Hey everyone,

I'm struggling with understanding mathematical proofs in research papers. I have a good grasp of basic concepts such as calculus (single variable calculus and basic knowledge of multi-variable calculus), linear algebra, and basic probability.

I was wondering if any of you could recommend some sources (preferably videos or lecture series) to help me become more familiar with advanced mathematical concepts found in research papers.

For example:(source)

https://preview.redd.it/m19pwqkwkdna1.png?width=1104&format=png&auto=webp&v=enabled&s=5cb83feec7e92d4e7f991f7c22cda8483c39c377

In papers, I have frequently encountered concepts like, KL divergence, mathematics in higher-dimensional space, hessian, topology, Random projections and many more;What are the subject/module names I need to study to confidently read and understand proofs in papers?

Thanks in advance!

Comments

You must log in or register to comment.

Nerveregenerator t1_jbzo0x3 wrote on March 12, 2023 at 11:27 PM

#2,217,212

Do problems involving the equations on paper and also read and copy down articles that are written on them.

RoboiosMut t1_jc00wmj wrote on March 13, 2023 at 1:06 AM

#2,217,795

I have an idea, maybe ask Chatgpt to make some stories to explain those abstract concepts

deephugs t1_jc0lhog wrote on March 13, 2023 at 3:54 AM

#2,218,612

First try and understand every symbol in the equation, there are cheat sheets online. Second, most math concepts have a wikipedia page you can read, go down those rabbit holes and sooner or later you will find common threads and start to build an understanding. Finally, just put the time in, math is like everything else and just takes lots and lots of practice.

amhotw t1_jc0mf55 wrote on March 13, 2023 at 4:02 AM

#2,218,639

If you are serious, I would recommend working on Rudin's Principles of Math Analysis. It might take a day (or more...) to wrap your head around a single proof but at the end you'll be ready to read anything (of course you might need to check some definitions.)

For KL divergence, entropy etc., Info Theory book by Mackay is great.

For hessian, well it is just calculus; the second derivative of a multivariate function. To understand its uses, you would need some understanding of numerical analysis and concave programming. For the latter, Boyd's optimization book is a classic. I don't remember a good book on numerical analysis but some diff. eqn.s books have nice chapters on it.

nirnamous OP t1_jc0mvz9 wrote on March 13, 2023 at 4:07 AM

#2,218,660

Replying to amhotw (#2,218,639)

Thank you very much.

Your comment is very helpful.

I'll refer these sources.

nirnamous OP t1_jc0n7vx wrote on March 13, 2023 at 4:10 AM

#2,218,672

Replying to amhotw (#2,218,639)

Just asking (Not trying to offend you or anything)
Why you asked whether this is serious ? Are above are very basic things ?

amhotw t1_jc0r0nn wrote on March 13, 2023 at 4:48 AM

#2,218,785

Replying to nirnamous (#2,218,672)

I just meant this would take significant amount of time. I think it is impossible to do research in a quantitative field without understanding these so I would say it is well worth the investment. But most people are not concerned with research or even understanding the methods.

GufyTheLire t1_jc3evhf wrote on March 13, 2023 at 7:24 PM

#2,222,325

Replying to RoboiosMut (#2,217,795)

I've tried that once. Asked ChatGPT why L0, L1.. Ln norms, so seemingly different, were all named in a similar way. It correctly listed the norms' definitions and use cases, but failed to generalize the concept and made up some bullshit reason why they are named like that. Took me some time down the Wikipedia and Google rabbit hole to find out about Lp spaces and substitute different p values in the definition of p-norm to get the real reason

RoboiosMut t1_jc3ptw7 wrote on March 13, 2023 at 8:34 PM

#2,222,768

Replying to GufyTheLire (#2,222,325)

How about show this reference to chatgpt and ask again?