acting out the format of the Thomistic scholarly classroom -- itself a technological advance over the olde Greeks sitting around drawing in the sand.
A great Great cause. thank you professor.❤️.
ruclips.net/video/XQIbn27dOjE/видео.html 💐
Perfect!!!
what is a definition of the cross when you write S^1 \cross S^1 ?
The cross here means "cartesian product". Sincerely,
Tobias Osborne
Can someone explain why these videos are so huge? I tried to download one for offline viewing and it is already 5Gig and growing. Something must be wrong.
Dear Robert,
The video is recorded at 4k, and the file I upload to youtube is about 20GB. RUclips then transcodes it to all the lower resolutions. Which version are you downloading? If it is 1080p then the file will still be large, e.g., somewhere around several GB (assuming a bitrate of 8Mbps). If it is 720p it should be more manageable. Another problem is that the video is so long and even low bitrates, e.g., 1Mbps, mean that a video which is 1.5 hours long already needs approx 0.5 GB. I hope that helps.
Best wishes!
Sincerely,
Tobias
MIDNIGHT RUN LETS GOOOOOOOOO
Thank you for uploading very very interesting lecture!! I 'm very excited to learn this topic!
is there just 4 problem sheets?
There will be another sheet (to be posted soon). Sincerely,
Tobias
ok, thank you so much
Counter example for 1:05:00. Think of R^3 as the union of all planes parallel to the x-y plane.
Many thanks for the counterexample! Sincerely,
Tobias Osborne
@@tobiasjosborne : In fact, a good reason to assume the space is second countable is that you don't want an n-dimensional space mapped onto (surjection) an (n+1)-dimensional space.
I hope I can make it to the end of the course. Mathematicians should try to interact more with physicists. :-)
He's like the Chuck Norris or the Arnold of theoretical physics.
i'm here thanks to reddit...
The deep trench? Lol
Obscenity at 58:00.
Here a supplement of this course : www.worldcat.org/title/structure-of-dynamical-systems-structure-des-systemes-dynamiques-a-symplectic-view-of-physics/oclc/909302372?referer=di&ht=edition
Available in french here : www.jmsouriau.com/structure_des_systemes_dynamiques.htm
Why is the a femoid?