Math subjects you hate - Like /sci/, but on KF

[Un Platano]

I don't think this even counts as a real math imo, but statistics. Statistics can go get fucked by Satan's volcanic dick.

Statistics has some unique concepts with entirely different means than uour typical math problem that set it apart from any other field of math, but where even I draw the line is when they make you calculate regressions by hand. Complete waste of time for something that can be done by any spreadsheet program from the last 30 years, and in the lack of a computer capable of even this can be pretty well guessed at using a ruler and a pencil. If you can't figure out where the line should go just by looking at it, you probably shouldn't be doing a linear regression of it.

There's a way to do it with questionably greater efficiency using linear algebra, but no matter which way you slice it, there's no avoiding it: regressions are a bitch to solve.

 

[Unyielding Stupidity]

Imaginary numbers are completely pointless. Why would you ever need to calculate anything with square roots of negative numbers in any context, outside of theoretical mathematics? Most other topics have at least SOME practical usage, but not imaginary numbers.

 

[FuckedUp]

Imaginary numbers are completely pointless. Why would you ever need to calculate anything with square roots of negative numbers in any context, outside of theoretical mathematics? Most other topics have at least SOME practical usage, but not imaginary numbers.

As I said on the first page, differential equations. I know off the top of my head that it has a specific application in physics.

 

[Ughubughughughughughghlug]

As they're introduced in typical high school math class they are indeed pointless and dumb. They don't actually utilize them in any introductory course, they just give you some basic definitions and properties and then move on. In reality imaginary numbers have lots of theoretical and applied uses. They're fundamental to many proofs in higher subjects of math, and are used to model lots of real world phenomena, such as power factor in electrical systems (side note: fuck phasors and fuck electrical engineering)

In a lot of ways I think students would be better off ignoring the concept of imaginary numbers until much later on, because until you learn why they're useful they just serve to cloud your mind. The only reason they're taught is because the subjects that do use them will assume you already know the properties of imaginary numbers just as you do those of polynomials, angles, and shapes. They don't want to give you a rundown on imaginary numbers in every single class you take.


There is math everywhere around you, in everything you see and hear and feel and every other sense you have, but you'll never find it if you don't want to look for it. It's a lot like how humans can be illiterate and still be fine.

If they're going to teach imaginary numbers, they need to go ahead and teach complex numbers and complex arithmetic too. Just imaginary numbers by themselves are not interesting or helpful. Having numbers expressed as a 2D plane instead of a number line, though, and having the arithmetic operations explained to you, makes it seem like a major improvement over real math.

 

[Un Platano]

If they're going to teach imaginary numbers, they need to go ahead and teach complex numbers and complex arithmetic too. Just imaginary numbers by themselves are not interesting or helpful. Having numbers expressed as a 2D plane instead of a number line, though, and having the arithmetic operations explained to you, makes it seem like a major improvement over real math.

They do that, those are the aforementioned properties that basic algebra courses go over. The problem is that properties alone are not useful. While you can teach that |1+i|=sqrt2, there's no application for it as presented in any algebra class. "When am I ever going to use this?" is a question in math classes that I absolutely hate, because in any introductory course there are plenty of examples given of how basic algebra or trigonometry or any other area of math can be applied to real scenario, and it's a tacit admission that you simply don't want to have to think.

But complex numbers are the exception to that. There are no real applications given to it when it is introduced. You could use it to solve the roots of a polynomial with no real roots, but that's not a helpful result at the level of basic algebra and doesn't correspond to any real phenomena that an algebra 2 student is likely to understand. Since they are not useful until much later on, it's not apparent that they have any uses at all.

 

[Ughubughughughughughghlug]

They do that, those are the aforementioned properties that basic algebra courses go over. The problem is that properties alone are not useful. While you can teach that |1+i|=sqrt2, there's no application for it as presented in any algebra class. "When am I ever going to use this?" is a question in math classes that I absolutely hate, because in any introductory course there are plenty of examples given of how basic algebra or trigonometry or any other area of math can be applied to real scenario, and it's a tacit admission that you simply don't want to have to think.

But complex numbers are the exception to that. There are no real applications given to it when it is introduced. You could use it to solve the roots of a polynomial with no real roots, but that's not a helpful result at the level of basic algebra and doesn't correspond to any real phenomena that an algebra 2 student is likely to understand. Since they are not useful until much later on, it's not apparent that they have any uses at all.

The beauty of complex algebra is justification in itself for knowing it.

 

[Win98SE]

I'm pretty sure I have some kind of selective exceptionalism when it comes to math becasue fuck me, I don't think I should have as much trouble as I do with basic things. It's always been a struggle and most of my math teachers were awful until college.

People need different approaches to learning it. At least in the US, the lessons are "one size fits all", and if you just so happen to fall between the cracks there's very little in place to catch you. Once I realized I was falling behind, I started looking up resources online and learning a lot of the concepts - something made a lot easier by YouTube and a website called Khan Academy. Once I got into Calculus I found a tutor and was fine with more direct help where I could ask questions.

 

[Pickle Dick]

math

 

[Cyclonus]

How come dividing anything by zero is "undefined" but ask about the square root of minus one and the mathematicians come up with some bullshit about imaginary numbers?

 

[Radical 38]

Kind of off-the-topic, but does anyone on here know good reads on mathematical methods (such as vector calculus)? I’d appreciate any recommendations, thank you!

 

[Un Platano]

Imaginary numbers are completely pointless. Why would you ever need to calculate anything with square roots of negative numbers in any context, outside of theoretical mathematics? Most other topics have at least SOME practical usage, but not imaginary numbers.

Generally math that uses complex numbers relies not just on the foundational properties of them, but one one specific equation utilizing them: Euler's equation. Euler's equation states e^(ix) = cosx + isinx. When you stop and think about it, it's a strange conclusion- an exponential function equals a cyclical function? It's hard to convey how important this is without having a solid understanding of the mathematics behind it. Exponential functions arise naturally as solutions to differential equations that can model all kinds of things in the world, and using Euler's equation we can develop concise solutions to problems that would otherwise be impossible to solve. In this case, it's not using the fact that i=sqrt(-1). It relies on the orthogonality of cosx and isinx to solve an exponential equation.

Electrical and signal engineering utilizes imaginary numbers in a completely different way, albeit still using Euler's formula. Unlike differential equations, electrical systems begin with a periodic function- in this case, the alternating current that gets produced by a power plant and sent all the way to your house and into all your electrical components. It's difficult to calculate the resistance and impedance of these systems because their state is always changing due to the alternating current. If you measure the voltage at any two points in time, you will get different results because of the wave nature of the voltage source. What complex numbers allow us to do is to create a model of an electrical system that is independent of time, since by Euler's formula we can take a periodic function and turn it into an exponential. By make a time-independent model, it becomes possible to solve issues regarding the power factor of an electrical system, which can improve the efficiency of an electrical system. This is especially important if you have a machine shop with lots of motors that cause a high inductive load and give you a terrible power factor, and if you do not correct it you will soon get an angry letter from your power company about power factor correction.
This is a specific application of the Laplace transform, which is a more general way to turn any time-based function into a time-invariant function based on complex variables. Laplace transforms are also used in differential equations to solve even worse equations than the ones you apply Euler's formula directly to. There are further applications of complex numbers past this, and in fact there's a whole damn class on it called complex analysis that studies the unique properties of other functions with complex variables, but that is currently beyond my knowledge.

What all of these uses have in common is that none of them directly utilize the most basic identity of complex numbers that is i=sqrt(-1), and that is the problem with how complex numbers are taught. The actual implications of complex numbers are much more nuanced than what an introduction to them will reveal to you. Students focus too much on the definition of i because that is all they are given, and that is why they arrive to the conclusion that they are not useful. In a way it's like teaching someone the alphabet of a language they haven't been taught. Until they do learn to speak the language, the alphabet will be useless beyond meaningless faffery. Solving the square roots of negative numbers is that same faffery.

 

[Positron]

Imaginary numbers are completely pointless. Why would you ever need to calculate anything with square roots of negative numbers in any context, outside of theoretical mathematics? Most other topics have at least SOME practical usage, but not imaginary numbers.

Quantum physics is all about complex numbers. You can't get many of our modern techs, like laser and computers, without quantum physics.
Theroetical Physicist Roger Penrose thinks complex number is sheer magic.

What all of these uses have in common is that none of them directly utilize the most basic identity of complex numbers that is i=sqrt(-1), and that is the problem with how complex numbers are taught. The actual implications of complex numbers are much more nuanced than what an introduction to them will reveal to you.

The problem is that it is very hard to get into applications until the student is very well versed in complex analysis, not to mention the student must have a good grasp on Physics first.

 

[Ughubughughughughughghlug]

How come dividing anything by zero is "undefined" but ask about the square root of minus one and the mathematicians come up with some bullshit about imaginary numbers?

Because dividing by zero is retarded.

What do you do when you multiply something? Like a x b? You're basically saying "add a to itself for b times," or "add b to itself for a times."

Then dividing is the opposite of that. When you say a / b = c, you're saying that "b added with itself for c times makes a." Note that a/b and b/a are NOT the same, even though ab and ba are.

Now, apply that logic to zero. Say a / 0 = b. So you're saying that 0 added with itself b times equals a.

So how many times is b? How many times do you add 0 to itself to get to a?

If a isn't 0, you'll NEVER get to a.
If a is 0, it could be ANY NUMBER of times.

If you do allow for dividing by zero, you can also easily construct proofs that any number is equal to any other number, which is in and of itself a proof that it can't be done.

There are variations of mathematics that add in ideas like saying a/0 = infinity or other fixes, but they're used for specific purposes.

 

[FuckedUp]

Because dividing by zero is exceptional.

What do you do when you multiply something? Like a x b? You're basically saying "add a to itself for b times," or "add b to itself for a times."

Then dividing is the opposite of that. When you say a / b = c, you're saying that "b added with itself for c times makes a." Note that a/b and b/a are NOT the same, even though ab and ba are.

Now, apply that logic to zero. Say a / 0 = b. So you're saying that 0 added with itself b times equals a.

So how many times is b? How many times do you add 0 to itself to get to a?

If a isn't 0, you'll NEVER get to a.
If a is 0, it could be ANY NUMBER of times.

What if you think of a / b as "b can fit in a this many times"? 0 can certainly fit in a infinitely many times. And it's commonly accepted that 1 / ∞ = 0, so 1 / 0 = 1 / (1 / ∞ ) = ∞ / 1 = ∞.

 

[Ughubughughughughughghlug]

What if you think of a / b as "b can fit in a this many times"? 0 can certainly fit in a infinitely many times. And it's commonly accepted that 1 / ∞ = 0, so 1 / 0 = 1 / (1 / ∞ ) = ∞ / 1 = ∞.

That’s an interesting way of looking at it. The reasoning I was familiar with is that as you bring the denominator closer to 0, 1/x gets infinitely large, but your explanation makes even more sense.

Defining things divided by 0 to equal infinity does exist as a concept in some mathematics, and especially in non-Euclidean geometry. But it’s not helpful in a normal sense and doesn’t round out algebra the way complex numbers do.

There’s also the issue of there being different infinities. Depending on the math you’re doing, that may or may not be a relevant issue.

 

[Un Platano]

What if you think of a / b as "b can fit in a this many times"? 0 can certainly fit in a infinitely many times. And it's commonly accepted that 1 / ∞ = 0, so 1 / 0 = 1 / (1 / ∞ ) = ∞ / 1 = ∞.

I'd argue that this is a rather simplistic take on dividing by zero, and it's only "commonly accepted" in the sense that most people are naive about the subject. There isn't a single field of mathematics where 1 / 0 = ∞ is a meaningful statement. Under basic algebra, it simply makes no sense under the axioms of multiplication. Consider this proof if we accept the premise that 1 / 0 = ∞:
Given two integers a and b where a = b+1,
(a-b)a = (a-b)(b+1)
a^2 - ab = ab + a - b^2 - b
a^2 - ab -a = ab + a -a - b^2 - b
a(a - b - 1) = b(a - b - 1)
a = b
b = b + 1
0 = 1
Can you see it? The problem comes in the the fourth line. a - b - 1 = a - (b + 1) = a - a = 0. It's obscured, but at this step we are dividing both sides by zero, which allows us to come to the nonsense conclusion that 1 = 0. In fact, if we accept that 1 / 0 = ∞ is a valid statement and try to use it, we can arrive to the conclusion that any number equals any other number. It's because the statement itself is nonsense. We cannot accept the premise that 1 / 0 = ∞ is a valid statement because it is not consistent with the basic properties of algebra.

If we introduce the concept of a limit, then we can take it further and say that lim(x>0) 1/x = ∞, but this a fundamentally different statement from 1 / 0 = ∞ because it communicates more about the nature of the infinity. And that's where the statement actually fails under mathematical systems which allow for limits approaching infinity- infinity is not a number but a domain called hyperreals. The statement 1 / 0 = ∞ is as meaningful as saying 2 + 2 = a complex number. While true, it doesn't tell us a whole lot about how that infinity behaves. You run into a problem trying to use mathematical propereties on a vague statement like that because it merely specifies that one element is a subset of the other, a property that cannot always be inverted. By attempting to use mathematical properties we can arrive to the conclusion that a complex number - 2 = 2. This can be made a true statement, but only for a particular complex number. It cannot be made into a general statement because there are complex numbers for which the statement is not true. It is for the same reason we cannot say 1 / 0 = ∞. That is where the limit statement becomes important, because it tells us the characteristics of how the function approaches infinity. Without this distinction, it would be impossible to evaluate a solution to a function such as f(x)=(x^2)/sinx at 0, for which a solution does exist and is different from the solution to g(x)=x/sinx despite the same dividing by zero present in both of them.

 

[Mrs Paul]

All of it, basically. Yes, I know math is very important. I still fucking hated it, and preferred social studies and literature.

 

[Rack Of CDs]

I'm trying to re-learn Algebra since I had a miserable time with it in High School. Manipulating numbers makes sense but I'm really struggling with Cartesian Graphs. Having two points and making a line makes sense but the slope makes no sense to me.

Why is it "rise over run" and not "run over rise"?

Why is a slope "positive" when it continues forever into negative coordinates?

 

[Bass]

I always had trouble with alg1 and alg1, because the teachers i had in school for them wouldn't stop and explain why you had to do certain steps to solve equations. She expected you to figure it out on your own time, we have to move on because Houghtin-Mifflin said so. So I just fell further and further behind.

It was really fun being in honors and AP subjects but having to be in mouth breathing retard level math classes. Fuck you Ms Quigley, fuck you with a rusty spoon.

I shined in geometry though. Having a visual representation of what the hell we were doing really helped me out. Then alg 2 happened and it 2a right back with the retards. We only had to do 3 years of math in high school, so I struggled to get my D- and never took math again.

I've started looking up YouTube videos on algebra, and I'm actually doing okay at teaching myself since some random YouTuber five more of an explanation than Ms Quigley ever did.

 

[Kosher Dill]

Why is it "rise over run" and not "run over rise"?

Convention, more or less. In the sort of functions you graph in beginning algebra, there's typically one independent variable that you assign to the X-axis ("run") and one dependent variable that you assign to the Y-axis ("rise"), and the graph shows the relationship between them.

Imagine a graph set up in the conventional way, with time on the X-axis and temperature on the Y-axis. "Rise over run" would give you an indication of how the temperature is changing over time. But "run over rise" would be like trying to see how the time of day varies with the temperature, which doesn't make very much sense.

More complicated mathematics doesn't necessarily follow the "one independent variable vs one dependent variable" scheme, but that's another story.

Why is a slope "positive" when it continues forever into negative coordinates?

Roughly speaking: it's "positive" when if the independent variable increases, the dependent variable also increases, and vice versa. Whereas it's "negative" if the dependent variable decreases as the independent variable increases, etc.