Comment by 🗡️ The_Jackal
Re: "I have another math question, and it's if this introduction…"
@jsreed5 Oh, thank you for clarifying. I made it this advanced because given my memory I wanted to put as much info as I could for myself that I could handle in that introduction and clear things up for myself I might wonder if I come back to it, like the definitions listing it as 'coeffecients multiplying variables exponentiated by nonnegative integers'. The implied x⁰ and x¹ made sense to me, so I included it for myself. I'm writing them like this because I should be half way through college, but I don't even have a GED yet (I never made it past 8th grade math and I'm wondering how far I even went into that), and I want to be an electrical engineer and maybe look into some chemistry. That's a LOT of catching up to do.
With that said, do you have any suggestions on how I could get what I wrote across but more concise?
Feb 03 · 3 months ago
7 Later Comments ↓
👻 darkghost · Feb 03 at 16:12:
I have some chemistry in my background. You don't need very advanced math to do it for the most part. Algebra gets you far, statistics helps, and things like calculus can help with things like rates and integration for areas under curves, but once you get to calculus you're using a computer for everything anyways.
🗡️ The_Jackal [OP, Weapons dealer, possibly mutant killer] · Feb 03 at 16:33:
@darkghost I had wanted to try getting some nuclear physics alongside the electrical engineering, but I doubt there's colleges or universities around me that would offer that, so I went back to the idea of chemistry. This isn't all just because I think I might get a high paying job, I got tired of not really knowing anything and wanted to 'pursue knowledge'. Specifically with a main focus in digital electronics like computers, all about the hardware, software, etc. and maybe something like chemistry or physics. Studying reality itself would be interesting to me. I'm also trying to build a foundation in math for all of this, and so far Khan Academy and random bits of searching on the topics are the best I have right now. I know some good textbooks would be better. I just hope this can prepare me for the GED, because math was always my weakest skill.
👻 darkghost · Feb 03 at 17:31:
Understanding how things work is the number one way to avoid being scammed. But it helps in everyday life as well. A study course focused on the GED will be most beneficial for passing the GED and the other skills will help you beyond it. After the GED, some leading universities have free courses online such as Stanford and Harvard with the option of paid certificates of completion. They're not degree programs but they'll help level up skills, maybe help you find a passion. My 2 cents as an internet stranger.
🗡️ The_Jackal [OP, Weapons dealer, possibly mutant killer] · Feb 03 at 17:38:
@darkghost Thank you. I do have a book on the GED and found a website for getting ready for the GED, but I'm so far behind in math I really should catch up with something like Khan Academy and take notes like I'm doing beforehand. Speaking of calculus, it's like how I'd always use a calculator for something like 343 times 567. I'll use a calculator, but I still want to understand the concept behind it and probably be able to do it with enough time if I did it on paper/didn't have a calculator or program for it. I'd also like to try keeping a notebook for myself that goes as indepth as I can in a way I can understand for myself, and then probably use other notebooks to have notes that might simplify them out for me, but that's for much later. I only have the one book for now, but it's messy and will definitely need redoing in anotner book later. My main worries when I write a note like I did in this post is if I just got it blatantly incorrect or got a small detail wrong that could bite me in the ass later.
🗡️ The_Jackal [OP, Weapons dealer, possibly mutant killer] · Feb 03 at 23:37:
@jsreed5 I wondered after this, if I were to correct the part about finite terms, would there be anything left that's incorrect? I went ahead and corrected the part about 'coeffecients of variables raised to powers' but left the section regarding x⁰ and x¹ in for myself if I come back confused after sometime and see that as a definition before looking at my notes, because when I first searched I would see definitions like that. So far if I were to summarize it, would 'A polynomial is an algebraic expression which is a sum of terms that only contain the operations of addition, subtraction, multiplication, or exponents. It cannot have negative numbers, variables, fractions, or mixed numbers as exponents nor include the radical sign (square root symbol) or division by a variable' be correct? Excluding a short introduction to degrees, at least. After doing some looking around, I found something about the 'power series' which I heard had things called polynomials but weren't quite polynomials like the ones you're introduced to in introductory algebra.
omg no, don't listen to the infinite guy, polynomials are finite, for the infinite stuff they have a separate name "power series", cause those abominations are so far removed from actual polynomials that it's not funny anymore.
Your stuff is totally correct, I just meant that it's too much information for an intro, like if you were writing a book or something, but if it's notes for an exams it all makes sense. Exams test breadth instead of depth, otherwise most people would fail them and the all them institutions would make no money.
Polynomials are extremely basic, and you can define them with just addition and multiplication and that's all you need to understand them. If it were me, I might've even defined multiplication to really drive the point home how basic we are talking. Now actually putting that on paper in a way you could fight an examiner over its correctness, that's some hard work (and you would need to fight, cause you would get bashed just for going out of line), so yeah, better stick with what you've got there.
👻 darkghost · Feb 04 at 10:12:
Agreed polynomials are pretty simple. They're purposely scope limited to be the format of (number)(variable)^(integer exponent) + (number)(variable)^(integer exponent) + (repeat this pattern a finite number of times)
2x + 4x² + 5x³ + 2x⁴ + 9x⁵ + 5x⁶ - 3x⁷ - x⁸ is an example.
Original Post
I have another math question, and it's if this introduction to polynomials I wrote for myself is any good. The things in parentheses like (positive whole numbers) are for later if I come back to do a quick read-through given my less than stellar memory. A polynomial (from the Greek word poly, meaning many, and the Latin nomial, meaning names or terms) is an algebraic expression which consists of variables (also referred to as indeterminates) and coefficients that only involves the operations...