Math thread

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I wish I was good at math. My teachers were always dicks so I never caught on, but I would like to get back into it and 'learn it right' so to speak. Is there a linear hierarchy in mathematics or are they all considered parallel in terms of required understanding? I know that trig is required for calculus but that's about it. What is the most streamline route is what I'm asking.
 
MarvinTheParanoidAndroid dijo:
I wish I was good at math. My teachers were always dicks so I never caught on, but I would like to get back into it and 'learn it right' so to speak. Is there a linear hierarchy in mathematics or are they all considered parallel in terms of required understanding? I know that trig is required for calculus but that's about it. What is the most streamline route is what I'm asking.
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There isn't a linear hierarchy as such. The mathematics that you and I are capable of understanding isn't so much about solving equations or formulae so much as it is what you can define, what you can take for granted and what you can deduce consequently. What I would recommend doing is trying to get a hold of some undergraduate mathematics lecture notes and read through them in your own time. See if there's someone you know at a university that hands out paper notes and get them to scoop you up some or get them to send you their pdfs. I'd do it myself but I don't want posts to identify me really well on this website, if you understand.

Balliol College Oxford has a good reading list too for people that get invited to interview. My favourite book out of all of them though is Journey into Mathematics: An Introduction to Proofs. It's not the best book, especially once you've gone to university for this stuff but it is without a shadow of a doubt the best book for people who want to restart their maths study I've ever seen. It's best read in the context it gives at the beginning, as a textbook for some course that some guy is doing on Proof and Mathematical Foundations. I'd also recommend Algebra and Geometry, An Introduction to Linear Algebra, Beyond Infinity and In Pursuit of the Unknown. The first and second ones are good university-level textbooks that I still go back to just because they're REALLY good for foundational knowledge and the other two are pop-maths books that are not cringe and are quite based that go over how we define infinity and the history of mathematics and its contemporaneous place in the world in 17 equations respectively.

Dm me or anyone else with a big brain in this thread though if you want some more direct maths help or just post some stuff in this thread here. I love this shit AND I love physics too and as someone in that position I can tell you that we're fucking dying to talk about this stuff.
 
I suck dicks for double posting yes
Cyclonus dijo:
In daily life and in 90% of jobs you don't need anything more than the basic maths you learnt in primary school. But if you fail maths you're going to end up sweeping streets. The whole education system is fucked up.
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The best thing you can do is practice. Pre-university mathematics, at all levels, is all about practice. Practising times tables, practising prime-number factorisation, practising problem solving, practising line construction, practising loads of stuff that once you're at uni you do so little of you actually start to forget some of it. Most people in this thread will have done Calculus at some point in their life. I know a guy who got over 90% average in the second year of his Mathematics Course and has forgotten how to integrate most trigonometric functions. Not even people who do undergraduate mathematics do your maths anymore, the value of those courses coming from the students surreptitiously developing very powerful problem-solving skills and highly abstract isomorphising and homeomorphising abilities, as well as programming abilities standard to most contemporary STEM courses. You hit the wall of antiquation with this material very quickly. There is an argument to be made that to get on these courses in the first place, you should have an instinctive understanding of the objects and realms of study discussed and that the system is geared towards that. You're then assuming that everyone wants to be a mathematician whilst everywhere from this very thread to Radio, TV and the internet at large you'll see most of everyone saying how much they hate maths.

If I became education minister in the UK, the first thing I would do is get kids taught the ACTUAL basics, the actual things that you learn at good universities as the commonly accepted axioms of mathematics and go from there and go very slowly. By the time they turned 13, they could probably derive the Fundamental Theorem of Arithmetic like it' s nothing, meaning that come 17-18 they would know just about everything on the 1st year of any solid maths course currently taught. Universities could then hit more material and pre-university students can get some of the actually sought-after skills from maths degrees without having to do a maths degree and the keen bastards who want to do a maths degree have a fantastically firm grounding. It would take years but of course it would, people bitch about this all the time and kids lives can actually be ruined if they don't do the intellectual equivalent of balancing a ball on their nose for the ringleader, of course it would take years to solve a problem like that.
 
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Construct a formula using basic algebraic operations only (addition, multiplication, powers, modulo) using real number representations to calculate the addition of any two elements in GF(3), the two elements may be identical or different
 
SageInAllFields dijo:
Construct a formula using basic algebraic operations only (addition, multiplication, powers, modulo) using real number representations to calculate the addition of any two elements in GF(3), the two elements may be identical or different
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Remind me what GF(3) is?
EDIT: I suck dicks, I know what it is now. Give us a second I need to bathe.
 
I thought I lost these. So I'll keep them here here.
1572775736623.png
1573015257706.png
 
So I decided to try my hand at learning Trig and found this nifty little video.
But then at the 13:38 mark he pulls out a calculator to solve how to convert tangent 43 degrees to meters. Real helpful. Does anyone know how to do that without a calculator?
 
MarvinTheParanoidAndroid dijo:
But then at the 13:38 mark he pulls out a calculator to solve how to convert tangent 43 degrees to meters. Real helpful. Does anyone know how to do that without a calculator?
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If you'll allow me to math-sperg for a bit:
  1. He's not "converting tan(43°) to meters", he's calculating the value of tan(43°), which is a dimensionless quantity.
  2. Calculating the value of tan(43°) is actually pretty involved, and most people historically just used tables for this sort of thing:
    425px-Bernegger_Manuale_137.jpg
    i.e. he'd just go look up what 43° corresponded to in the 'tangent' column of his trig table and use that value (the table here puts it at 0.9325).
  3. "But then how do they get the values for the tables?" Very tediously. Historically they'd use trig identities like the half-angle formulae:
    ql_28d345d08d4994a229442c7c40297fea_l3.png

    and the addition formulae:
    ql_a41717a7792ae34c4053731d58234444_l3.png

    Those get you the values for sine and cosine (where you'd start from the geometrically well-known angles, like sin(45°)=√2/2, and then successively divide those as much as you want to get the other values, possibly interpolating along the way). Then the tangent column is straightforwardly calculated using:
    ql_3f5b2d070425605b0b69d0589cd77948_l3.png
 
Yotsubaaa dijo:
If you'll allow me to math-sperg for a bit:
  1. He's not "converting tan(43°) to meters", he's calculating the value of tan(43°), which is a dimensionless quantity.
  2. Calculating the value of tan(43°) is actually pretty involved, and most people historically just used tables for this sort of thing:
    Ver archivo adjunto 1828797
    i.e. he'd just go look up what 43° corresponded to in the 'tangent' column of his trig table and use that value (the table here puts it at 0.9325).
  3. "But then how do they get the values for the tables?" Very tediously. Historically they'd use trig identities like the half-angle formulae:
    Ver archivo adjunto 1828820
    and the addition formulae:
    Ver archivo adjunto 1828829
    Those get you the values for sine and cosine (where you'd start from the geometrically well-known angles, like sin(45°)=√2/2, and then successively divide those as much as you want to get the other values, possibly interpolating along the way). Then the tangent column is straightforwardly calculated using:
    Ver archivo adjunto 1828814
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So then how do you come out with an actual number?
 
MarvinTheParanoidAndroid dijo:
So then how do you come out with an actual number?
Presiona para expandir...
What do you mean? In the video he has the formula:
ql_5ab0e1d25c183f9cc9e12ddcd93869f5_l3.png

Computing tan(43°) gives you 0.9325, which you multiply by 22.5(meters) to get your answer (which will be in meters so that both sides of the equation have the same units of meters).
 
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