Functional Analysis Overview

In this video, I give an overview of functional analysis, also known as infinite-dimensional linear algebra. Functional analysis is a fascinating sub-field of math that combines both linear algebra and analysis, with a sprinkle of topology. Among others, I prove that boundedness of linear operators is equivalent to continuity, and I give an example of an unbounded operator, and I go over major theorems like the open mapping theorem or the closed graph theorem. Finally, I give a brief overview of Hilbert spaces. Enjoy!

[robertschlesinger]

Your overview videos are not only great introductions for the uninitiated, but are excellent reviews for those needing a refresher on the subject. Please keep posting overview videos. You are providing a valuable contribution to the mathematics and science communities.

[ReCaptchaHeinz]

Thank you!! I am studying maths, and this gave me a quick reminder of some definitions n theorems. You are a very nice person, and you make the world better.

[dhaka_mathematical_school]

Incredible! The most efficient one hour I spent on Youtube. Thanks so much, Dr. Peyam. You're awesome.

[benjaminbrat]

So nice, as always!
50 min of functional analysis is just what I needed =)

[Newtonissac]

I was having a rough day. Came home to 50 mins of Dr. Peyam reviewing functional analysis. A very satisfying end to an otherwise rough day. Thanks.

[ucojq]

Great 3000ft overview! It's so easy to get lost in the trees of functional analysis (e.g. which results hold for p=1 or infinity). Super helpful!

[scose]

This video is great for researchers in other fields who have encountered functional analysis "in the wild" but never studied it yet. Thanks!

[WhattheHectogon]

"Alright, thanks for watching!"

No, thank you!

[SlipperyTeeth]

This is the single greatest video I've seen in the past 3 years.

[likestomeasurestuff]

Thanks! And let me point out, that the friendly atmosphere you have makes the topic even more appealing than it is for itself already.

19:45 bless you, by the way

[gregwong]

The material certainly did not excite me on first encounter but your enthusiasm is so infectious. Am reviewing this material to properly understand the mathematical spine of quantum mechanics and you’ve inspired me to take it back up with a different attitude. Thanks professor!

[RS-vwny]

Thank you for the video
Engineering student here (2nd year) and considering taking a functional analysis module available in a Master's program that I'm interested in. This video was very helpful since I wanted to know the main topics of functional analysis

[TheWombatGuru]

Had my first lecture in functional analysis today, and it wasn't really clear to me what functional analysis was about. Thanks to this video I now kind of know what I'm doing, and I understand the proofs! Thanks Dr. Peyam!

[AnilKumarnn]

I love how brilliant you are, and how you talk.

[TheMauror]

Anyone else whatched this until the end like me? Damn! cool video Dr peyam!

[duncanw]

Only just done calculus 3 but watched every minute. Also I think calling functional analysis a sub-field is an understatement. Hilbert spaces are in just about everything!

[duckymomo]

Yay I’ve always been curious about functional analysis

[MichaelRothwell]

Thanks, Dr. Peyam, I really appreciated this. It took me way back to when I did my PhD in operator algebras, specifically C*-Algebras.

[tofu]

heard a good joke in my last lecture
what is a yellow, complete and normed vektorspace? a Bananach space

[Songvbm]

Dr. Peyam, I am one of your subscribers, who has fallen in love with math after watching your approach to mathematics. I am currently studying functional analysis for my masters and I would love it if you kindly consider to suggest some comprehensive books in functional analysis that contain topological and measure theoretic preleminaries, normed spaces, topological vector spaces, banch algebra, operator theory, hilbert & sobolev spaces, distribution theory, harmonic analysis, integral equations, functional equations, c*-algebras etc in one volume. Thank you for this overview, it is valuable for my learning.