kasdeya
kasdeya
whenever I try to read Math Things it’s always super cryptic and using normal words in vague and esoteric ways like “an algebra is a set of values, a set of operators that it is closed under and some laws it must obey” and I’m just like, okay I don’t know what most of those words are supposed to mean and I can’t google them but I at least know what an operator is and what a value is so I think I get the gist? “an algebra is when there are values and operators and laws are involved somehow”
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@kasdeya abstract algebra is what you want if you want to read more, but honestly you really don't, you got the gist of it. Basically it's defining the system that is being used, in a maths context.
Values being like, integers only, or all real numbers?
Do you use standard arithmetic, or modulo (like in coding), or how do you operate on the values in general.
And then how do you define edge cases, or anything you are taken as given.
We all have a pretty standard set of defaults, which is taught in algebra class. Like the commutative property, associative property, all of that. But that's our current understanding of how things work, that doesn't make it inherently true. So it can be useful to define/change the rules and system in theoretical mathematics, or when looking into things from a specific or restricted perspective.
It's more important on the theoretical side of things, especially in proofs. It is actually kinda like the maths version of declaring the dependencies for what you are about to read. I think some of learning to read maths stuff is learning all the stuff it is okay to skim to and come back to later if you need to, cause they really do like to be formal in how they state things. (I say, as I formally state...)
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@Shivaekul ooh okay so I did actually understand everything that I needed to about that! it’s good to know that abstract algebra is the thing to look up though if I run into this again. also this is interesting, and to be honest I really like the idea of math that is written in such a way that nothing is taken for granted like that. because I think a lot of math papers rely on implicit cultural knowledge within academia which I find frustrating
I think some of learning to read maths stuff is learning all the stuff it is okay to skim to and come back to later if you need to, cause they really do like to be formal in how they state things
ohh, interesting. I felt like I was doing something wrong by not understanding some (sometimes most lol) of the word choices in certain math things but I’m glad that that’s normal. and thank you for explaining all of this! it helps a lot
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@kasdeya I highly recommend "A transition to advanced mathematics" (Smith, Eggen, and St. Andre) if you want to start getting into more advanced/theoretical mathematics. I have the fourth edition and found it super helpful, both when working on my degree and even after. It breaks down the maths we know and gets into how it is constructed and why it works. Also super good on logic and proofs. Chapters 1-4 are really useful imo, and then it starts getting more theoretical and advanced.
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@Shivaekul ooh omg thank you! that is really good to know - I’ve actually been looking for some kind of book that would help me understand more advanced math stuff. I got a used college algebra book but I kinda chose that completely at random lol. it just sounded reasonably advanced but when I skimmed through it nothing looked like I wouldn’t be able to understand it
It breaks down the maths we know and gets into how it is constructed and why it works.
also this sounds amazing to be honest. I’ve always wanted a ground-up approach to math like that, instead of “memorize these axioms and formulas”
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