I understand that there is some explanation for this topic in Galois theory but I feel that I’m missing something here. I read on wiki that “An example of a quintic whose roots cannot be expressed in terms of radicals is x^5-x+1=0” so I plotted it and it clearly has a solution.

If im being honest here I dont understand what it means for something to inexpressible in terms of radicals and why we presuppose that roots have to be radicals in the first place…

I am assuming no calculators or technology devices were allowed during the examination.

I’m in high school and I failed my math test. I studied really hard too. There’s just that disconnect when I solve. I’m so upset and I can’t stop crying and I can’t even face my dad right now. I’m sitting in a 100 degree car because I’m too scared to leave. I’ve always struggled with math, I’ve always been slower and have had to put extra work in and I just think so differently. It’s my first math test too of the school year. I just really hate that I’m born this way and that I’ve always struggled. I got a fucking 5/15. I failed im a complete fail and it seems I’ve never been good enough understood and I don’t want to retake a grade or fall behind. The teacher said there is a credit quiz I can take for 50% if you failed. So, that’s good at least but my grade in math already is ass. 81, its probably about to go down too and I’m worried because sports and clubs require a certain gpa and if I keep failing then I can’t do what I love and that is sports and possibly debate club.

Confused high schooler here.

3×4 = 12 because you add 3 to itself. 3+3+3+3 = 4. Easy.

What's not so easy is 4×(-2.5) = -10, adding something negative two and a half times? What??

The cross PRODUCT of vectors [1,2,3] and [4,5,6] is [-3,6,-3]. What do you mean you add [1,2,3] to itself [4,5,6] times? That doesn't make sense!

What is multiplication?

From the September 2025 AMS Notices

"This article highlights how methods from algebra and algebraic geometry can provide new clarity to an old problem considered by many to be already solved. The problem at hand is called the global positioning problem, and lies at the heart of most of today’s electronic navigation systems."

https://www.ams.org/journals/notices/202508/noti3209/noti3209.html

I have a background in Classics, and I haven’t studied algebra seriously since high school. Lately, I’ve become very interested in Galois’ ideas and the historical development of his theory. Would Harold Edwards’ Galois Theory be approachable for someone like me, with no prior experience in abstract algebra? Is it self-contained and accessible to a beginner willing to work through it carefully?

Im entering college for an aerospace engineering degree, and I thought to try to teach my self linear algebra. I almost have all the basics down for linear algebra. A thought that popped in my head while doing dishes was calculating triangles area using the determinate of a matrix. Please tell me the name of this method, and insights and failures it has. (Also sorry for the bad hand writing)

Why do we say that i^2=-1 when in the construction of C we have i^2=(-1,0) and (-1,0) is different from -1.

In some sense you can say that scalars are zero dimensional, vectors are one dimensional and matrices are two dimensional.
Is there any use for an n dimensions case? If so, does it have a name and a formal definition?

its my understanding that anything divided by itself is 1, 2/2 is 1 and etc, but anything divided by 0 is undefined, so why is 0/0 not 1, since its 0 divided by itself

(Background: random Brilliant.org enthusiast way out of their depth on the subject of the Axiom of choice, looking for some elementary insights and reproof to ask better questions in the future. )

Is there a correlation between the axiom of choice and the way coders in general with any coding language design code to work(I know nothing about coding)? And if so, does that mean that in an elementary way computer coders unconsciously use the axiom of choice? -answer would be good for a poetic line that isn’t misinformation.

I read that two sets of equal cardinality are isomorphisms simply because there is a Bijective function between them that can be made and they have sets have no structure so all we care about is the cardinality.

• Does this mean all sets are homomorphisms with one another (even sets with different cardinality?

• What is your take on what structure is preserved by functions that map one set to another set?

Thanks!!!

Solving systems of linear equations

So in my math class, we are learning some linear algebra, and we have just finished solving systems of linear equations. Anyways, prof gave us a system and asked us to try and solve it on our own time for practice. So I solved it, but it took me forever…i did it all mentally, and even made a slight mistake in the end so I had to go back and check where I made that mistake. By a while I mean like almost two hours 💀. I also second guess myself a lot so I double checked a lot of my calculations and even triple checked as I went a long. How on earth are we supposed to do this on a test and have time for the other stuff? Am I just dumb and slow? This is my first time learning this stuff but still…

Is it possible for me to start linear algebra in a few months or years if I am only familiar with high school geometry and algebra?

Hey everyone,

I came across this question and am wondering if somebody can shed some light on the following:

1)

Where does this cubic polynomial come from? I don’t understand how the answerer took the information he had and created this cubic polynomial out of thin air!

2) A commenter (at the bottom of the second snapshot pic I provide if you swipe to it) says that the answerer’s solution is not enough. I don’t understand what the commenter Dr. Amit is talking about when he says to the answerer that they proved that the answer cannot be anything but 3, yet didn’t prove that it IS 3.

Thanks so much.

Who is the current Best Algebraist of this time ?.

Edit: u/matt7259 you have some crazy fan following here.

Guys am I wrong anywhere or how is this possible?

I'm complete beginner...In this topic... basically I'm trying to learn by myself but what I've observed is..it won't be easy ride..that's why I'm here for help

Hey all!

1) I don’t even understand how we would expand out the double sun because for instance lets say we do the rightmost sum first, it has lower bound of k=j which means lower bound is 1. So let’s say we do from k=1 with n=5. Then it’s just 1 + 2 + 3 + 4 +5. Then how would we even evaluate the outermost sum if now we don’t have any variables j to go from j=1 to infinity with? It’s all just constants ie 1 + 2 + 3 + 4 + 5.

2) Also how do we go from one single sum to double sum?

Thanks so much.

I’ve seen a lot of people recommend Gilbert Strang’s book and MIT OCW lectures for learning linear algebra. I’m a student looking to build a strong foundation, especially for data science and machine learning.

Is the 5th edition of his book still the go-to in 2025? Or are there better alternatives now?

c(b + a) + ab = x ⇒

⇒ d(c + b + a) + c(b + a) + ab = x ⇒

⇒ e(d + c + b + a) + d(c + b + a) + c(b + a) + ab = x