Functional Analysis Book for Beginners

This is a response to a question I received from a viewer. They want to learn functional analysis using the math book Introductory Functional Analysis with Applications by Kreyszig. They also want to know how long to study every day. Do you have any advice for learning functional analysis or other math? If so, please leave a comment.

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[Jim-besj]

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.

[TheRealSalemSaberhagen]

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.

[exxzxxe]

Yes, Kreysig is excellent. An even more elementary, intuitive approach that emphasizes applications is
"Computational Functional Analysis" by Ramon Moore.

[javiermonreal]

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.

[Blazej]

...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.

[matteogirelli]

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!

[KAUSTUBHCHAKRABORTY]

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.

[sadmansr]

Thanks a lot for answering my questions! ❤️ It helps a lot.

[anupampalchoudhury]

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.

[eulerappeareth]

Sadman: How many hours should I spend learning functional analysis?
The Math Sorcerer: YES!

[steliostoulis]

Im taking functional analysis next semester, thank you for the video

[StaticBlaster]

Happy Pi Day, Math Sorcerer. I hope you made or perhaps bought an apple, pumpkin, cherry, rhubarb, blueberry, etc. pie.

[codnba]

Yes, this book is very good as a first course. I also like the book by Haïm Brezis after that.

[travisporco]

That Kreyszig book is absolutely great.

[frankreashore]

Totally agree with your choice. Great book.

[douglasstrother]

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.

[ianmii]

Excellent book for Functional Analysis!!!

[ravitheja]

First study these lectures on Functional analysis.

From NPTEL(Indian IITs):

From MIT:

At this point, you'll now have the basic understanding on all the topics. Now do all the problems in the above textbook.

[Kaassap]

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.

[schrodingcheshirecat]

Check the syllabus of your school. Check what text they use