6:53 An ultranet or a universal net is a special kind of net. A net is an ultranet or universal iff its eventuality filter is an ultrafilter. Thus, the theory of ultranets is a reformulation of the theory of ultrafilters. An explicit example is the eventually constant ultranet. Now the crazy thing is that although other ultranets exist, other explicit examples of ultranets do not exist! This is because free ultrafilters or nonprincipal ultrafilters are intangibles - things which exist but for which there does not exist any explicit example! This is why it's hard for people to visualise a general ultrafilter - because they literally can't! If anyone's interested in more details please refer to the amazing book by Eric Schechter titled "Handbook of Analysis and its Foundations". Also, congrats on passing your exam! 🥳
Congrats on passing!!! 🎉Also a huge thank you to making those videos, I’m applying to pure math phd programs this year and watching your videos really give me an idea of what to expect, which is super helpful for me
I also pass my graduate course on topology with max great. It was a re exam, since I failed the first time… I study for 3 month of the summer and solve every exercise in Munkres(the exam was on all Munkres, every singles chapter..) and other books and online notes, and finally pass with 100% the course, it was a hell, but know I know too much topology xD I also made more than 600pages of notes and solved exercises xD. Now without any rest I have commutative algebra and graduate measured theory… Oooof..
Awesome! I'm taking my first topology class this fall so I'm excited to learn about the early chapters of Munkres. I'm glad a big source of stress is now gone.
Jokes on you, I love watching your math things and "clicking the button" :P Also, you are incredibly inspiring to see you do this. I am currently at a point where I am having trouble finding motivation to continue working on several things in life, but seeing you push through and motivate yourself is really helpful and inspiring. Thank you so much for doing what you are doing!
congrats! i'm glad you passed. i have no idea what anything that you talk about means, but i enjoy watching these videos to see what mathematical thinking is like. very cool stuff.
Congrats on passing the quals! I had a similar experience with my quals: I was very confident for topology and very unsure about algebra. I'm sure it feels great to be done.
Thanks! It definitely does feel like a weight has been lifted - when I am doing reading or working on problems there is a more relaxed and less pressurized feeling to it from what I have noticed so far and it’s great!
Hey dude, can you give me some guidance on this? I have sucked at math ever since i was in upper middle school. I think that my foundations are lacking. I love maths but i just can seem to get it right. I struggle with trigonometry and calculus, to name some. TLDR: if i want to build my basics what order(of topics) should i follow?
Sometimes practice is the best remedy. There are several different online resources that are fairly comprehensive for covering topics in arithmetic, trigonometry, and calculus that are relatively sequential. Khan academy is fairly good at building up ideas, however I would recommend using a textbook for the subject (especially in calculus) to supplement the video explanations and to get access to a wider variety of practice problems. It is essential that you actively and intentional attack problems when learning mathematics However, when learning (or re-learning) on your own it can be frustrating to read a question and not know what to do. It's okay to look up solutions to problems at the beginning to develop your tool set for approaching different problem types as long as you can return to the problem later on and argue the solution on your own. Sometimes this takes a few times of seeing the pattern/method used to show a solution or prove a result before you can recreate the solution for a particular problem or attack similar problems on your own. The patterns are there in mathematics it's all about noticing and applying them in the right ways.
Well now I have to watch out for internet creepers AND people trying to download my brain against my will, * sigh * the digital world never ceases to amaze me.
That title scared me
Got’em 😅
Says the Bad News xD
6:53 An ultranet or a universal net is a special kind of net. A net is an ultranet or universal iff its eventuality filter is an ultrafilter. Thus, the theory of ultranets is a reformulation of the theory of ultrafilters. An explicit example is the eventually constant ultranet. Now the crazy thing is that although other ultranets exist, other explicit examples of ultranets do not exist! This is because free ultrafilters or nonprincipal ultrafilters are intangibles - things which exist but for which there does not exist any explicit example! This is why it's hard for people to visualise a general ultrafilter - because they literally can't!
If anyone's interested in more details please refer to the amazing book by Eric Schechter titled "Handbook of Analysis and its Foundations".
Also, congrats on passing your exam! 🥳
Thanks!
Congrats on passing!!! 🎉Also a huge thank you to making those videos, I’m applying to pure math phd programs this year and watching your videos really give me an idea of what to expect, which is super helpful for me
Thanks, every grad program is different but I hope my content gives at least some applicable context!
I also pass my graduate course on topology with max great. It was a re exam, since I failed the first time… I study for 3 month of the summer and solve every exercise in Munkres(the exam was on all Munkres, every singles chapter..) and other books and online notes, and finally pass with 100% the course, it was a hell, but know I know too much topology xD I also made more than 600pages of notes and solved exercises xD.
Now without any rest I have commutative algebra and graduate measured theory… Oooof..
Measure theory is one of my favorite things! Good luck
Any chance you'd be willing to post or upload those solutions anywhere??
Awesome! I'm taking my first topology class this fall so I'm excited to learn about the early chapters of Munkres. I'm glad a big source of stress is now gone.
Thats great! It will probably feel super abstract if you haven’t seen any topology before but i hope you enjoy it!
I discovered this channel today and i couldn't have been any more glad. Congrats on passing! I just met you but i m so proud of you. Good job!✨
Thanks! I'm glad you found it!
Jokes on you, I love watching your math things and "clicking the button" :P
Also, you are incredibly inspiring to see you do this. I am currently at a point where I am having trouble finding motivation to continue working on several things in life, but seeing you push through and motivate yourself is really helpful and inspiring. Thank you so much for doing what you are doing!
Thanks Scott! I'm glad you find some value in what I do here!
congrats! i'm glad you passed.
i have no idea what anything that you talk about means, but i enjoy watching these videos to see what mathematical thinking is like. very cool stuff.
Thanks!
Congrats on passing the quals! I had a similar experience with my quals: I was very confident for topology and very unsure about algebra. I'm sure it feels great to be done.
Thanks! It definitely does feel like a weight has been lifted - when I am doing reading or working on problems there is a more relaxed and less pressurized feeling to it from what I have noticed so far and it’s great!
I'm stressed out and tired just watching this can't imagine a whole math phd lol
it has been a ride for sure thus far
Well Done Sir. Amazing. As scary as this sounded it would be more scary if you did not pass given the amount of effort! Congrats.
Truly yes, screams of joy were heard throughout my apartment upon receiving the result
I can't imagine you failing with as much time and enthusiasm you put into it.
Sometimes time and enthusiasm are not enough but I’m still putting in the work!
Congratulations 🎉🎉🎉
Thanks 😁
GREAT CHANNEL-Kudos!
Congratulations, Nathan! I like to see you saying “I’m done!” like a boy ! 😂
Thanks Kiko!
I remember that feeling of never having to take another written exam. Congrats!
Thanks! It definitely is a great feeling!!
I am a little late to this, but CONGRATS on passing!!! Well earned!!!!
Thanks!
Congrats
Internet, this is my mother - protect her at all costs.
Congratulations on passing all of your tests. Try to take a break if you can!
Thanks! Truly is the goal to find sometime to breathe may just hide under my desk haha 😅
I’m incredibly happy for you
I look forward to seeing your…
Thanks!
I was in grad school and had a complete mental breakdown from the grind and quals. Had to drop out
Yup that's real, seen it happen to a few folks (not necessarily in my program)
@@CHALKND It was truly awful, I commend you for being able to stick it out. For me it was analysis that was just an insurmountable task and broke me.
You are a star!!
💫
Great vid
Thanks!
Congratulations
Thanks!
Hey dude, can you give me some guidance on this? I have sucked at math ever since i was in upper middle school. I think that my foundations are lacking. I love maths but i just can seem to get it right. I struggle with trigonometry and calculus, to name some.
TLDR: if i want to build my basics what order(of topics) should i follow?
Sometimes practice is the best remedy. There are several different online resources that are fairly comprehensive for covering topics in arithmetic, trigonometry, and calculus that are relatively sequential. Khan academy is fairly good at building up ideas, however I would recommend using a textbook for the subject (especially in calculus) to supplement the video explanations and to get access to a wider variety of practice problems.
It is essential that you actively and intentional attack problems when learning mathematics
However, when learning (or re-learning) on your own it can be frustrating to read a question and not know what to do. It's okay to look up solutions to problems at the beginning to develop your tool set for approaching different problem types as long as you can return to the problem later on and argue the solution on your own. Sometimes this takes a few times of seeing the pattern/method used to show a solution or prove a result before you can recreate the solution for a particular problem or attack similar problems on your own. The patterns are there in mathematics it's all about noticing and applying them in the right ways.
I am a self taught math person. I was going to ignore stats. Because... well it's boring but it does seem to be important in business...
Yo I love you good job
Wow these tests sound exhausting
Can atest that i am exhausted
Now if we could just download all of your knowledge into our brains....
Well now I have to watch out for internet creepers AND people trying to download my brain against my will, * sigh * the digital world never ceases to amaze me.
Nice 🧡
Thanks 🤗
the amount of times I hear "I should probably take stochastics" in pure math
Gotta get a job somehow if academia doesnt work out 😞
Did you wear mascara for this video?
Nope