Statistics Calculus - Is there a shorter roadmap to understanding calculus for statistics only?

[MathHelp]

Hi there,

I wanted to learn some calculus for statistics but it seems like pre-calculus will take many months. If you look at this page from Khan Academy, it does not look like it will be something I can understand for a long time:

Precalculus | Math | Khan Academy

I was wondering if the path to calculus would be shorter if there is something very specific I want to achieve.

What I would like to do is learn one aspect of statistics through calculus - would anyone be able to offer me a roadmap for that? You can choose the part of statistics that the roadmap applies to.

My overall goal is to have a very strong understanding of statistics and eventually understand calculus through statistics. This roadmap would just be a start - I would continue to learn calculus. I happen to find statistics to be a strong motivator for me as I can easily see the direct application to it in my life.

Any help would be appreciated. 

Edit: I'm referring to basic 1st year statistics. Although I am not formally enrolled in a course. I work fulltime and just study a statistics book in my sparetime.

Edited November 3, 2022 by MathHelp

[exchemist]

2 hours ago, MathHelp said:

Hi there,

I wanted to learn some calculus for statistics but it seems like pre-calculus will take many months. If you look at this page from Khan Academy, it does not look like it will be something I can understand for a long time:

Precalculus | Math | Khan Academy

I was wondering if the path to calculus would be shorter if there is something very specific I want to achieve.

What I would like to do is learn one aspect of statistics through calculus - would anyone be able to offer me a roadmap for that? You can choose the part of statistics that the roadmap applies to.

My overall goal is to have a very strong understanding of statistics and eventually understand calculus through statistics. This roadmap would just be a start - I would continue to learn calculus. I happen to find statistics to be a strong motivator for me as I can easily see the direct application to it in my life.

Any help would be appreciated. 

Edit: I'm referring to basic 1st year statistics. Although I am not formally enrolled in a course. I work fulltime and just study a statistics book in my sparetime.

It looks as if this is part of a general mathematical course. Learning basic differential calculus is relatively easy and doesn't require much of all that stuff. I learned it when I was 15, as part of the old UK O-Level syllabus. I don't think statistics helps much with learning calculus. You just need to draw functions as a graph and see how you can make approximations to the slope of the line that, in the limiting case, give you an exact value. There are various videos on this. Looking at them quickly I thought this one was fairly clear.

 

The chief mathematical idea is the idea of limits, what happens to an algebraic quantity when one variable gets smaller and smaller and tends to zero.   

But then the power of knowing the slope of a function at any point on its graph is that that represents its rate of change. This leads onto all sorts of applications. For example the rate of change of distance with time is velocity and the rate of change of velocity with time is acceleration. Also, the point a slope becomes zero is a maximum or a minimum (or sometimes a point of inflexion) of the curve, so you can find maximum and minimum values of functions this way. And there are lots more applications of course.

Integral calculus is the inverse process, in effect calculating the area under a portion of a curve. There are teaching modules on that too. 

So I think you should be able to short-circuit the modules of the Khan Academy course and go directly to calculus, provided you are OK with algebra and graphing functions and can understand limits. 

(I speak as a chemist rather than a mathematician. It may be that a proper mathematician would disapprove of the short cuts I am suggesting.) 

 

 

 

Edited November 3, 2022 by exchemist

[studiot]

3 hours ago, MathHelp said:

Hi there,

I wanted to learn some calculus for statistics but it seems like pre-calculus will take many months. If you look at this page from Khan Academy, it does not look like it will be something I can understand for a long time:

Precalculus | Math | Khan Academy

I was wondering if the path to calculus would be shorter if there is something very specific I want to achieve.

What I would like to do is learn one aspect of statistics through calculus - would anyone be able to offer me a roadmap for that? You can choose the part of statistics that the roadmap applies to.

My overall goal is to have a very strong understanding of statistics and eventually understand calculus through statistics. This roadmap would just be a start - I would continue to learn calculus. I happen to find statistics to be a strong motivator for me as I can easily see the direct application to it in my life.

Any help would be appreciated. 

Edit: I'm referring to basic 1st year statistics. Although I am not formally enrolled in a course. I work fulltime and just study a statistics book in my sparetime.

 

Firstly let me say that you can do a great deal of statistics without knowing or doing any calculus.

Calculus is a calculating tool (hence its name) for many other disciplines and its principles need to be learned separate from and previous to the applications.

So sorry there are no 'shortcuts' for staticians.

You can save a great deal of time and effort however by passing over the clever detail and tricks that someone intending to work out a lot of calculus will need.
You only need to understand what is going on.
Calculus is mostly used in the proofs of formulae in its statistical applications and your teachers will probably say things like

The average value of a function in the interval a to b is given by the integral of the function divided by (b-a).
So you will need to know what an integral is.
But you will not need to calculate it, just how to use the formula.

From that point of view calculus is divided into two parts  the differential calculus and the integral calculus, with the latter being more important in statistics.

[MathHelp]

I am not wanting to learn calculus for statistics. I am wanting to use statistics as a goal to help me learn calculus. So while I don't need calculus to understand statistics, my final goal is to have a good understanding of calculus.

I already know the fundamentals of statistics so just want to use that as something to attach new memories to - learn calculus with a context if that makes sense.

Thanks for both your replies.