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Deltaville
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27 Jan 2016, 1:40 am

ScrewyWabbit wrote:
Deltaville wrote:
ScrewyWabbit wrote:
IMHO, it can be hard for two reasons.

First, you really need a solid foundation in the math that comes before it, algebra and to some extent trigonometry especially. If you aren't comfortable simplifying equations, factoring them, etc. then its a bit like trying to build a house of cards - while sitting in a car with bad shock absorbers driving on an unpaved road.

Second, at least taking calculus in college in the US on a normal semester system, the pace is such that you really need to keep up. If you fall behind its really tough to catch up again. Most first semester calculus courses are split in to two halves - derivatives first, and then integrals. If you get lost in the derivatives part, its something like starting over when they reach integrals, assuming your grade in the course isn't already hopelessly lost.

Beyond that, its all very logical if you can follow along. Easy is not the right word, but graspable.


If easy is meant to be taken as a relative term, than calculus certainly can be construed as an 'easy' branch of mathematics. If you ever tried real analysis or any other hyper advance sub branches of calculus like I have, such as halmitonian integrals, then calculus certainly qualifies as 'easy.'


Well, yes, of course its relative. Most math subjects are not as difficult as what comes after them, if you learn them in the usual order. To the person who has never taken calculus then, its generally more difficult than the math they've taken before and not unreasonable, I think, to expect that to such a person when first learning it, it may seem difficult. It is probably fair to say that the jump between calculus and what comes before it (Math Analysis, Trigonometry, etc.) is quite a bit larger than the jump between any other two math subjects that the new Calculus student would have experienced up to that point in their learning.

Also, I'd suggest that learning a math subject that requires you to use a previous math subject as the foundation for what you are doing tends to make you much more versed in that previous math subject than you may otherwise have been, and may even make it seem easier, in retrospect, than it was when you first learned it.


Not in my case, all the mathematics course that I took came to me naturally. But I guess I concur with the notion that Calculus was a step up from precollege mathematical disciplines. It would be a fairly odd conclusion to determine otherwise, at least for the majority of students.


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marshall
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28 Jan 2016, 4:03 am

It depends on the person. Having good visual-spatial intelligence really helps with calculus. At a pure level, calculus is about certain types of relationships between functions of real variables, but in application it helps to visualize problems and use geometric reasoning. It's useful to think of derivatives as slopes of curves and integrals as areas under curves.



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29 Jan 2016, 10:54 am

I was also in special education schools and didn't have much math. I got a C in college algebra and a D in Pre-Caculus despite having a tutor for Pre-Calc. D wasn't a high enough grade since it was a required class for my major but I ended up switching majors and not needing it.



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29 Jan 2016, 12:28 pm

I have just started taking it and have completed 1 unit. I found some of it really hard, like the stuff on formal definition of a limit. But the stuff that was on the test wasn't too bad.



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29 Jan 2016, 12:49 pm

It's not that hard. Just apply the rules of logic. No fallacies, no authority to fear, no loser to punch when you feel like it, no vagueness---much easier than talking to people.


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marshall
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29 Jan 2016, 6:52 pm

Spiderpig wrote:
It's not that hard. Just apply the rules of logic. No fallacies, no authority to fear, no loser to punch when you feel like it, no vagueness---much easier than talking to people.

Yea. This is one things I like about math. The rules are all very definite. There are no absurdities or weird exceptions. Nothing is random and everything fits together perfectly. This isn't the case for things like languages or legal systems.



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29 Jan 2016, 7:37 pm

Rudin wrote:
slave wrote:
BobinPgh wrote:
It's been awhile since I have been in school, but I have found out in recent years that maybe I would have had a better career if I was not so afraid of the math when I was younger. I had special education when I was a tween and not much math. I later had algebra at the public high school but I decided against a lot of careers and better college because I kept on hearing that this math called calculus is SO HARD! Even my sister, now a dentist, says it was difficult (and yes, she did need it to get into dental school). Worse yet, a psychiatrist I saw as a teen told me that it was "very abstract and no way you would understand it" and was I supposed to believe it? Nobody ever said what this math was, only it is SO HARD! I even chose a college that turned out to be awful because it did not require this math class and I could have gone to much better schools if I only had Calculus.

Later, I would try to study math like college algebra myself from books but I found that it is very difficult to go to even study after work when one is on the spectrum. I feel so exhausted from work I cannot even open a book. I hear that NT people work full time and go to school full time and now, I wonder if they are lying.

So all of you who are on the spectrum and good at advanced math, what is the truth? When you took the class, was it really that bad? Did you get a decent grade? Was I misinformed? It turns out that our high school, few people go to college even today so would I have heard this at a better school? Looking forward to the answers.


I feel compelled to point out that Calculus is not ONE specific type of Maths, but rather it is a large category of Mathematics.

Individuals may find certain sub-disciplines within Calculus to be more or less difficult than the other.

There are many options for studying Calc. or even Pre-Calc. should you desire to try it on your own.

Btw, there are Autists that suck at Maths, some have dyscalculia, some are good at it and don't like it and some are Maths geniuses and love it.


I can see why people with dyscalculia dislike elementary and early highschool maths, since it involves lots of arithmetic. Maths is more than that though, maths is more about logic and truth.

Some of the best mathematicians and scientists had horrible arithmetic skills. Albert Einstein got his wife to do all the arithmetic for his general theory of relativity. One famous mathematician (I forget who) didn't know his basic multiplication facts. Alexander Grothendieck once said that 57 is a prime number (which it is not 57=3x19).


But math only deals with numbers....so how does it factor into logic and truth, I mean I suppose I can see the logic bit due to mathmatical calculations and such that can allow for a 'logical' conclusion. But as for truth I doubt mathmatics holds all the truths of the world or anything. But yeah I really can't wrap my head around mathematics so there is that.


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29 Jan 2016, 11:11 pm

^Even a math midget like myself can see how math, and logic, at least overlap.

To take a simple example from algebra: If A=B. and if B=C, then A must also equal C.

That statement can be applied to anything else in life as easily as it can be to quantities..



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31 Jan 2016, 1:26 am

Meistersinger wrote:
When it comes to algebra and calculus, it's all Greek to me! (This coming from someone who has enough trouble adding 1 and 1 and getting -32767.

Me too, fortunately... :mrgreen: :mrgreen:



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31 Jan 2016, 7:29 am

Not everything written with Greek letters is Greek.


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Deltaville
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01 Feb 2016, 12:35 am

marshall wrote:
Spiderpig wrote:
It's not that hard. Just apply the rules of logic. No fallacies, no authority to fear, no loser to punch when you feel like it, no vagueness---much easier than talking to people.

Yea. This is one things I like about math. The rules are all very definite. There are no absurdities or weird exceptions. Nothing is random and everything fits together perfectly. This isn't the case for things like languages or legal systems.


Once you get to the most advanced levels in mathematical real analysis, that notion ceases to be relevant.


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marshall
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01 Feb 2016, 9:49 pm

Deltaville wrote:
marshall wrote:
Spiderpig wrote:
It's not that hard. Just apply the rules of logic. No fallacies, no authority to fear, no loser to punch when you feel like it, no vagueness---much easier than talking to people.

Yea. This is one things I like about math. The rules are all very definite. There are no absurdities or weird exceptions. Nothing is random and everything fits together perfectly. This isn't the case for things like languages or legal systems.


Once you get to the most advanced levels in mathematical real analysis, that notion ceases to be relevant.

No. Logic still holds pretty tight in real analysis. When you understand it, it all makes sense. It's just a matter of getting to that point.

The only math I found unsettle was mathematical logic and axiomatic set theory. There are some paradoxes there, and there's ambiguity on how you choose your axioms. Once you construct the integers it's all okay though.



Deltaville
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01 Feb 2016, 9:55 pm

marshall wrote:
Deltaville wrote:
marshall wrote:
Spiderpig wrote:
It's not that hard. Just apply the rules of logic. No fallacies, no authority to fear, no loser to punch when you feel like it, no vagueness---much easier than talking to people.

Yea. This is one things I like about math. The rules are all very definite. There are no absurdities or weird exceptions. Nothing is random and everything fits together perfectly. This isn't the case for things like languages or legal systems.


Once you get to the most advanced levels in mathematical real analysis, that notion ceases to be relevant.

No. Logic still holds pretty tight in real analysis. When you understand it, it all makes sense. It's just a matter of getting to that point.

The only math I found unsettle was mathematical logic and axiomatic set theory. There are some paradoxes there, and there's ambiguity on how you choose your axioms. Once you construct the integers it's all okay though.


Reread my response.

Complex indices in many mathematical disciplines produces more than a single definite solution. For instance complex values generates more solutions in matrices and formulaic relationships.


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01 Feb 2016, 10:07 pm

Deltaville wrote:
marshall wrote:
Deltaville wrote:
marshall wrote:
Spiderpig wrote:
It's not that hard. Just apply the rules of logic. No fallacies, no authority to fear, no loser to punch when you feel like it, no vagueness---much easier than talking to people.

Yea. This is one things I like about math. The rules are all very definite. There are no absurdities or weird exceptions. Nothing is random and everything fits together perfectly. This isn't the case for things like languages or legal systems.


Once you get to the most advanced levels in mathematical real analysis, that notion ceases to be relevant.

No. Logic still holds pretty tight in real analysis. When you understand it, it all makes sense. It's just a matter of getting to that point.

The only math I found unsettle was mathematical logic and axiomatic set theory. There are some paradoxes there, and there's ambiguity on how you choose your axioms. Once you construct the integers it's all okay though.


Reread my response.

Complex indices in many mathematical disciplines produces more than a single definite solution. For instance complex values generates more solutions in matrices and formulaic relationships.


Yes but what I believe marshall was talking about was that all mathematical theorems are true under a certain set of axioms with with no exceptions. Unlike other more applied sciences where there is in an increase in complexity, but decrease in generality. This is the hierarchy of the sciences:

1: Mathematics/Logic
2: Physics
3: Chemistry
4: Biology
5: Psychology
6: Sociology

I've created a 1 to 1 correspondence between each of the sciences with a natural number from 1 to 6. As the natural number assigned to a certain science gets smaller, the generality increases while the complexity decreases. As the natural number assigned to each science increases, the generality decreases while the complexity increases.

There is also a chain, if you will. Physics is applied mathematics, chemistry is applied physics, biology is applied chemistry, psychology is applied biology and sociology is applied psychology.


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Deltaville
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01 Feb 2016, 10:10 pm

This is why Mathematics is the apex of reason and logic.

I always loved Math. I loved it to the point that I graduated with a degree in it :)


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Deltaville
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01 Feb 2016, 10:15 pm

Rudin wrote:
Deltaville wrote:
marshall wrote:
Deltaville wrote:
marshall wrote:
Spiderpig wrote:
It's not that hard. Just apply the rules of logic. No fallacies, no authority to fear, no loser to punch when you feel like it, no vagueness---much easier than talking to people.

Yea. This is one things I like about math. The rules are all very definite. There are no absurdities or weird exceptions. Nothing is random and everything fits together perfectly. This isn't the case for things like languages or legal systems.


Once you get to the most advanced levels in mathematical real analysis, that notion ceases to be relevant.

No. Logic still holds pretty tight in real analysis. When you understand it, it all makes sense. It's just a matter of getting to that point.

The only math I found unsettle was mathematical logic and axiomatic set theory. There are some paradoxes there, and there's ambiguity on how you choose your axioms. Once you construct the integers it's all okay though.


Reread my response.

Complex indices in many mathematical disciplines produces more than a single definite solution. For instance complex values generates more solutions in matrices and formulaic relationships.


Yes but what I believe marshall was talking about was that all mathematical theorems are true under a certain set of axioms with with no exceptions. Unlike other more applied sciences where there is in an increase in complexity, but decrease in generality. This is the hierarchy of the sciences:

1: Mathematics/Logic
2: Physics
3: Chemistry
4: Biology
5: Psychology
6: Sociology

I've created a 1 to 1 correspondence between each of the sciences with a natural number from 1 to 6. As the natural number assigned to a certain science gets smaller, the generality increases while the complexity decreases. As the natural number assigned to each science increases, the generality decreases while the complexity increases.

There is also a chain, if you will. Physics is applied mathematics, chemistry is applied physics, biology is applied chemistry, psychology is applied biology and sociology is applied psychology.


The chart seems pretty accurate.


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