I agree -- abstract algebra is elementary and some aspects of it can (and should), be taught in high-school. AA is a domain of maths which people won't even encounter if not studying a STEM field and such crash course could serve as a good outreach/vulgarisation material.
I really liked the materials in the link and think they are suitable for talented high-schoolers. Cox-Little-O'Shea is a fantastic book I studied as an undergrad and learned a lot from it, I wish someone would expose me to it earlier in life.
There's plenty of good math software for algebra which is not very popular (SageMath comes to mind as the most commonly used) and even more code that is simply inside knowledge. The problem is that people in the academia are not being paid for writing software but for publishing articles, even though the community value of a good package outweighs many papers. For example, good luck finding something that will compute non-commutative Groebner bases :)
During my maths phd time in France I really enjoyed so-called "colles". It was a 1h long 1 on 1 conversation with the student where (s)he was given a complex problem (way too difficult to simply solve in an hour) and a sequence of hints and smaller, easier tasks, leading to the solution. I would often help the interviewee when stuck/correct computations, let them follow the wrong path to make them realize why it was wrong and generally allow for unsupervised exploration of the task. Even though quite often students were not able to get to the end, or even close, I could get a decent idea about their knowledge and understanding of the matter. When I first did it, I instantly thought that's a good way to do a job interview -- being prepared and interactive, have a conversation instead of one way question-answer traffic.
The caveat: I needed to really think through the problems beforehand, understand other possible solutions, traps and potential dead ends (ie. spend time on it).
When a few years later I was asked to do some recruiting at my company (DS/R&D positions, not SE), first thing I did was to prepare a few sets of interconnected problems, to gauge the person's knowledge and how does (s)he think when encountering a new problem with all necessary tools at hand. The problems were difficult but I never expected anyone to actually solve them.
I did dome technical interviews as a candidate, being asked about random math puzzles/algos one can google in 30 sec and which are already implemented in standard libraries -- even though I usually could solve most of them I sincerely wish such interviewers would ef off and stop wasting my time. We are grown-ups, I already spent my fair share of time solving elementary riddles during high school math competitions and I'd like to be treated like a serious professional. During my years as a ML Engineer/dev I never EVER needed to implement a single tree/graph/whatever algorithm from scratch. Also, many adults have a life, family, other full-time job and grinding leetcode is not something anyone should be expected to do.
To be honest, quite a few times I doubted that the interviewer would know how to solve a similar problem without having the solution checked in company's interview problems database. Also, time pressure and stress are a buzzkiller.
As for multiple interview rounds -- a non-starter. Recently, while exploring the market, a top-tier betting company asked me to do a take home, 4h technical interview and then another long take-home (unpaid, of course). I told them that they are ridiculous and asked to never contact me again. I'm at liberty to do so as I have a job I'm happy with and zero need to actually change it, but if someone has been laid off I can see people get grinded to death -- both mentally and physically -- by such interview processes.
I really liked the materials in the link and think they are suitable for talented high-schoolers. Cox-Little-O'Shea is a fantastic book I studied as an undergrad and learned a lot from it, I wish someone would expose me to it earlier in life.
There's plenty of good math software for algebra which is not very popular (SageMath comes to mind as the most commonly used) and even more code that is simply inside knowledge. The problem is that people in the academia are not being paid for writing software but for publishing articles, even though the community value of a good package outweighs many papers. For example, good luck finding something that will compute non-commutative Groebner bases :)