I can probably add the perspective of a physicist training where analysis is an integral part of the mathematics education (typically taking ~1/3 of the time of a bachelor degree (bachelor~=3yrs)). In addition, I (partially) work (study) in the applied mathematics nowadays (CFD/PDEs, numerical methods) and without doubt, analysis tools are still everyday ingredients to understand what's going on. So definetly: Yes
Ask HN: If I work with applied mathematics should I still study analysis?
11–20 of 24 posts
Re: Ask HN: If I work with applied mathematics should I still study analysis?
#12(1) I don't think this is necessarily the right place to ask this. HN is not particularly known for mathematics, it's better to ask at a math focused site like https://math.stackexchange.com/
(2) My generic answer to the question is - NO. You can be a good quant, engineer, etc. without having the knowledge of how to prove the theorems in a real analysis undergraduate course. However, knowing the proofs may be helpful if you decide you want to do write theoretical research papers in a particular area, even just for the sake of "mathematical maturity".
Re: Ask HN: If I work with applied mathematics should I still study analysis?
#13Can anyone recommend analysis textbooks suitable for self study?
Re: Ask HN: If I work with applied mathematics should I still study analysis?
#14It's ridiculously easy to apply a method which is not applicable if you are not at least a little aware of the theory behind it. You will get wrong results and you will never know why. The wrong results might never be found out because the impact is so complicated that you cannot even point out the source. I have sadly seen this happen too often in various places. But because our other systems are robust enough, this issue (even though it affects things) is not really heeded to until something really catastrophic happens (like 2008 crash).
Re: Ask HN: If I work with applied mathematics should I still study analysis?
#15Hard to say, we don't know what your calc, diff EQ, LA, probability/stats etc classes were like. You could self study Pugh, Abbott or Spivak. At a bare minimum you can read Lara Alcock/s little red book on analysis. Or you might unfortunately be in the position that you don't quite have the support group, focus or prep for Pugh or Abbott's books.
The other question is, what are you giving up to study real analysis? If you don't have great software engineering skills, along with related skills (linux/network admin, database design/tuning) there's a good argument that you would be better off developing those skills instead.
Re: Ask HN: If I work with applied mathematics should I still study analysis?
#16Can anyone recommend analysis textbooks suitable for self study?
Calculus, by Spivak (an analysis textbook despite the name). I found this book clear, with good exercises, and it starts at the very beginning. I think the most difficult exercises are in the early chapters, so stick with it!
Re: Ask HN: If I work with applied mathematics should I still study analysis?
#17The closest thing to feeling like I had a genuine superpower came after I studied a bunch of pure mathematics – the (richly interconnected, actually conceptually easier to manipulate after you've grown accustomed to them) building blocks of applied mathematics – and was then able to dazzle people who had only been exposed to applied mathematics with genuinely new, and often beautiful, perspectives on things they thou…
I feel the same way. Intellectually it seems like it's been all downhill since leaving grad school :).
Re: Ask HN: If I work with applied mathematics should I still study analysis?
#18Can anyone recommend analysis textbooks suitable for self study?
I wouldn't recommend Spivak for self-study and a first exposure to analysis. It's known to be notoriously difficult even for good students.
I learned from this Dover book[1]; I think it's pretty good. From there you might move up to Baby Rudin[2], but it might have a lot of typos, or big gaps in the exposition that are taken to be obvious but require several steps to fill in, since that was certainly the case for Papa Rudin[3].
[1]: https://www.amazon.com/Introduction-Analysis-Dover-Books-Mat... [2]: https://www.amazon.com/Principles-Mathematical-Analysis-Inte... [3]: https://www.amazon.com/Real-Complex-Analysis-Higher-Mathemat...
Re: Ask HN: If I work with applied mathematics should I still study analysis?
#19Can anyone recommend analysis textbooks suitable for self study?
Without knowing your background, Pugh's and Abbott's are usually good choices as are Schramm's Dover, and while not really analysis texts, don't forget the classic fundamentals/foundations books by Courant/Robbins What is Mathematics, Ian Stewart/D Tall Foundations of Math, Felix Klein etc
Here's lots of reviews: https://www.maa.org/tags/real-analysis
https://math.stackexchange.com/questions/tagged/real-analysi...
https://www.reddit.com/r/math/wiki/faq#wiki_what_are_some_go...
Re: Ask HN: If I work with applied mathematics should I still study analysis?
#20It really depends. For learning and using ML/DL it hasn't helped me much, the bottleneck is stats and linear algebra for that field. Even if it helps, is it the most valuable and broadly useful tool you can add to your current toolkit as of right now? Likely not. Learning to write proofs helped in other ways, the content wasn't actually terribly important.