I would love to see a video on your explaining how you actually read a textbook and take notes. I always find whenever I try to take notes I either just rewrite the whole book or write nothing it all, so it would be really cool to see your process, perhaps just going over a page in a book and pointing out the types of things you'd write out for yourself, and also touching on generally how many pages you find yourself reading a day.
It’s been awesome watching your journey. As a Senior math student eyeing a master’s program next year. It lets me know a lot of the struggles I’m going through isn’t just me.
Information theory is one of the most beautiful sub-fields in mathematics. Highly recommend getting into the field. Also, if you have the chance, I’d recommend reading up on computational complexity theory if you like the stuff on Kolgomorov complexity. Complexity theory is to computer science what thermodynamics is to physics.
Wow...as someone that holds a PhD in electrical and computer engineering, those top three books bring back a lot of memories! I studied those subjects mostly as an undergraduate to better grasp control systems and digital signal processing. I can only imagine how different they may be from a purely mathematical perspective! At the time I took those courses, I thought they were "advanced mathematics". Probably not from a mathematicians perspective though. 🙂
Cool to see Classical and Modern Fourier Analysis on your desk! I actually took Harmonic Analysis under Dr. Grafakos at Mizzou. He was an awesome professor. He has a new book coming out soon! Keep an eye on it. It's called Fundamentals of Fourier Analysis. It is a much more digestible book, and he explains concepts very clearly in it.
Hi, let me comment on the Grafakos book, since I use it quite a bit as a graduate student. I would say that you can focus on the first four chapters, which is basically what a typical taught course will cover anyway. I view the remaining chapters as "special topics", which for now is enough to just flip through and admire. Chpt >=5 contains several important results and ideas, but pls do not FOMO... this will become second nature to you if you decide to work in the area, like it or not ;) Grafakos and Tolstov = Harmonic analysis on Rn. There is another flavor of harmonic analysis, one that works on topological groups instead of Rn. You have witnessed the beginnings in the final chapter of Katnelson. So when someone says they work in harmonic analysis, be sure to first distinguish which one it is! =)
I’m only a rising second-year undergrad, but watching you talk about this is so informative, interesting, and inspiring! It’s also really cool getting to gain perspective on what part of grad school can be like (which I’m interested in going to). Love your videos, keep at it!!
I love your videos! As a high school senior thinking about pursuing a PhD in astrophysics, your videos provide context of what it is really like to be in a PhD program, albeit for mathematics (which I presume is at least somewhat similar to what I would expect in astrophysics). Thanks for giving me something interesting and informative to watch!
Bro I was never thinking about grad school, but after a couple life moments, its interesting that after I started looking at it as a option, was recommended these vids after a while
You should do research in Fourier/Harmonic Analysis which can be extended towards PDEs. It has a bit of measure theory, complex analysis, and functional analysis.
If you are doing mathematics for so long, could you tell me if the following strategy is viable. Regarding reading math book, let say I read the text as soon as I encounter a new theorem, I rewrite it on a piece of paper (I don't look at the proof), and next I'm trying to prove it for myself. If I get stuck I briefly (for a few seconds) look at the proof and continue to prove it for myself. When it is done, I verify it with whats in the real proof and move on.
I am also talking to different professors trying to get my first research project in the Chemical & Biological Engineering department. Trying to get this research gig started as early as possible :DD
Hey Im working on Fourier Series by Tolstov right now for self study, never seen fourier analysis before. It more like a calculus book than analysis. The subjects are all over te place. I think it assumes few analysis knowledge. Thats why it skips and jumps back to certain convergence topics. It makes it less enjoyable to read because subjects stay open.
If you're possibly interested in applying your stuff in the future, Information Theory underpins a ton of electrical engineering, computer science, and more. There would be a lot of really interesting applied work you could do out there... (same broadly applies to Fourier Analysis)
Can you make a video about how you read a thick mathematical book like they type you were going over. I mean math books are just so dense in complex equations etc on every page. Are you reading a chapter for the main ideas then going back and trying some problems?
Hey man! awesome vids! Quick question, how do you deal when the problems you solve don't really have a solution for you to check? I mean, I always get insecure when I solve something and I can't check it anywhere.
Hi so im a Incoming grade 7 student (13 yrs old) and im asking for an advice, for like math i can't find a good UA-cam videos to practice and learn math any mathematicians? you can recommend....
Any book suggestions for real analysis for an undergraduate (applied math) who has taken some complex and numerical analysis but no true familiarity with real?
"Real Analysis for the Undergraduate: With an Invitation to Functional Analysis" by Matthew Pons is a solid text. I used it when I first learned real analysis.
Honestly with advances in inflation and interest rates, its not crazy to think you might get a $200,000,000 starting salary. Good luck living in a major city with that little income though.
I would love to see a video on your explaining how you actually read a textbook and take notes. I always find whenever I try to take notes I either just rewrite the whole book or write nothing it all, so it would be really cool to see your process, perhaps just going over a page in a book and pointing out the types of things you'd write out for yourself, and also touching on generally how many pages you find yourself reading a day.
+
Real
this would actually be extremely helpful
Who needs 200 mil. Solve Collatz's conjecture and gain immortality.
A man can dream 😴 💭
You should do your thesis on finally finding x.
Here it is ➡️➡️➡️➡️x
enter the hall with the walkout song X gon give it to you before starting the presentation
Better yet, finding the area of a circle
It’s been awesome watching your journey. As a Senior math student eyeing a master’s program next year. It lets me know a lot of the struggles I’m going through isn’t just me.
It is reassuring to know you are not the only one who struggles with a topic.
You can do small podcast episodes with your other grad school friends ~ We'll all enjoy it
I second this
I like the idea but it would be difficult to pull off. My friends might be uncomfortable in front of the mic. But never say never.
"Okay, this book has just become goated." One of my favorite lines from these videos.
Information theory is one of the most beautiful sub-fields in mathematics. Highly recommend getting into the field. Also, if you have the chance, I’d recommend reading up on computational complexity theory if you like the stuff on Kolgomorov complexity. Complexity theory is to computer science what thermodynamics is to physics.
As a statistician I see information theory everywhere
You've come a long way, we are proud of you 🫡
Wow...as someone that holds a PhD in electrical and computer engineering, those top three books bring back a lot of memories! I studied those subjects mostly as an undergraduate to better grasp control systems and digital signal processing.
I can only imagine how different they may be from a purely mathematical perspective!
At the time I took those courses, I thought they were "advanced mathematics". Probably not from a mathematicians perspective though. 🙂
Yo those are still advanced mathematics from a person who barely passed highschool math 😭
Cool to see Classical and Modern Fourier Analysis on your desk! I actually took Harmonic Analysis under Dr. Grafakos at Mizzou. He was an awesome professor. He has a new book coming out soon! Keep an eye on it. It's called Fundamentals of Fourier Analysis. It is a much more digestible book, and he explains concepts very clearly in it.
Hi, let me comment on the Grafakos book, since I use it quite a bit as a graduate student.
I would say that you can focus on the first four chapters, which is basically what a typical taught course will cover anyway. I view the remaining chapters as "special topics", which for now is enough to just flip through and admire. Chpt >=5 contains several important results and ideas, but pls do not FOMO... this will become second nature to you if you decide to work in the area, like it or not ;)
Grafakos and Tolstov = Harmonic analysis on Rn. There is another flavor of harmonic analysis, one that works on topological groups instead of Rn. You have witnessed the beginnings in the final chapter of Katnelson. So when someone says they work in harmonic analysis, be sure to first distinguish which one it is! =)
I’m only a rising second-year undergrad, but watching you talk about this is so informative, interesting, and inspiring! It’s also really cool getting to gain perspective on what part of grad school can be like (which I’m interested in going to). Love your videos, keep at it!!
Information theory! You should definitely give it a good look. There are a lot of fun applications in various areas.
I used that Tolstov book for my capstone. It’s a good one
I love your videos! As a high school senior thinking about pursuing a PhD in astrophysics, your videos provide context of what it is really like to be in a PhD program, albeit for mathematics (which I presume is at least somewhat similar to what I would expect in astrophysics). Thanks for giving me something interesting and informative to watch!
Taking notes is not a big deal more especially if you have read through the material prior to coming to class.
I WAS SO NERVOUS WAITING FOR THIS VIDEO, LETS GOOOO CONGRATS! GET THAT PHD!!!!!!!!!!
Bro I was never thinking about grad school, but after a couple life moments, its interesting that after I started looking at it as a option, was recommended these vids after a while
You should do research in Fourier/Harmonic Analysis which can be extended towards PDEs. It has a bit of measure theory, complex analysis, and functional analysis.
So proud man again congrats
If you are doing mathematics for so long, could you tell me if the following strategy is viable. Regarding reading math book, let say I read the text as soon as I encounter a new theorem, I rewrite it on a piece of paper (I don't look at the proof), and next I'm trying to prove it for myself. If I get stuck I briefly (for a few seconds) look at the proof and continue to prove it for myself. When it is done, I verify it with whats in the real proof and move on.
I tried to focus less on obsessive note taking for Calc 2 and got crushed. It’s highly inefficient but it works for me
I am also talking to different professors trying to get my first research project in the Chemical & Biological Engineering department. Trying to get this research gig started as early as possible :DD
Hey Im working on Fourier Series by Tolstov right now for self study, never seen fourier analysis before. It more like a calculus book than analysis. The subjects are all over te place. I think it assumes few analysis knowledge. Thats why it skips and jumps back to certain convergence topics. It makes it less enjoyable to read because subjects stay open.
If you're possibly interested in applying your stuff in the future, Information Theory underpins a ton of electrical engineering, computer science, and more. There would be a lot of really interesting applied work you could do out there... (same broadly applies to Fourier Analysis)
Can you make a video about how you read a thick mathematical book like they type you were going over. I mean math books are just so dense in complex equations etc on every page. Are you reading a chapter for the main ideas then going back and trying some problems?
I will likely cover this in an upcoming video!
Information theory ❤️❤️❤️
Hey man! awesome vids! Quick question, how do you deal when the problems you solve don't really have a solution for you to check? I mean, I always get insecure when I solve something and I can't check it anywhere.
There is a second edition of the info theory book by Cover. It is a classic.
Can you make a video on advice for being a beginner TA for a class? I’m quite worried about this tbh.
Looking for more videos on convex geometry. It plays a role in my research as well.
Pretty sure the heisenberg group is named after the physicist Werner Heisenberg, not breaking bad.
Just solve one of the millennium prize problems, duh.
Just solve one of the hardest problems known to mankind, that even the smartest people in the world do not understand. Duh!
I’m still in undergrad but I’m personally more interested in subjects like Fourier Analysis and Complex Analysis.
Please don't stop making videos, you have something here.
I think the reasoning behind taking stats is smart. Stats are used for soooo many things.
Hi so im a Incoming grade 7 student (13 yrs old) and im asking for an advice, for like math i can't find a good UA-cam videos to practice and learn math any mathematicians? you can recommend....
The original math channel was Khan Academy. He has a website now that I think you might find useful.
hey man, how did the fitness project go? i think an update would be cool
The qual problems are scary, but this question is even scarier lol
Any book suggestions for real analysis for an undergraduate (applied math) who has taken some complex and numerical analysis but no true familiarity with real?
"Real Analysis for the Undergraduate: With an Invitation to Functional Analysis" by Matthew Pons is a solid text. I used it when I first learned real analysis.
What do grad statistics class look like
Thriftbooks gang
Hypothetically speaking how many days would it take for you to finish a 1000 pages book?
Again,congrats for passing.
Honestly with advances in inflation and interest rates, its not crazy to think you might get a $200,000,000 starting salary. Good luck living in a major city with that little income though.
200 million?
INFORMATION THEORY PLZ!
Going the applied route i see. In my opinion pure math is a lot more interesting.
Surely it depends on the topic?
This is not applied math
tell book on abstract algebra for beginner
Algebra chapter 0 by Aluffi
Thomas Hungerford is the one I used.
i start a book. i find exercise difficult, loose my interest and give up@@PhDVlog777
Do maths
Hypothetically speaking how many days would it take for you to finish a 1000 pages book?
Again,congrats for passing.