Explain to me the secrets of Calculus

I will not take a Calculus class, but I know it contains a multitude of mind opening secrets, creating a sort of enlightenment wherein your perspective of the world and everything you know changes, but like a psychedelic drug, you can never describe it unless you make someone else go through it.  I refuse to go through the experience, but try to explain to me, a mere mortal, what these mind opening secrets and changed perceptions are.

>>1
Wrong. You start to get at some topology and whatnot, but it doesn't do anything for anything. All you do is learn more about quantifiers and how to use them, which is important for the definition of limits. But other than that, there is nothing.

Logic does that, not Calculus

>>3
That's right, if you want to learn more, g2logic, not calculus.

Just take the fucking class, like your mom took it last night.

>>2


Coffee cups just don't equal donuts, no matter how you look at them.

Topology freaks me out 0_o


anyway, to answer OP's request, no.

For God's sake, learn calculus, even if you just do basic differentiation and integration along with a few applications of both, you really understand where a huge amount of knowledge can be calculate mathematically.

I just want to know what it means when people say that anyone relying on math before calculus lacks understanding of math, and that their whole perception of math changes after calculus, until everything fits together in a way that it never did before, but only after you've been through Calculus (I ask if the basics of Calculus could be taught at Algebra, or at least an overview, and am told no, you have to get there to understand it first).  What was your perspective and understanding of mathematics prior to Calculus?

You can briefly explain to someone that Geometry is the study of two dimensional shapes and trigonometry is the calculation of angles.  Yet Calculus lacks such a concise definition.  It seems to be something like "the study and application of advanced mathematics."    

>>6
They're not equal. They're topologically equivalent. For one thing, they have the same fundamental group. What is important in topology is not the actual things (i. e. coffee cups and toruses), but rather generalities. Topology speaks of generalities, and thus speaks of things that apply to a whole range of things, like both coffee cups and donuts.
>>7
It means that you don't know basic topology and analysis. Topology and analysis are very important for basic math understanding.
>>8
Anyone who has not taken one of the differential, topological, and algebraic geometries certainly does not understand the modern study of geometry.

apparently ineffably important

Calculus's main topics are differentiation, which deals with finding the slope of a graph at a single point, and integration, which involves the area between a function and the x-axis

differentiation gives you slope
integration gives you area

there, just saved you 6 credits of boring

oh and you can do it on multiple axes

theres another 3 credits

So you could explain the basic idea of topology to Algebra students?  Some students would appreciate math a lot more knowing the big picture first.

>>14
So in a "space" of things, you get certain elements. These "spaces" have points in them, and the topological space also designates what is "around" those points, called "neighborhoods." The definition of continuity is generalized in that now you have it as when there is a neighborhood of f(x), there is a neighborhood of x with its image contained in that neighborhood. It's the same thing as simple idea of the fact that when points are "around" x, then points are "around" f(x), when f(x) is continuous. And continuous functions with a continuous inverse are called "homeomorphisms," and properties that are preserved by such continuous mappings are called "topological properties." It is the simple investigation of things that are the same under continuous mappings.

>>14
You could use printed alphabet as example. C, I, J, L, M, N, S, U, V, W, Z are same, D and O are same, like that.

>>16
Not very instructive. Continuity and "neighborhoods" are very important concepts that are used often.

>>17
Yeah but I don't know what you just said.  Is this a brief introduction, or are they actually going to be covering some detail like that.

>>18
Brief introduction is neighborhoods and continuous functions.

the simplest definition of calculus is "the study of infinitesimal change"

>>1

My love of math certainly hit me when I took my first Calculus class back in high school.  Partly because I had a very good teacher (not unlike having a good experienced friend with you during your first psychedelic trip makes that experience better).  I hope that you really have taken shrooms or the like, because I'm going to be comparing the two experiences to explain. 

First off, in order to "be enlightened", as you say, you must have a very solid understanding of all previous maths.  I saw a lot of my fellow students back in Calc 1 get too bogged down by the simple algebra and geometry.  If the stuff isn't nearly intuitive to you already, I don't think you'll be able to see things the same as I did.

Much like with a psychedelic, I had a realization, or sense that "all is one".  I could see how all the previous classes I had taken were leading up to this.  Calc is the first time where a person isn't really learning much new anymore, they're learning how to combine all the tools at their disposal into one very elegant and logical system.

It was as if I was peering into the machinery of the mathematical machine, free to study how all the cogs and gears were working together seamlessly.  I've come to really understand "mathematical beauty".  When I try to explain it to others, or explain to them why I chose math as a major they just give me a confused look, but it really is there.

Just like shrooms is much better with music, I think Calc is much better with Physics.  I think it's quite astounding how some arbitrary system we humans invented as a means of counting could turn out to describe the physical world so well.  Sure, when you get into more advanced stuff you'll find that a lot of that early physics stuff kind of falls apart at higher levels, and techno/trance music sucks when you're not tripping your balls off.

Finally, many times a psychedelic will permanently change how a person views the world.  I looked back on some of the previous things I had learned, stretching all the way back to elementary school.  All the equations, algorithms and little "tricks" I had learned over the years made sense.  They were no longer simply things to be memorized, but pieces of the same beautiful system.  A system that started out with some caveman trying to quantify his world.
_________________________________________________________________

TL;DR: Previous maths come together in calc, and it can blow your mind

>>1
Read SICP.

>>21
You really think that Calculus is the greatest math? You should go onto Differential Geometry, Algebraic Topology, Algebraic Geometry, and Analytic Number Theory.

>>23
can't be bothered, lazy, other hobbies

>>23

This is >>21 here,  I never said Calc was the greatest math,  and I don't think that it is. My love for math was simply realized in my very first calculus class.  Of course since then I've gone on to take many more high level math courses, all of which were much more interesting.  Calculus is simply my "first love", so to speak.

I was answering the OP, and explaining how Calculus changed my outlook on mathematics as whole. I wasn't discussing my all time favorite math.

So without Calculus, I will not know the meaning of love

calculus should be required of anyone pursuing a college degree. if you have to take a semester of history, psychology, english, then you shouldn't be able to matriculate without some actual math.

If I ever need advanced math, I will use someone who has taken those courses. 

>>27

calculus.

not actual math.

advanced arithmetic.

etc.

math is proof.

qed.

///

I like arithmetic

I treat Calculus like I treat the expertise of a carpenter, whom I hire to do work.

can calculus fix my shitty bathroom?