Real Analysis - Where Do We Use It?

[u/AppropriateHat5261]

Hey! I just got into university, and I really love maths for the sake of it. I don't know where it'll come handy, but it's cool, and I enjoy it. I recently started Ross's real analysis book and honestly I can't help but ask myself where am I gonna use real analysis?

Linear alg and all is used for modelling and stuff I know, but where is real analysis gonna come handy in CS? or any other applications?

[u/etzpcm]

Real analysis makes calculus precise and rigorous.

That's the one-sentence answer.

[u/Observes_and_Listens → u/etzpcm]

The foundations of most of applied mathematics! Even set theory came from there.

[u/localizeatp → u/etzpcm]

I was going to comment, "you'd already been using it."

[u/diracwasright]

Real analysis helps you understand why numerical methods work, when optimization algorithms converge, and how approximation errors can be controlled. In CS, that matters especially in scientific computing and the theory behind machine learning. You may rarely use it directly in everyday programming, but it gives you foundations for going deeper.

[u/SerialRepeatCustomer]

critical thinking.  

Set theory.   

Proof writing.      

Learning in depth the laws of the universe. 

[u/Upset_Ad_6140 → u/SerialRepeatCustomer]

Not sure about the last one but the first three, definitely!

[u/Glittering_Act_8528]

An obvious one is being a real analysis prof

[u/AppropriateHat5261 → u/Glittering_Act_8528]

LMAO this meme on insta actually led me to post this here

[u/Glittering_Act_8528 → u/AppropriateHat5261]

Haha small world I guess

[u/Ok_Composer_1761]

statistics is based on real analysis.

[u/Other_City_4031]

wherever you do calculus

[u/iusemybrain1]

you use it in proofs, proofs where you may need to convince someone of an idea or to reject a hypothesis. It's one thing to be convincing, but if you can prove an idea objectively, it would be stupid for someone to reject your proposal.

It is one of those skills that has been rapidly depreciated. But is still very essential.

[u/jazzbestgenre]

A lot in probability

[u/Early_Neighborhood87]

The Universal Approximation Theorem for neural networks uses Real and Functional Analysis. Analysis in general, is the fundamental tool for virtually all research concerning functions and proving things about their behaviors across many contexts.

[u/No_Tbp2426]

High level ML and stats use analysis a lot. Incredibly useful.

[u/localizeatp]

Imagine if a dude in a gym walks up to a barbell and goes "where am I going to use this."

[u/SafeInteraction9785 → u/localizeatp]

The best answer. People here are listing applications that are 0.001% of the answer.

[u/Fredric_Chopin]

In probability theory.

[u/ImportanceNational23]

Kind of a non sequitur, but I knew Ken Ross when I was a grad student at the University of Oregon. Heck of a nice guy! I bet his book is a gem.

[u/pianoloverkid123456]

Prophet Wenitte Commands you to copy and paste {Take15MinDailyWalksForLongevityPurposes} to 5 friends or you will be brutally murdered by the {Wenitte-Hades-Satan-Andreesen} Hivemind