Thanks so much for recording these lectures. It enables me to read Rudin, which I prefer to our course textbook. I'm also impressed by your use questions and interaction with students to prompt us to think our way towards answers rather than just telling us... and also that you manage to entertain as well in the process. ;) Great series, and I hope you continue on to part II of analysis for the benefit of the rest of the world!
So clear, so informative and such great storytelling! I am a math prof also and I appreciate the level of knowledge and talent for communication it takes to be a great lecturer - and you are a GREAT lecturer. I thoroughly enjoy your excellent expositions and I thank you for these gifts.. I will forward these to my colleagues and all my students! Live long and prosper!
I agree with the earlier comments. These are very high quality lectures. I recently started trying to work through Rudin's book on my own, but these lectures give extra insights and anticipate my misconceptions. Thanks for making them free!
I really enjoy these lectures and especially the corresponding blog. I love a professor who can deliver a lecture without using notes and really understands the material. The only criticism I have, which is meant to be given respectfully, is that at times, a few times, he can come across as condescending. I think this is unfortunate because it is clear how much he cares about doing a good job of teaching. Maybe it is just the tone. At any rate, take it for what it's worth and thanks.
At 45:00 there's a talk about real numbers having interior points under (R,discrete) that says all points are interior points in that condition. What I'm confused about is, then what about having isolated points under the same condition? I thought under the discrete metric all points can be isolated points. But if that's the case then it means that under that condition it can have all the points to be interior points and the isolated points at the same time. But is that possible?
45:00 His example is not very good. In E=X, *every* point of E is an interior point of E. Just take any neighborhood of p in E. I think he got mixed up.
I guess you're talking about 10:08 "The closed ball is just a single point x". He's not talking about r=1 here. At 10:02 he says "if r is ... an half".
I wish mathematics lecturers in my university were like this, I'm doing advanced real analysis and our lecture is the opposite of this Professor as he just treats you like some Doctoral student LOL.
Modular sheave can transform non orientiable surface to different orientation much like a Möbius strip can transform to a klien bottle where the metric space are covariant
Thanks so much for recording these lectures. It enables me to read Rudin, which I prefer to our course textbook. I'm also impressed by your use questions and interaction with students to prompt us to think our way towards answers rather than just telling us... and also that you manage to entertain as well in the process. ;) Great series, and I hope you continue on to part II of analysis for the benefit of the rest of the world!
In my opinion the students are very perceptive and make very useful contributions to the lesson.
So clear, so informative and such great storytelling! I am a math prof also and I appreciate the level of knowledge and talent for communication it takes to be a great lecturer - and you are a GREAT lecturer. I thoroughly enjoy your excellent expositions and I thank you for these gifts.. I will forward these to my colleagues and all my students!
Live long and prosper!
Prof. Su is the President of the Mathematical Association of America. WOW!
Thank you Prof. Su for these excellent lectures. We are using Rudin in our course aswell but have no lectures (live or video) so this is great.
I agree with the earlier comments. These are very high quality lectures. I recently started trying to work through Rudin's book on my own, but these lectures give extra insights and anticipate my misconceptions. Thanks for making them free!
That last comment on the density of sets was everything. Thanks professor!!
You are amazing! Dr. Francis is a Super hero for me for the way he teaches. Thanks. Khan
The point about "if"s in definitions was really good.
I really enjoy these lectures and especially the corresponding blog. I love a professor who can deliver a lecture without using notes and really understands the material. The only criticism I have, which is meant to be given respectfully, is that at times, a few times, he can come across as condescending. I think this is unfortunate because it is clear how much he cares about doing a good job of teaching. Maybe it is just the tone. At any rate, take it for what it's worth and thanks.
really nice lecture .. helped me before going through rudin !
@dalcde
You don't consider a half-open door to be open?
At 45:00 there's a talk about real numbers having interior points under (R,discrete) that says all points are interior points in that condition.
What I'm confused about is, then what about having isolated points under the same condition? I thought under the discrete metric all points can be isolated points. But if that's the case then it means that under that condition it can have all the points to be interior points and the isolated points at the same time. But is that possible?
At 10:24 you said Prof...that with Discrete metric, closed ball for r
I think he's talking about open balls. Open balls for all r less than equal to 1 will just be the singleton set containing the center of the ball.
Think you are right.
45:00 His example is not very good. In E=X, *every* point of E is an interior point of E. Just take any neighborhood of p in E. I think he got mixed up.
I guess you're talking about 10:08 "The closed ball is just a single point x". He's not talking about r=1 here. At 10:02 he says "if r is ... an half".
need an hd so i can see the board. great audio tho
I wish mathematics lecturers in my university were like this, I'm doing advanced real analysis and our lecture is the opposite of this Professor as he just treats you like some Doctoral student LOL.
Modular sheave can transform non orientiable surface to different orientation much like a Möbius strip can transform to a klien bottle where the metric space are covariant
💯
ha ha BALLS
hehehe - i am loving this lecture, but was thinking the same thing
18.23 looks like a face