/lit/ - Literature

>>14215557
Apostol Calc

i dunno lol

If you're serious about learning math, specially after being out of school for a long time, you should go to Khan Academy. I'm not even joking. Go there, start with the basics: basic geometry, basic arithmetic, basic algebra. Then, little by little, make your way up the ladder until the platform can't offer you much else. When you've learned this basic stuff, then you can get a textbook or something. But you can't learn calculus without trigonometry, for example, and you can't understand trig if you don't know geometry and you can't do basic algebra.

>mathematics

>>14215557
I’m more or less in the same boat as you and didn’t find it useful. It’s more philosophical than what you need at this stage I think.

>>14215619
Mathematics is the purest form of philosophy and the humanities.

>>14215627
What do you do all day?

>>14215636
I don't agree but shitting on it would be brainlet tier nonetheless; it's great but it's different

>>14215613
this is good advice
t. maths graduate

>>14215655
Fix math so that factorization isn't reliant on guesswork.

>>14215613
Ill check this out. Also Is elements any good? Or is it outdated?

>>14215665
it isn't, strictly speaking. but a radically improved algorithm for prime factorization would destroy the security of the digital world as we know it

>>14215636
cope

>>14215688
Holy shit

>>14215688
that took me a second, fuck.

>>14215688

>>14215688
NOO STOP IT CANT BE
HOW WILL I JUSTIFY CUTTING THROUGH THE DIAGONAL OF TRAFFIC INTERSECTIONS NOW?!?!?!??!
AHHHHHHH

>>14215596
While Apostol's is an excellent book, it's probably among the hardest book relative to its level (all content expected to be covered during the first semester in college).

Also, his definition of integrals helps to show the relative independence of differential and integrals, but it's counter-intuitive.

I think Spivak did a better job.


>>14215613
Also MIT Opencourseware.

>>14215671
Elements by Euclides? It's not exactly outdated, but you can find the very same contents better explained in new books.
As time goes by, old discoveries are understood better and people need less time to explain them. New geometry books will cover the same content than Euclides in less pages and better.

If you want to read a book I'd pick something of linear algebra. It's simple and more interesting than calculus which you're already familiar from high school.

>>14215688
>What are absolute values?

Is this any good?

>whitehead
how come nobody has posted it?

>>14215557
I did terrible in high school, then subsequently joined the military. After fucking around in uniform for around 9 years, I decided to get out and go to college to become an engineer. I started (re)learning basic algebra at 28.

I’m 31 now and am attending an excellent engineering university, so there’s hope. Khan Academy is awesome. Also, I took a math placement test at my local community college before transferring to uni. They used this placement testing/software called ALEKS. Essentially, you go in and just bomb the test. You are then assigned custom modules that aim to improve your weak areas. You can take the test up to five times, each time aiming to improve your placement. I’d see if your local CC has something like that. If not, Khan Academy by itself is wonderful, so long as you’re willing to put in the work.

Also, college is great because of all the beautifully tight vagina. I come to /lit so I can figure out what is popular amongst the 19 year old marxists, so I can fuck their potential girlfriends. Feels good.

bump

>>14215683
Nah. We'd be quick to switch over to lattice-based methods.

>>14215688
What did he mean by this

>>14217271
Brainlet. He's saying that he likes right triangles. Not "wrong" triangles.

>>14217249
Interesting. Do you have any recommended reading on lattice-based methods. And are there any crypto-currencies using this that you're aware of?

>>14217271
2222 what this means?
i^2+1^2=0^2
-1+1=0
The triangle can't exist
What's so funny?

>>14215688
WHAT THE FUCK DOES THIS MEAN

>>14215688
Can /lit not grasp high school algebra/trigonometry?

>>14215688
we realize this is literally imaginary, and does not exist anywhere? Like I know its cute that it is a 'triangle' but its literally not a triangle. So therefore we can't just fucking use the pythagorean theoram on 3 random numbers (one of them being fucking imaginary) A to scale drawing of this would literally be nothing. It doesnt exist in any accurate representation of space.

>>14217687
This. The math is ez but what's so funny about it

>>14217687
The reason we study triangles, or trigonometry at large, is because we can apply the geometrical properties of triangles towards mathematical knowledge. Even though your small brain cannot comprehend this, larger brained people use imaginary numbers for numerous real-world applications. Also, we CAN use pythagorean theorem on three numbers, this would calculate the distance to a point in 3D space (x, y, z coordinates).

https://en.wikipedia.org/wiki/Fourier_transform

Go back to writing your marxist poetry.

>>14217748
So can you explain the joke?

>>14217748
ok so the only argument that you made in that bit of word spew that is somewhat valid is that people can use imaginary numbers for "NUMEROUS REAL-WORLD APPLICATIONS" So lets see em fuck face eh? Where are these examples and why are they so NUMEROUS that I haven't heard of a single ONE.
>>14217763
see >>14217619

>>14217748
You stupid fuck, i cannot be represented by a triangle. The other anon was right :3

>>14217783
I understand the math in:
>>14217619
I just don't know what's funny about it... Is there a play on words or something I'm not seeing past the math?

>>14217801
the idea is that non stem majors wouldnt get the process and thus wouldn't be as enlightened as this anon that know the shortest path is the hypotenuse, that is to say that the stem majors path is more efficient than the humanities path, as they would foolishly pass by the way of side length of 1 and side length of HOLY NEVERENDING SUCKING RIPPLING VOID OF HELLISH RESOUNDED UNSOUNDED UNCONFOUNDED side length HOLY SHIT IMAGINARY i.

>>14217519
Pythagoras' formula works on a basis of normalization. It is not ((a^2) + (b^2))^(1/2), rather ((|a|^2) + (|b|^2))^(1/2)

Functions have domains. If you do not respect the domain, you end up with undefined results. One of the axioms of using complex numbers in geometry is obeying the necessity of normalization. The imaginary plane isn't ordered, and it isn't euclidean. Ignoring these properties and pretending like the absurd results are significant is absolutely ludicrous.

>>14217801
>>14217783
There is nothing funny about it. People using mathematics to make jokes are sad people because generally speaking mathematics isn't very funny.

But honestly, what the FUCK man. This retard thinks that i is representable by a line.

>>14217822
Just shut the fuck up.

EVERYONE SHUT THE FUCK UP. YOU CAN'T SEE IMAGINARY PEOPLE CAN YOU? I CANT WALK DOWN THE STREET AND RUN INTO THE FUCKING HAMBURGLAR RIGHT? WELL GUESS WHAT. SAME THING FOR i!!!!

>>14217783
>>14217748
>>14217700
>>14217687
>>14217619
Just read a wikipedia article if you can't pick up a book. Distance in the complex plane between A and B is fully defined by the absolute value of (A-B) which is just its product with its conjugate. Distance is fully sound and the pythagorean theorem holds with absolute value. The frog image is just evidently incorrect reasonong to anyone who read at least to pages on complex numbers.

>>14217783
>let's see 'em fuckface
Electrical engineering, 3D graphics, structural engineering, fluid systems, etc.

>>14217850
It's not that kind of "imaginary"

>>14217783
Probably bait, but this is /lit, so its impossible to tell. The signals that are being sent back and forth from your computer and router were designed using analysis in the time and frequency domains. When designing a signaling system, it is far easier to perform calculations in the frequency domain.

https://en.wikipedia.org/wiki/Fourier_transform
https://en.wikipedia.org/wiki/Laplace_transform

These two transformations transform functions of time to functions in the frequency domain, which generally involves complex (both real and imaginary) numbers.

This allows us to see certain characteristics of our signalling system that would otherwise be strenuously difficult to determine in the time domain.

>>14217850
The are as real as any number system. Just like the "rational" aren't any more rational than the reals.

>>14217876
We aren't talking about a function though are we? We are talking about a dimension, you people keep on going on and on about how the domain choice matters and this isn't Euclidean space etc etc

What we are really debating is whether or not you can even represent a negative value in the physical plane through a line, which is nonsense. The line itself is the physical distance within the given plane, you could technically have an infinite line but the least it's value could be in the given plane is 0. Do you at least see what I'm getting at?

>>14217875
It actually is.

>>14217890
No, please respond to this
>>14217905

>>14217905
Why does that matter at all? Mathematics is the language of the universe. Your focus on whether something can be recognized on a "physical plane" or whatever is irrelevant to the nature of reality.

>>14217925
BEEEEcause it's being represented in a PHYSICAL drawing, and that was the whole point of the retarded joke that everyone is now realizing they should have called retarded.

Nice book recommendations fags

t. OP

>>14217925
>it's represented in a physical drawing
Undefined things can be defined arbitrarily. This isn't a new idea, it's why they are undefined in the first place.

>>14217933
That's not a physical drawing! It is a visual representation that is generated by small LEDs on your computer or phone screen. The signals that are sent to your screen to represent this triangle were engineered using complex analysis lmao (imaginary numbers).

>>14217956
Now you're just being irrational. ;)

>>14217963
Better go get my tinfoil hat

>>14217963
THE MATHEMAGICIANS HAVE INFECTED REALITY!!! AAAAAA FUCK!!! SAVE ME GUENON!!!! SAVE ME PARMESIAN-DES!!! AAAAAA!!!

>>14217910
>>14217905
Sure I see what you are getting at. But in the complex plane there are no distances represented by negative numbers. Again it doesn't matter that the squares of complex numbers can be negative because distance is defined as the absolute value which is always non negative. Why is it defined like that? precisely to corespond to intuition, just like the definition of distance in the cartesian plane. The pepe image doesn't corespond to intuition, because it is mathematically false

>>14217987

>>14218003
The dank may may makes the assumption that we are representing the triangle in the complex plane. Furthermore, representing a triangle in an x-y plane makes it no more "real" than a representation in the complex plane.

>>14218032
In the complex plane 2i !> & !< 3i, a difference of 0 in the drawing makes sense because "distance" as we define it does not exist in the complex plane.

>>14218032
Yeah I guess, there is the ontological question of mathematical objects (or maybe there isn't by the kantian Transcendental Aesthetic); anyways it is not the question of superiority of cartesian real number coordinates over the complex plane

>>14218053
>as we define it
Distance in the complex plane is well defined trough absolute values, I don't get what could be unclear here

>>14218053

>>14218071
Only because absolute values remove you from the complex plane.

>>14218032
Ridiculous meta-troll. The original joke was indeed stupid and if I didn't say so myself I would think someone was samefagging their own post.

>>14218088
What may appear to be a "meta-troll" to you would not be considered so by someone decently versed in mathematics. Or philosophy for that matter.

>>14218086
Geometricaly distance is defined as a function from the catesain product of the set of points with itself to nonnegative real numbers, satisfying a few conditions (reflexivity, and so on). One model for this is the cartesian plane, another is the hyperbolic, and as one of them the complex plane. Of course distance would only obtain non negative value in any model, otherwise it would be meaningless to call it distance; yet the significant fact is that its domain is complex

>>14216313
Yea yea retroactively refuted by Guenon and Parmenides blah blah blah

>>14218104
You're saying that there is such a thing as an 'imaginary axis' for a physical length. Ridiculous.

>>14215688
What are axioms?

>>14218086
That's the point, distances don't live in the complex plane.

>>14215688
1 = √1 = √(-1×-1) = (√-1)×(√-1) = i^2 = -1.

Heh. Nothing personel, mathematicians.