One thing that could be useful is to keep a linear algebra book handy when studying functional analysis. Probably 75% of theorems in a linear algebra textbook start with "Let V be a finite dimensional vector space." When V is not finite dimensional, one is often in the realm of functional analysis, but many concepts will be familiar from linear algebra. Contrasting similar concepts, definitions, theorems, etc. from the two subjects can enhance understanding.
@exxzxxe
Жыл бұрын
Yes, Kreysig is excellent. An even more elementary, intuitive approach that emphasizes applications is "Computational Functional Analysis" by Ramon Moore.
@TheRealSalemSaberhagen
Жыл бұрын
Hello there, professor. I am Dave. I have to thank you for all the unimaginable work you put into making these great and amazing videos filled with educational content. You are a hero, sir. Don't try to underestimate yourself. Teachers are a type of hero. And we must give you praise for all the effort that goes into educational channels like this.
@javiermonreal42
Жыл бұрын
Hii! I am a gradute student in math and for me my favorite book of functional analysis when it comes to a first course on this topic is functional analysis by H. Brezis, its a really good book, very clear and if you are interested on differential equations it also introduces to many different objects as Sobolev Spaces and Unbounded operators. There are also a lot of solutions out there for this book so i really really recommend it for self study.
@sadmansr1054
Жыл бұрын
Thanks a lot for answering my questions! ❤️ It helps a lot.
@mfaracing
2 ай бұрын
Hi Sadmar, have you made it? Did that work for you? I want to study it also, that's why I am asking about your experience.
@matteogirelli1023
Жыл бұрын
Hi Math Sorcerer! I'm studying a master's in Economics and I just discovered that my favourite subject, macroeconomics, at the PhD level is entirely grounded in functional analysis (for dynamic programming and stochastic control). I'm a little scared since you said that functional analysis is arguably the hardest math subjects together with abstract algebra. Thanks for your book suggestions and your warnings, I'll start studying on my own well in advance!
@Blazej1983
Жыл бұрын
...when I took (linear) functional analysis course at my university we used "Elements of the Theory of Functions and Functional Analysis (A. N. Kolmogorov, S. V. Fomin)" and "Introduction to functional analysis (Angus E. Taylor)", but I also highly recommend "Linear Operator Theory in Engineering and Science (Arch W. Naylor, George R. Sell)". I also recommend to revise the knowledge from advanced linear algebra before someone "enters" functional analysis :-) A lot of theorems, concepts etc. will be very similar in (linear) functional analysis to those in advanced linear algebra.
@eulerappeareth
Жыл бұрын
Sadman: How many hours should I spend learning functional analysis? The Math Sorcerer: YES!
@sadmansr1054
Жыл бұрын
Lol 🤣
@anupampalchoudhury10
Жыл бұрын
This book is too underrated. This covers a pretty good amount of material (more than a first course on FA) in a very friendly manner.
@daniellindner826
Жыл бұрын
Thank you for these advice videos ❤️
@TheMathSorcerer
Жыл бұрын
You are so welcome!
@KAUSTUBHCHAKRABORTY
11 ай бұрын
My fav books on functional analysis • Introductory FA - Kreyszig • Methods in Classical and FA - E Hille • F A - Brezis • F.A by R E Edwards • FA in Normed Spaces - LV Kantorovich, GP Akilov • A Course in Analysis - Vol. V: Functional Analysis, Some Operator Theory, Theory of Distributions - N Jacob Also I like Lax, Dunford (operator th.), J V Neerven etc.
@StaticBlaster
Жыл бұрын
Happy Pi Day, Math Sorcerer. I hope you made or perhaps bought an apple, pumpkin, cherry, rhubarb, blueberry, etc. pie.
@steliostoulis1875
Жыл бұрын
Im taking functional analysis next semester , thank you for the video
@douglasstrother6584
Жыл бұрын
Skim through the whole book, cover to cover, first. Get a sense of the contents before diving into the details. An hour of concentrated effort is a good starting point. Put "Study Time" on your calendar, as part of your routine. Burn-out is a real risk: overdoing it does more harm than good.
@TheMathSorcerer
Жыл бұрын
Excellent advice, thank you!!!
@sadmansr1054
Жыл бұрын
Thank you for the advice.
@codnba136
Жыл бұрын
Yes, this book is very good as a first course. I also like the book by Haïm Brezis after that.
@travisporco
Жыл бұрын
That Kreyszig book is absolutely great.
@alexgoldhaber1786
Жыл бұрын
The book by Karen Saxe is phenomenal.
@frankreashore
Жыл бұрын
Totally agree with your choice. Great book.
@schrodingcheshirecat
Жыл бұрын
Check the syllabus of your school. Check what text they use
@ianmi4i727
Жыл бұрын
Excellent book for Functional Analysis!!!
@Kaassap
Жыл бұрын
Im currently racing through some analysis 2 material, preparing for kolmogorovs fa book. Kreyzig seemed too dense for my goal: learning about kernels, hilbert spaces and fourier theory. Need this for spectral kernels in deriving cross covariance function in guassian processes.
@ravitheja4206
Жыл бұрын
First study these lectures on Functional analysis. From NPTEL(Indian IITs): kzitem.info/door/PL5022A32B9BCFE3E4 From MIT: kzitem.info/door/PLUl4u3cNGP63micsJp_--fRAjZXPrQzW_ At this point, you'll now have the basic understanding on all the topics. Now do all the problems in the above textbook.
@Jim-be8sj
Жыл бұрын
Great advice. The NPTEL lectures on the subject (and many others) are excellent.
@EternalDarknessAboveTheBlueSky
Жыл бұрын
@TheMathSorcerer Thanks for more recommendations. Do you have any recommendations for economics books?
@billbez7465
Жыл бұрын
With the analytic power of Wolfram Alpha, are answers to questions in a textbook as important as they use to be? Thank you
@TheMathSorcerer
Жыл бұрын
Yeah they still are, especially for a subject like this one. Wolfram is awesome though for other stuff though👍
@writerightmathnation9481
Жыл бұрын
@@TheMathSorcerer Personally, I think complete solutions are overkill; something should be left for the reader to do. Also, with systems like Wolfram Alpha available, certain kinds of problem solutions should not be included, and students should be encouraged to solve those themselves, and taught ways to check their work using systems like Wolfram Alpha, and for many of the more theoretical problems, only solution sketches and hints should be provided, and readers/students should be encouraged to check some details that support their arguments (calculations, formulas, derivations, etc) using computer algebra systems. One of my biggest disappointments to date is that when I try to get students to check their work before submission falls on deaf ears, and other faculty often don't even try to get them to do so, and administrators support students who just want to complain that I don't do all of their work for them. Texts that support the idea that faculty should solve all problems for the students before the end of the course undermine my efforts to get students to put in some effort to train themselves to build self-confidence in ways that lead them to move away from using provided solutions as a crutch.
@AbiodunOguntoye-th6ez
4 ай бұрын
How to get the pdf cover of the book?
@mariotabali2603
Жыл бұрын
Fun fact: That book was dictated by GOD to Erwin Kreyszig
@OnlyOnePlaylist
Жыл бұрын
What kind of applications does the book cover?
@north6898
Жыл бұрын
hello sir, ive recently started my journey in self studying math. I've been behind on math for about 6-7 years because of terrible decisions. I wanted to ask in your opinion, what form of self studying is best ? through books/textbooks or video lectures. I feel as though self studying through the books would allow for retaining more information ?
@yuto2497
Жыл бұрын
You could always catch up! I'm currently on 10th grade and even though calculus is so advanced for my class, that for the love of understanding higher physics equations, I'm self-learning math on my own. I recommend doing both text and video lectures, although this depends on the person if it works for them or not. I'd recommend doing the text first (Atleast a lesson ahead your chosen video lecture) so you can plan what lecture should you do next and connect some dots after, that's what I did: I'm currently self-studying calculus with a VERY thick calc book with the assistance of free video lectures from MIT's OpenCourseWare here on KZitem (I watch an old one, like from the 70/80's). And a tip, when you do problems, do a lot of them and do it in a very quiet place. Lastly, have rests frequently! Because your brain needs to digest the information you just acquired and it needs time to connect the dots and not over-fatigue or worse, burn-outs. Edit: There is no better way of learning other than enjoying what you are learning.
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