lol, yeah I noticed that I messed up with the audio recording for the first several videos of this series. Should probably get to fixing that issue in the future...
Thanks for these videos. I don't really have a strong enough background to fully appreciate them now but it's nice being able to peek ahead at more advanced math. I'm actually an undergrad in physics but I'm planning on applying to grad school in maths. Would you be willing to offer some advice/insight? In particular, I'm finding it hard to judge how acceptable my math background will be etc.
As a physics undergrad you're probably going to be able to do a graduate degree in mathematics. Of course, you're going to have to put in some work, but as long as you don't feel overwhelmed by the material you've read so far (with regards to mathematics) I don't see why you wouldn't be able to go further. For reference, this lecture series covers what would typically be considered a graduate level mathematics course, and most people would find at least some of the topics I cover in these videos quite challenging to come to grips with, and in this group I would include the typical grad student. If you haven't already, and if you want to get some experience of what graduate level math courses are like, I'd recommend that you take a course in functional analysis. The reason for this is that functional analysis is usually the course where most students get acquainted with graduate-level mathematics for the first time, at least if we're talking about pure maths. There are many more things I could say about doing a math PhD, and in fact I'm actually planning to make a video about it now that I've finished my own PhD a couple of weeks back. Feel free to ask any kind of question, and I'll do my best to try and give a thoughtful answer.
One question, for the supremum norm to be finite one would need to consider continuous bounded functions that vanish at infinity and not also unbounded functions as well or am I missing something?
Reading your comment, I'm not convinced that continuous functions that vanish at infinity really could be unbounded when talking about locally compact Hausdorff spaces. Consider the definition of "vanishing at infinity": Let X be locally compact and let f be a continuous function that vanishes at infinity. Explicitly, this means that for every e>0 there is a compact subset K of X such that |f(x)|< e whenever x is outside of K. Clearly, f is bounded on the complement of K in X, but moreover since K is compact, the restriction of f to K is continuos and hence bounded. It follows that f must be a bounded function.
my right ear enjoyed this
lol, yeah I noticed that I messed up with the audio recording for the first several videos of this series. Should probably get to fixing that issue in the future...
I thought my one phone speaker was just plugged up lol
very helpful sir....thank you
Thanks for these videos. I don't really have a strong enough background to fully appreciate them now but it's nice being able to peek ahead at more advanced math.
I'm actually an undergrad in physics but I'm planning on applying to grad school in maths. Would you be willing to offer some advice/insight? In particular, I'm finding it hard to judge how acceptable my math background will be etc.
As a physics undergrad you're probably going to be able to do a graduate degree in mathematics. Of course, you're going to have to put in some work, but as long as you don't feel overwhelmed by the material you've read so far (with regards to mathematics) I don't see why you wouldn't be able to go further.
For reference, this lecture series covers what would typically be considered a graduate level mathematics course, and most people would find at least some of the topics I cover in these videos quite challenging to come to grips with, and in this group I would include the typical grad student.
If you haven't already, and if you want to get some experience of what graduate level math courses are like, I'd recommend that you take a course in functional analysis. The reason for this is that functional analysis is usually the course where most students get acquainted with graduate-level mathematics for the first time, at least if we're talking about pure maths.
There are many more things I could say about doing a math PhD, and in fact I'm actually planning to make a video about it now that I've finished my own PhD a couple of weeks back. Feel free to ask any kind of question, and I'll do my best to try and give a thoughtful answer.
One question, for the supremum norm to be finite one would need to consider continuous bounded functions that vanish at infinity and not also unbounded functions as well or am I missing something?
Reading your comment, I'm not convinced that continuous functions that vanish at infinity really could be unbounded when talking about locally compact Hausdorff spaces. Consider the definition of "vanishing at infinity": Let X be locally compact and let f be a continuous function that vanishes at infinity. Explicitly, this means that for every e>0 there is a compact subset K of X such that |f(x)|< e whenever x is outside of K. Clearly, f is bounded on the complement of K in X, but moreover since K is compact, the restriction of f to K is continuos and hence bounded. It follows that f must be a bounded function.
@@TheArmchairIntellectual Thanks a lot for answering, that helped me and thanks for your series!!