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Functional Analysis 1 | Metric Space - How to Measure Distances?

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Please do the quiz to check if you have understood the topic in this video: thebrightsideofmathematicscom/courses/functional_analysis/overview/
Comment from : @brightsideofmaths

Distance metric and non euclidian distance
Comment from : @basschot3302

Really nice great job your teaching style is fully different from others I really appreciate 🙏🙏 thank you sir
Comment from : @vaishaligautam886

What are the prerequisite to start this playlist can u guide author ?🎉
Comment from : @kiit8337

thanks for the intro, but its very basic
Comment from : @Destruction_of_Ermac

Excellent Thanks a lot
Comment from : @lcfrod

Muito Bom!
Comment from : @LuanaBarbosadaSilva-p1r

❤🎉🎉🎉🎉🎉🎉❤
Comment from : @RaeTheActuary

Writing is great 🎉brAnd fresh 😅brNice 👍
Comment from : @Amanpreetkaur-cp4fs

at @3:10 why is the cartesian product of x and x
Comment from : @soumyaadabala

I think that the notion of metric space belongs more to topology People say functional analysis is an infinite dimensional linear algebra However it is true that many structure has metric space property
Comment from : @sandorszabo2470

is functional analysis closely related to variational calculus or not ?
Comment from : @cerbahsamir8617

Great job! 👏
Comment from : @nnofficial2414

This is a wonderful presentation, I need this on controlled metric space
Comment from : @maths4fun103

When you started with "hello and welcome", I knew I was in for some awesome mathematics lolbrCan't wait to watch this series :)
Comment from : @MathIguess

Hi, I recently finished your series on complex analysis which was fantastic Do you plan to cover reproducing kernel Hilbert space sometime in the future for the functional analysis series? There is a growing interest in RKHS due to the popularity of machine learning, but quality online content on RKHS is currently lacking I would appreciate it if you could consider it! Many thanks
Comment from : @chanwoochun7694

Thank you bright side You are making my math degree a lot easier!
Comment from : @lukephillips7239

Is the metric d the same as the metric tensor g
Comment from : @mikamikamusic7792

It's my summer holidays and i begin this playlist Next semester we have a course of Functional Analysis and it's said to be VERY difficult, one of the hardest courses
Comment from : @putin_navsegda6487

Best in this field Thank you very much
Comment from : @tilkesh

shidaa
Comment from : @enochtetteycommey7907

Do you have something about convex optimization, convex analysis?
Comment from : @arthurlbn

You guys, producing such high quality content for pure math, are just incredibly helpfull Truely an inspiration If I make it through my math major, I hope I can produce someday some pure math videos too, about uncovered topics :)
Comment from : @nayjer2576

❤
Comment from : @sarkarsubhadipofficial

very good
Comment from : @bakytzhansapy7369

@brighsideofmaths brCheck out my review video on metric spaces: youtube/pNAjI3RQp3A brbrI covered a nice example that goes along very well with your introductory video
Comment from : @fabiangabel

Thanks ❣️❣️❣️❣️
Comment from : @Tareq--ri6qe

You are a german guy
Comment from : @MilesTailsPrower1192

Hello :) Thanks for all your videos, they are awesome without exception Have you ever thought of doing a series on Perturbation Methods or Approximation Theory? Regards
Comment from : @davidizquierdo8769

Functional Analysis, better version of Real/Complex Analysis 👏🏻
Comment from : @ishaangoud3180

Simply outstanding didactics, aiming to understand and not just a heavy proof-driven functional analysis course! Really good to understand the subject and get (geometrical) intuition Thanks for sharing your videos! By the way (and out of curiosity), do you like the Kreyszig Introductory Functional Analysis book? I think the way you explain is similar to this book
Comment from : @dvolpatto

Metric space? More like "The fact that more people don't know about this is a disgrace!" Thanks for putting up so much amazing content on YouTube
Comment from : @PunmasterSTP

we want too see as much as functional analysis there is with your clear and concise explanation talent, we don't want to waste it but we want every ounce of it
Comment from : @ichkaodko7020

Subscribed today 🥰
Comment from : @paominlienguite2397

deutsch-englischer Dialekt xD
Comment from : @philippfarag

The best channel ever for high school students like me who's aiming for a Math major in their undergrad
Comment from : @zhouryan6960

really helpful;
Comment from : @keishamselex1689

I love it
Comment from : @trantrunghieu2332

Are you following a text book for this course, thank you!
Comment from : @Spacexioms

hey! sorry, a question: what program do u youse to draw and write?
Comment from : @daviidayala4987

Those lines are not clear and i can not watch exactly
Comment from : @shabnamghalichi8534

This accent is thicc!
Comment from : @stsowi

it's incredible to have found this special math courses here
Comment from : @李子熠

0:30 what it is about functional analysisbr1:58 metric space
Comment from : @qiaohuizhou6960

You are amazing! I like how you explain every property with graphs :)
Comment from : @FloriUchiha789

Will this course cover all topics in functional analysis ?
Comment from : @xeno5031

Excellent way
Comment from : @letslearnmathstudents4174

Nice video dawg, terry crews certified
Comment from : @schatjepatatje767

Sound interesting, i like it
Comment from : @suwandi178

loving this! could you maybe have a takeaway problem at the end with a solution as well? A big drawback when learning math independently is not being able to know if you're right or not
Comment from : @108titan

hahn banach theorem along with some examples (how to extend function using this result?)
Comment from : @survivor1620

Does anyone know if metric spaces have to be strictly convex? If not, how can you define distance between two points without having the line segment that connects them entirely contained in the space?
Comment from : @willkimoto1218

thanks so much your explaination is very clear and easy to understand
Comment from : @AliAhmed-jw8gy

Pure Mathematics content on a didactical level like this is very rare on youtube Keep up the great work
Comment from : @keyyyla

So, you just skip a bunch of interesting things, and jump right into metric spaces? Ah Was expecting more of topology indeed
Comment from : @MindeyI

God bless I have Functional Analysis the comming semster as a non mathematician and your videos are a great way to prepare for (and maybe even master) it :D
Comment from : @Xaarfai

so good
Comment from : @yBazo82

Please discuss some applications to quantum mechanics,bro i love your videos🤩
Comment from : @mayankvashishtha5714

hallo gutes video hast du das thema auch auf deutsch zufällig?
Comment from : @achillesmichael5705

Great videos!
Comment from : @mattetor6726

Oops!! Got little bit late to hop in here for the new series 😁
Comment from : @strai5150

thanks sir
Comment from : @qi1436

Worthwhile basic video I look forward to the sequels
Comment from : @robertschlesinger1342

Sweet! Would it be too much to cover positive-operator-valued measures? Coming from qm
Comment from : @jackdavis6315

yes yes yes!
Comment from : @changhanchao9654

These videos are fantastic and are a real highlight of my days 💯💯
Comment from : @rgoswami

I would love to see how hilbert spaces play a crucial role in Fourier AnalysisbrI also head that functional analysis is the bridge to Harmonic Analysis I like to see that but not sure if that’s asking too muchbrAlso unbounded operators lol
Comment from : @ivanleon4961

Thankyou so much for making videos on function analaysis brYou are a very good mathematics profacer
Comment from : @sejuprajapati2005

Sir please on Banach Spaces, Linear TransformationAnd sir , Simmons is enough for reference on Functional Analysis? Or Any??
Comment from : @Jeffrey561

we appreciate your efforts to make ugly math understandable hhhh pleas keep them coming and we will support your content through paypal
Comment from : @user-du3ow9er1y

Recently I have watched some of your measure theory videos They are very clear! Happy to see a new course on your channel! Thank you and, please, keep up the good work!brbrMy wishlist: any standard course on Functional Analysis with focus on EXAMPLES would be OK
Comment from : @ekaptsv

Greatkeep bringing them all
Comment from : @adithyagiri7933

Super interessant, ich freue mich bereits auf diese Serie Ich habe dieses Semester Analysis III für Ingenieure (komplexe Analysis) abgeschlossen und damit das letzte Mathemodul meines Studiums leider beendet Ich möchte mich nun neben meines Studiums weiter in Bereichen der Mathematik bilden und deine Videos sind eine gute Grundlage dafür Danke dir! Übrigens, hast du vielleicht mathematische Literaturempfehlungen für einen Ingenieuren mit folgenden Kenntnissen:brbrKenntnisse in der linearen AlgebrabrKenntnisse in mehrdimensionaler und komplexer AnalysisbrKenntnisse in Integraltransformationen und partiellen DGLsbrbrDenn leider ist die fortgeschrittenere interessante Literatur meist für Mathematikstudenten ausgelegt :/
Comment from : @funnykira1330

Hell yes man I'm so excited for FA :))
Comment from : @YorkiePP

Thank you for doing these videos!
Comment from : @remlatzargonix1329

I picked this course for next semester, its the one im most excited for Hopefully this stupid virus wont interfere again and force us to study from home
Comment from : @Domzies

Woohoo! I'm so glad you're covering FA! 😁
Comment from : @nzuckman

Hoorray, functional analysis! Here's a wish list:br- Arzela Ascolibr- Banach Steinhausbr- Spectrum of non-compact operators
Comment from : @TheSandkastenverbot

This is awesome, I just recently looked into functional analysis a little bit If you could explain what exactly it means to complete a metric space and why it's an important concept that would be great It is one of the first concepts I came across yet I had trouble understanding it Great video can't wait for more
Comment from : @zazinjozaza6193

Hmm, how do metric spaces in functional analysis relate to the notion of a metric in differential geometry? I know they must be different, since in DG you can have negative distances, and the metric is a local property rather than a function on pairs of points
Comment from : @ZanyRocket

Greaaat! Thanks a ton!!!
Comment from : @juliogodel

Great video and as usual good explanation! :)brBut a question: what is the difference between a norm and a metric? Because as I understood it it has the same propertiesbrThanks!
Comment from : @thiloherold7087

Thanks for starting this new series Looking forward to it
Comment from : @m2rahman

Thank you so much for this video I have my Msc semester exam next week and this video will help to clear my doubts Looking forward to more videos
Comment from : @shilpasolanki2114