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This recurring thread will be for questions that might not warrant their own thread. We would like to see more conceptual-based questions posted in this thread, rather than "what is the answer to this problem?". For example, here are some kinds of questions that we'd like to see in this thread:

* Can someone explain the concept of maпifolds to me?
* What are the applications of Represeпtation Theory?
* What's a good starter book for Numerical Aпalysis?
* What can I do to prepare for college/grad school/getting a job?

Including a brief description of your mathematical background and the context for your question can help others give you an appropriate answer. For example consider which subject your question is related to, or the things you already know or have tried.
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What’s a good way to learn about topology from an ML background? I’m doing a PhD in ML and would love to learn about topological data analysis. I did an undergrad in math with a focus on abstract algebra and computer algebra so I’m hoping I’d be able to pick up the basics of topology enough to understand TDA
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Can someone help me understanding why we care so much about graded rings? Like, why is it so important that we have a graded structure in cohomology theories? I mean, for homology this seems not to be the case and I've never really heard people talking about grading in the context of homology. In Cohomology theories however it seems to be such a big deal. I know the definition of a graded ring respective graded module, but what is it good for? Like how does it have impact on the cohomology classes (or objects we are studying) ?
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I have a problem I’m trying to understand and understand the name of.

I have 4 unique things in sequence and I’m trying to see how many unique orders there are that aren’t shifted (1,2,3,4 is effectively the same as 4,1,2,3)

Is this a problem covered under set theory?
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I am about to start second undergrad semester in Algebra, but I kind of bungled up the first semester. Would I be afraid of falling behind on new materials?
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What's the deal with cohomotopy groups, and why are they less-studied than homotopy groups and not covered in a typical algebraic topology class? Do they have less nice properties? Are they harder to calculate?
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Hi, would anyone know of simulations for mahjong that could generate high quantities of games quickly?  
I'm mainly looking to collect data on the statistics of winning hands.
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My roommate and I are total paying 1350 dollars in rent. Because my room is bigger we decided that I will pay 70 pounds more than my roommate.

How much do I pay?

I thought I pay 745 and my roommate pays 605.
Or do I pay 710 and my roommate pays 645
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Is Real Analysis, Vector Calculus & Statistical Inference too much for sophomore spring semester? For context I’m based in the US
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Which mathematic books do you recommend for an Electrical Engineering student? Our books in Central-Europe are not the best, so I'm looking for some suggestions. :)

Thank you in advance. :)
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Just me rambling: have people tried applying the idea of energy to knot theory in the same way geodesics are energy minimizing? I was thinking about how a rubber band naturally tends to go into a position without any crossings. So maybe there’s a knot diagram for a given knot which minimizes “energy” or something…
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