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Calculus: Is it Really That Hard?

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BTDT
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30 Dec 2015, 2:06 pm

It often helps to draw pictures of what I am trying to understand, rather than manipulating symbols according to rules.



Rudin
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30 Dec 2015, 5:09 pm

dcj123 wrote:
Its only hard if you don't grasp algebra, math is a cumulative and is kinda like levelling up in an RPG game. You can't be level 20 without having understood level 19. If you don't understand any prior level of mathematics before it, it will probably seem harder than it is. Also math difficulty is overrated, I myself am not that good at it but it boils down to time. Math my require more time to study and as such is labelled a harder subject cause people or college students don't want to do the work and would rather be smoking pot with friends. Not trying to stereotype college kids, but thats what me and everyone I knew was thinking in college.


There is a lot to know, but some of it should be obvious. I think some people taking calculus courses focus more on the rules and procedures to obtain certain results, sometimes without knowing the definitions.

For instance, one can calculate derivatives without knowing what they actually are because there are certain rules, i.e

d/dx (x^n)=nx^(n-1)
d/dx (sin(x))=cos(x)
d/dx(cos(x))=-sin(x)
d/dx (kf(x))=k [d/dx (f(x))]
...


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30 Dec 2015, 7:38 pm

Most people will systematically choose to memorize lots of redundant particular cases and very specific rules rather than learn where they come from and how to deduce them. I seriously wonder if my memory, which my parents, some teacher or other and even some classmates always praised, is in fact very poor, so normal people, who can memorize massive amounts of data almost effortlessly compared with me, find deductive reasoning hard only by contrast.


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30 Dec 2015, 8:05 pm

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.



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30 Dec 2015, 8:11 pm

got A's in two semesters of college calculus. it was fun, but the teacher was very good.



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30 Dec 2015, 8:44 pm

I was very good at Algebra, but I found Pre-Calculus difficult. Because of this, I considered not taking Calculus in high school my senior year. But, in the end, I decided to take the class (it was an AP course.) I am glad I did, even though it really has had no bearing on my career. I needed *much* less math for the music and education directions I took in college, and about 2/3 of the students in my calculus course were heading into STEM fields.

I found Calculus, in general, not much more difficult than Algebra. To me, it was just the next step up from Alg. II in difficulty. Calculus was the most FUN of all the maths I took, and I even was tempted for a short while to study mathematics in college instead of music.

I ended studying the equivalent of the first two semesters of college-level calculus. I remember nothing now, and it really has no bearing on my life. It probably did help me with some deeper logic skills (even Aspies can grow in their logic skills) and breaking down large problems into steps. One definitely does not see such long problems in Alg.II, for sure!



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31 Dec 2015, 8:14 am

Rudin wrote:
dcj123 wrote:
Its only hard if you don't grasp algebra, math is a cumulative and is kinda like levelling up in an RPG game. You can't be level 20 without having understood level 19. If you don't understand any prior level of mathematics before it, it will probably seem harder than it is. Also math difficulty is overrated, I myself am not that good at it but it boils down to time. Math my require more time to study and as such is labelled a harder subject cause people or college students don't want to do the work and would rather be smoking pot with friends. Not trying to stereotype college kids, but thats what me and everyone I knew was thinking in college.


There is a lot to know, but some of it should be obvious. I think some people taking calculus courses focus more on the rules and procedures to obtain certain results, sometimes without knowing the definitions.

For instance, one can calculate derivatives without knowing what they actually are because there are certain rules, i.e

d/dx (x^n)=nx^(n-1)
d/dx (sin(x))=cos(x)
d/dx(cos(x))=-sin(x)
d/dx (kf(x))=k [d/dx (f(x))]
...


Yes, first year calculus is more memorization. Second year calculus is more derivation. Thanks, I forgot about the delta/epsilon stuff. It has been many years since I took those courses. Understanding the principles behind the mathematics makes it more interesting, fun and useful.


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Rudin
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31 Dec 2015, 9:47 am

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).


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31 Dec 2015, 11:35 pm

Rudin wrote:
You can also calculate instantaneous rates of change, cannot be obtained by pre-calculus methods.


Not true. Remember, if you were to take the value of two functions and divide them out by a limit approaching zero, you can get the same result without differentiation. This is first principles, often taught in advanced algebra courses.


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Rudin
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02 Jan 2016, 8:39 am

Deltaville wrote:
Rudin wrote:
You can also calculate instantaneous rates of change, cannot be obtained by pre-calculus methods.


Not true. Remember, if you were to take the value of two functions and divide them out by a limit approaching zero, you can get the same result without differentiation. This is first principles, often taught in advanced algebra courses.


I don't think I understand. Do you mean taking the limit as b goes to a of (f(a)-f(b))/(b-a)?


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06 Jan 2016, 2:15 am

Pre-Calc was a nightmare, but the professor was awful. I've heard that Calculus is much easier.



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06 Jan 2016, 10:22 pm

For people who have difficulty with Calculus or math in general or for those who lack good resources, the Khan Academy on YouTube and the WikipPedia articles provide excellect quick, concise explanations of mathematical concepts.



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17 Jan 2016, 4:22 pm

Calculus isn't difficult. Calculus is just the study of how to find the slope of lines and accumulations/area under curves. Calc I is the easiest , followed by calc III which just 3 dimensional stuff, -while calc II is the hardest and most tedious. I think most people could do well in calc I as that is just the basics. If you have a learning disability, you may have a hard time with it - but other than that its not that difficult. I guess that the main reason people have a hard time with it is because its a new subject to them. Most people have studied some form of algebra (solve for x) since they were like in 6th grade. Even pre-calculus is just a review of algebra with some trig. When these people take calculus- they find it hard because they are finally doing something other than "solve for x".

Calculus deals with 2 topics- differentiation and anti-differentiation (integration).
In calc you find slopes of functions that couldn't be found using just algebra - functions like y=x^2 --thats called differentiation. An example would be - here is the function describing the position of a particle, compute the velocity.

The opposite is integration/anti-differentiation. An example would be : here is a function describing the velocity of a particle- find the function that describes its position.



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18 Jan 2016, 4:47 pm

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.



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26 Jan 2016, 12:25 pm

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.'


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26 Jan 2016, 4:58 pm

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.