Why is abstract algebra more coherent and intuitive than linear algebra?
implied definitions, human brains comprehend patterns, mechanic operations is more energy intensive
>>16910908Linear algebra is way more coherent wtf
>>16910908because linear algebra is built on abstract algebra? It's like asking why machine language is more intuitive than C++
>>16910908What's so difficult about linear algebra?I'm a literal midwit, might even be a fucking retard, but i don't find anything unintuitive regarding linear algebra Systems of linear equationsMatricesDeterminantsVector Vector SpacesEigenvalues and EigenvectorsWhat's the problem?
>>16910924Actually a fairly well reasoned explanation.
>>16911000The list you've given is a good first year undergrad course on linear algebra. That's where the topic starts, not where it ends.
>>16912415Literally every area in mathematics is unintuitive and difficult to understand when you get to the "where it ends" point.When people say X is harder than Y they're taking about the beginning, not the end
>>16910908Linear algebra is a subset of algebra, and vector spaces form just about the nicest category you could ever ask for, you stupid nigger.
>>16912495>Literally every area in mathematics is unintuitive and difficult to understand when you get to the "where it ends" point.Abstract algebra doesnt have one.
>>16910908Linear algebra is a lot more specific and applied. It involves doing actual calculations of useful quantities. This is naturally a bit more work than flogging yourself off about groups and such.
>>16910908I would argue this is probably a symptom of the linear algebra course you took or the book you used to study. There is a very real sense in which linear algebra is the *only* cohesive, intuitive field of math. So much so that often the main goal in solving certain other math problems is to turn the problem into a linear algebra problem, solve it in the linear algebra world, then turn the solution back into one that fits the original domain.
>>16913920>There is a very real sense in which linear algebra is the *only* cohesive, intuitive field of mathElaborate
>>16914610Every other category is pretty much described by how similar it is to vector spaces, and what the differences are.
>>16910908Abstract algebra is just discrete math.
>>16914702This sounds more like it's something you've encountered as someone coming from a domain dealing primarily with linear algebra.
>>16910908Is it?
>>16914933>a domain dealing primarily with linear algebra.You mean math?
>>16910908When I was a kid I remember realizing that no matter which order I picked 3 elements, I would end up with a cycle (either forward or backwards) after repeating the pattern indefinitely. I realized that this same pattern corresponded to rotating a triangle. I remember also realizing that if I had a collection of 4 elements, that this same logic didn't apply: there was something different about the way 4 "worked" I figured. I was like, 10 or so when I realized this kind of symmetry property, and didn't think about it again until I took 1st year abstract in uni.What I'm trying to say is that I think there's something really intuitive about thinking about symmetry as a set of elements that act upon themselves via some sort of process. Linear on the other hand isn't obvious in the same way. There's no reason you would ever really develop any intuition behind linear if you were just sitting around thinking about random shit, but with abstract the ideas are very natural and apply very naturally to our day to day lives.
>>16915180No, I think he means you are falsely equating "math" with "linear algebra" because you are a fucking delusional schizophrenic nigger.
>>16914712
somne of the proofs in linear algebra felt a little weird and harder to come up than abstract, like in spectral theory
>>16915461>you're equating...I'm not, you retard.
no, it isn'thttps://www.youtube.com/watch?v=ohDB5gbtaEQ
the trick is to learn it in your spare time
"Well, er, yes Mr. Anchovy, but you see your report here says that you are an extremely dull person. You see, our experts describe you as an appallingly dull fellow, unimaginative, timid, lacking in initiative, spineless, easily dominated, no sense of humor, tedious company and irrepressibly drab and awful. And whereas in most professions these would be considerable drawbacks, in linear algebra they are a positive boon."
>>16910908>more coherent as if there were degrees of being coherent.
>>16918371there are if you're not autistic
>>16918571yes, yes, great comeback. now show me a definition of coherence that admits gradations.
