#67 in Science & math books
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Reddit mentions of Introductory Functional Analysis with Applications
Sentiment score: 12
Reddit mentions: 14
We found 14 Reddit mentions of Introductory Functional Analysis with Applications. Here are the top ones.
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Here's my rough list of textbook recommendations. There are a ton of Dover paperbacks that I didn't put on here, since they're not as widely used, but they are really great and really cheap.
Amazon search for Dover Books on mathematics
There's also this great list of undergraduate books in math that has become sort of famous: https://www.ocf.berkeley.edu/~abhishek/chicmath.htm
Pre-Calculus / Problem-Solving
Calculus
Linear Algebra
Differential Equations
Number Theory
Proof-Writing
Analysis
Complex Analysis
Functional Analysis
Partial Differential Equations
Higher-dimensional Calculus and Differential Geometry
Abstract Algebra
Geometry
Topology
Set Theory and Logic
Combinatorics / Discrete Math
Graph Theory
P. S., if you Google search any of the topics above, you are likely to find many resources. You can find a lot of lecture notes by searching, say, "real analysis lecture notes filetype:pdf site:.edu"
An Introduction to Manifolds by Tu is a very approachable book that will get you up to Stokes. Might as well get the full version of Stokes on manifolds not just in analysis. From here you can go on to books by Ramanan, Michor, or Sharpe.
A Guide to Distribution Theory and Fourier Transforms by Strichartz was my introduction to Fourier analysis in undergrad. Probably helps to have some prior Fourier experience in a complex analysis or PDE course.
Bartle's Elements of Integration and Legesgue Measure is great for measure theory. Pretty short too.
Intro to Functional Analysis by Kreysig is an amazing introduction to functional analysis. Don't know why you'd learn it from any other book. Afterwards you can go on to functional books by Brezis, Lax, or Helemskii.
You may find Kreyszig's Introductory Functional Analysis with Applications interesting.
EDIT: NoLemurs suggested Shankar as a good text that proceeds from first principles. Another book famous for deriving beautiful results from basic physical ideas is Landau's Quantum Mechanics, though it is quite dense and not at all pedagogical.
Learn math first. Physics is essentially applied math with experiments. Start with Calculus then Linear Algebra then Real Analysis then Complex Analysis then Ordinary Differential Equations then Partial Differential Equations then Functional Analysis. Also, if you want to pursue high energy physics and/or cosmology, Differential Geometry is also essential. Make sure you do (almost) all the exercises in every chapter. Don't just skim and memorize.
This is a lot of math to learn, but if you are determined enough you can probably master Calculus to Real Analysis, and that will give you a big head start and a deeper understanding of university-level physics.
If you enjoy analysis, maybe you'd like to learn some more?
I really enjoyed learning introductory functional analysis, which is presented incredibly well in Kreyszig's book Introductory Functional Analysis with Applications. It's very easy to read, and covers a lot and assumes very little on the part of the reader (basic concepts from analysis and linear algebra). This will teach you about doing analysis on finite and infinite dimensional spaces and about operators between such spaces. It's incredibly interesting, and I highly recommend it if you enjoy analysis and linear algebra.
Another great analysis topic is Fourier Analysis and wavelets. I enjoyed the books by Folland Fourier Analysis and Its Applications. I don't believe that book has any wavelets in it, so if you're interested in learning Fourier analysis plus wavelet theory, then I highly recommend the very approachable and fun book by Boggess and Narcowich A First Course in Wavelets with Fourier Analysis. If you have any interest at all in applications (like signals processing), this subject is fundamental.
Hmm I'm surprised you've had point-set topology, linear algebra, and basic functional analysis but have yet to encounter locally convex topological vector spaces! No worries, you have most likely developed all oft the machinery to understand them. I agree with G-Brain, Rudin's function analysis will do. Most functional analysis books should cover this at some point. The only I use is Kreyszig. Hope that helps!
If you are interested enough in machine learning that you are going to work through ESL, you may benefit from reading up on some math first. For example:
Without developing some mathematical maturity, some of ESL may be lost on you. Good luck!
hey nerdinthearena,
i too find this area to be fascinating and wish i knew more on the upper end myself. i'm just going to list off a few resources. in my opinion, graduate school will concentrate a lot on progressing your technical knowledge, but will likely not give you a lot of time to hone your intuition (at least in the first few years). so, the more time you spend in undergraduate school doing so, the better.
helpful for intuition and basic understanding
more advanced but still intuitive
hopefully this helps. if i were to revisit geometric analysis, i would basically use the above books to help bone up my understanding, intuition, and technical skill before moving on. these are also mainly geometry books, so learning analysis (like functional analysis) would be good as well. i mainly have three suggestions there.
three general analysis favorites
For algebra, I'd recommend Mac Lane/Birkhoff. They may not be as comprehensive as some other texts but to me, they are more motivating, and will probably provide a better introduction to categorical thinking.
For linear algebra, I'm going to suggest something slightly unusual: Kreyszig's Introductory Functional analysis with applications. Functional analysis is essentially linear algebra on infinite dimensional spaces, and it generalizes a lot of the results in finite dimensions. Kreyszig does a good job motivating the reader. I can definitely sit down and read it for hours, much longer than I can for other books, and I definitely don't consider myself an analyst. However, it could be difficult if you are not familiar with basic topology and never seen linear algebra before.
I have a variety of books to recommend.
Brushing up on your foundations:
http://www.amazon.com/Beginning-Functional-Analysis-Karen-Saxe/dp/0387952241
If you get this from your library or browse inside of it and it seems easy there are then three books to look at:
More advanced level:
(An awesome book with exercise solutions that will really get you thinking)
Working on this book and Rudin's (which has many exercise solutions available online is very helpful) would be a very strong advanced treatment before you go into the more specialized topics.
The key to learning this sort of subject is to not delude yourself into thinking you understand things that you really don't. Leave your pride at the door and accept that the SUMS book may be the best starting point. Also remember to use the library at your institution, don't just buy all these books.
If you're coming from a more applied background (or physics / engineering) https://www.amazon.com/Introductory-Functional-Analysis-Applications-Kreyszig/dp/0471504599 is pretty easy to follow. Obviously it goes into the infinite dim too but it covers all the finite stuff first.
Kreyszig is the best first book on functional analysis IMO. For measure theory I liked Royden, specifically the 3rd edition.
I hate to disappoint you OP, but here are some books just in my wish list on Amazon that outdo that:
This has 14, 5 star reviews.
This has 20, 5 star reviews, and 1, 4 star review.
No worries for the timeliness!
For Measure and Integration Theory I recommend Elements of Integration and Measure by Bartle.
For Functional Analysis I recommend Introductory Functional Analysis with Applications by Kreyszig.
And for Topology, I think it depends on what flavor you're looking for. For General Topology, I recommend Munkres. For Algebraic Topology, I suggest Hatcher.
Most of these are free pdf's, but expensive ([;\approx \$200;]) to buy a physical copy. There are some good Dover books that work the same. Some good ones are this, this, and this.