I believe you. I’m just happy I didn’t choose to be an engineer I guess 
i thank my lucky stars there are those of you that think this way!
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I have a bigger problem with biology than say Physics and engineering.
Math in my opinion is just figuring out procedures and once you get that, it becomes easy.
Biology is a lot of rote memorization which I am terrible at.
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Any derivatives questions? or maybe probability ? That was my all time favourite topic.
Weirdo!!
I didn’t mind the math part of it but I was doing applied math. Field strength calculations in 3 and 4 dimensions. Biophysics of ion channel dynamics, for example.
Absolutely no way I could do any of that now. If you don’t use the math muscle, it withers away.
As for mathematics reflecting the real world : ah, no. It’s well beyond that. Math is an inventive discipline, not just a discovery one.
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Problems like these would even make Prince Andrew sweat.
I’d rather not. I’ll sit here and think about the nice warm waters of Wulai, or reminise about my school exam where a butterfly landed on my desk. Failed that subject, was worth it.
Was a red admiral!
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Does every continuous curve that doesn’t cross itself have an equation? If not, why do some continuous curves have an equation and others don’t?
I asked those questions of every math teacher I ever had all the way thru graduate school and none of them were able to answer them, though some of them pretended to answer.
Ask on the math forums used in the earlier thread.
My motive wasn’t to put math teachers on the spot. My thinking was what good was it having all these shiny tools for processing neatly packaged equations when the real world is such a messy place? In other words what happens when we leave the ivory tower and reality hands us a bunch of messy data to work with and we have to create some order out of the chaos?
every curve can be described by equations. smooth curves are easiest, messy hand-drawn curves may need many many parameters to describe, but theoretically all are doable. after all, they are just being drawn in 2D Euclidean space, so no problem.
or you can use mathematical software to build approximations to a reasonable degree and go home satisfied.
in the real world, the ideals still apply as they guide our use of approximations that are good enough when drawn to the appropriate resolution. and the chaotic stochastic math of things like markets do have entire fields of math developed around them, which work well enough.
messy data isn’t really amenable to pure math anyway. you’re looking at applications of math, where many tools exist to help you out.
i think some people are maybe missing the distinction between pure math and applied math here…
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if you’re using the mathematical definition of continuous curve, yes.
How do you know that? (serious question) A fun math challenge would be to find the equation for some random curve that’s not one of the obvious math functions.
A thermodynamics professor eventually “answered” my question by introducing me to finite element analysis:
Finite Element Analysis or FEA is the simulation of a physical phenomenon using a numerical mathematic technique referred to as the Finite Element Method, or FEM. This process is at the core of mechanical engineering, as well as a variety of other disciplines. It also is one of the key principles used in the development of simulation software. Engineers can use these FEM to reduce the number of physical prototypes and run virtual experiments to optimize their designs.
Complex mathematics is required in order to understand the physical phenomena that occur all around us. These include things like fluid dynamics, wave propagation, and thermal analysis.
Analyzing most of these phenomena can be done using partial differential equations, but in complex situations where multiple highly variable equations are needed, Finite Element Analysis is the leading mathematical technique.
What is the mathematical definition of continuous curve that you’re referring to?
Like imaginary numbers?
Those can be solved by substitution.
you can chop the curve up into bits, and define functions for each of the bits that match the curve in that section. the more messy the curve, the more bits you might need to chop it up into.
by definition, a curve is a continuous function. so every (continuous) curve can be described by a function (or a combination of various functions).
going further, there are distinctions in algebraic geometry between algebraic curves (those that can be represented as a polynomial of some order) and transcendental curves (those that cannot be represented a a polynomial). But transcendental curves have other mathematical descriptions that can be used, so yes, you can describe all curves mathematically. we are assuming you are talking about continuous functions here, of course. a scatter plot in 17 dimensions may not count as a curve!
if you want more detail, study yourself some differential geometry and prepare for some funky higher dimensional complex maths.
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Well Imaginary numbers is what makes the core of the wave equation, the core of the universe,literaly . without it all the quantum theory stuff wouldnt exist. They are used in real life indirectly in a way to prove equations that were thought to be impossible to prove.
Just because we common folks arent using them in daily life doesnt mean nobody is using them hhhh
They’re the backbone of the universe, yes. But those were discovered by mathematicians before their use was found.
They’re derived from mathematicians playing around, not from real life.
Imaginary numbers are used to model AC circuits.
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I’ve had every single differential equations class.