Math thread

Yotsubaaa said:
What do you mean? In the video he has the formula:
View attachment 1828855
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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Oh thank you, I must have misread what you wrote.
 
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So I'm thinking that Trig isn't enough for me, I'd like to learn all fields of math. Is there any good research material / textbooks / tutorials that teach all of it? @AnOminous mentioned once that he didn't truly understand Algebra until he read Isaac Asimov's book on it, and there's Khan university which I've heard is dogshit but I would like a second opinion of it. I'm reading entries on Wikipedia on math subjects but the articles all seem to have misspelled words.
 
MarvinTheParanoidAndroid said:
So I'm thinking that Trig isn't enough for me, I'd like to learn all fields of math.
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Good luck.
1911cf883961eec7b5480e104ff85e04.jpg
(And that's not even exhaustive.)

MarvinTheParanoidAndroid said:
Is there any good research material / textbooks / tutorials that teach all of it? @AnOminous mentioned once that he didn't truly understand Algebra until he read Isaac Asimov's book on it, and there's Khan university which I've heard is dogshit but I would like a second opinion of it.
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I think I've posted this blog before:

How to Become a Pure Mathematician (or Statistician)

a List of Undergraduate and Basic Graduate Textbooks and Lecture Notes - the blog
hbpms.blogspot.com hbpms.blogspot.com
It's basically an overview list of the different areas of mathematics that you'd be subjected to see during a typical Mathematics/Statistic undergrad degree, complete with links to recommended textbooks and free resources. Probably read it with a grain of salt (I very much doubt that the author actually read/worked through all of those books the way he's implying that he did), but as a sort of roadmap for where you want to head it's pretty useful.

Khan Academy is okay for anything at the basic Calculus/PreCalc/Statistics/Probability level (i.e. the stuff they teach in late high school/early college). Those people have always been Sal's target audience.

MarvinTheParanoidAndroid said:
I'm reading entries on Wikipedia on math subjects but the articles all seem to have misspelled words.
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Ignore Wikipedia for the most part. Most of the mathematics/science articles on Wikipedia are written in an embarrassingly terse and intimidating manner, by people who think they're a lot smarter than they actually are. It's pretty much a joke.
 
Yotsubaaa said:
Good luck.
View attachment 1829506
(And that's not even exhaustive.)


I think I've posted this blog before:

How to Become a Pure Mathematician (or Statistician)

a List of Undergraduate and Basic Graduate Textbooks and Lecture Notes - the blog
hbpms.blogspot.com hbpms.blogspot.com
It's basically an overview list of the different areas of mathematics that you'd be subjected to see during a typical Mathematics/Statistic undergrad degree, complete with links to recommended textbooks and free resources. Probably read it with a grain of salt (I very much doubt that the author actually read/worked through all of those books the way he's implying that he did), but as a sort of roadmap for where you want to head it's pretty useful.

Khan Academy is okay for anything at the basic Calculus/PreCalc/Statistics/Probability level (i.e. the stuff they teach in late high school/early college). Those people have always been Sal's target audience.


Ignore Wikipedia for the most part. Most of the mathematics/science articles on Wikipedia are written in an embarrassingly terse and intimidating manner, by people who think they're a lot smarter than they actually are. It's pretty much a joke.
Click to expand...
Oh yeah thank you for that, I forgot about this.
 
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What's the best way to make sure I'm actually remembering what I'm studying in my Math class. I'm worried I'll forget everything when the test rolls around.
 
If the Milky Way galaxy was 1 mm across, 1 million light years would be a centimeter. The Andromeda Galaxy would be about 2 cm away, and the huge fuzzy golden egg galaxy of IC 1101 would be about 4 cm across and about 10 meters away (1 billion ly). The edge of the observable universe would be about 465 meters away.

If 10 light years was 1 mm, this galaxy would be about 10 meters across, and about 10 centimeters thick (aside from the central bulge). This solar system would be a little speck, and the nearest star would be less than half a millimeter away. The central black hole would be about 3 meters away, and globular clusters around the galaxy would be around a centimeter wide.

(metric is so much easier to work with)
 
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Back in high school we lads liked to joke around about having a math debating club. Some 300 IQ level wits, we were.

The maths I liked were non-Euclidean geometries and polar roses.

Also, doing real analysis makes you feel like a god, it's like climbing a mountain going from just doing calculus (which is more than the vast majority of the population will ever do anyways) to deriving the proofs of it.

Rose-rhodonea-curve-7x9-chart-improved.svg.png

300px-Circle-limit-IV.jpg


I was never particularly good at arithmetic and had no awareness of potential at mathematics. Symbolic reasoning, though - the whole basis of proofs - went well. Only went into it because I found out that if I wanted to go to grad school in my field it required much more intense math than the undergrad did. After succeeding in that, realized I had potential in science, programming, engineering, just never knew it. Really regret that, but because of it I greatly value my Math major, forced me to learn how to actually work at something and learn my potential.

I've thought about revisiting non-Euclidean, because it was one of the things I worst at, and history of mathematics (wanted to take but it didn't fit in), but compared to just reading more history it really is a huge effort. I also never actually learned Euclid either, my college passed straight over Euclidean geometry entirely (so my geometry is actually pretty shitty).

MarvinTheParanoidAndroid said:
So I'm thinking that Trig isn't enough for me, I'd like to learn all fields of math. Is there any good research material / textbooks / tutorials that teach all of it? @AnOminous mentioned once that he didn't truly understand Algebra until he read Isaac Asimov's book on it, and there's Khan university which I've heard is dogshit but I would like a second opinion of it. I'm reading entries on Wikipedia on math subjects but the articles all seem to have misspelled words.
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If you're still looking into it, learn Set Theory. Modern math proofs are all written in set theory, it's the logical framework for everything we do. (Modern economics is also written up in set theory too, it's literally a discipline of mathematics where everything is given formal definitions in set theory and functions so you can express it without even using words.) Chartrand wrote the textbook I learned from, which just teaches set theory, mathematical logic, and several proof concepts that come out of the two (how to construct a contrapositive, how to prove by induction, etc.).
 
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Not a bee said:
i think it's on a line
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It's an inequality so it actually covers a region of a graph.
xy > 1
Can be put into the form:
y > (1 / x)
Which will look similar to the graph of y = (1 / x), except it will be a dotted line indicating that those values aren't included, and will include the region of y values grater than that graph.
Here is my extremely bad attempt at drawing this in paint. The red dotted lines show the asymptotes for y = 1/x. The blue dotted lines show the graph for y = 1/x. The blue "shaded" regions show the part of the graph covered by y > 1/x.

Screenshot 2023-02-14 014100.png
 
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Sorry for necro. Pls no bully.

I am trying to internalize the sum and difference angle formulas using this derivation:
1702420031919.png
I understand everything about this image except for one thing: where does it follow that angle α from triangle DEF is equal angle α in triangle ACE? Everything hinges on those two angles being equal and I just don't follow. Here's the original for reference.
 
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Friendly Primarina said:
Sorry for necro. Pls no bully.

I am trying to internalize the sum and difference angle formulas using this derivation:
View attachment 5561423
I understand everything about this image except for one thing: where does it follow that angle α from triangle DEF is equal angle α in triangle ACE? Everything hinges on those two angles being equal and I just don't follow. Here's the original for reference.
Click to expand...
Since ABF is a right triangle, the angle AFB is 90-(alpha+beta). Since AEF is also a right triangle, the angle AFE is 90-beta. Angle AFE = Angle AFB + Angle DFE, so 90-(alpha+beta)+Angle DFE = (90-beta) and Angle DFE = alpha.
 
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