# Order of self-studying

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Hello people!

I've started studying math on my own. I'm currently in high school, and there we are currently at quadratic equtions. I want to know what order of self-studying mathematics do you recommend? I started trigonometry course for beginners on youtube, and I want to cover them all one by one, trigonometry, logarithms, and sometimes in the future differential equations and calculus. I'm curious what do you think is the best order to do it? Mainly I'm interested in math because I want to pursue a career in physics or/and astronomy so I want to learn as much as possible so I don't have to do it later in life. Also, besides the order of studying, are there any courses that apply to that order that you recommend?

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38 minutes ago, Riba said:

Hello people!

I've started studying math on my own. I'm currently in high school, and there we are currently at quadratic equtions. I want to know what order of self-studying mathematics do you recommend? I started trigonometry course for beginners on youtube, and I want to cover them all one by one, trigonometry, logarithms, and sometimes in the future differential equations and calculus. I'm curious what do you think is the best order to do it? Mainly I'm interested in math because I want to pursue a career in physics or/and astronomy so I want to learn as much as possible so I don't have to do it later in life. Also, besides the order of studying, are there any courses that apply to that order that you recommend?

Hello, Riba and welcome.

Maths on your own huh ?

So is asking questions so remember to come here and ask if you get stuck.

Quadratic equations and basic trig ?
So you are in junior high then.

You haven't said which country you are in, but in the UK you will be doing some algebra (those pesky equations), some geometry, which goes with the trig, some modern maths such as sets and logic. There will also be lots of practice applications questions (both in maths symbols and in words).

This is all good stuff that leads into later material, normally encountered in senior high.
This is where you will encounter calculus first and perhaps a taste of differential equations.

But you will also encounter coordinate geometry and other topics.

There is no one order to 'do' the different topics in.

This is because Maths hangs together so you need a bit of one branch to be able to work in another branch.
With that under you belt you can use your new knowledge to expand both branches and perhaps a third, fourth etc.

One word of warning since your ambition is  (astro)physics.

Any course whether at school, college or online will be designed for the questions asked to be solvable using the material taught.

But no course teaches it all so they leave out the exceptions and difficult pieces, and never ask questions about them.

So it is easy for a student to be lulled into a sense of false security, thinking they know enough.

But in real Physics it is often the exception that you need.

Go well in your studies, I look forward to periodic questions from you.

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3 minutes ago, studiot said:

Hello, Riba and welcome.

Maths on your own huh ?

So is asking questions so remember to come here and ask if you get stuck.

Quadratic equations and basic trig ?
So you are in junior high then.

You haven't said which country you are in, but in the UK you will be doing some algebra (those pesky equations), some geometry, which goes with the trig, some modern maths such as sets and logic. There will also be lots of practice applications questions (both in maths symbols and in words).

This is all good stuff that leads into later material, normally encountered in senior high.
This is where you will encounter calculus first and perhaps a taste of differential equations.

But you will also encounter coordinate geometry and other topics.

There is no one order to 'do' the different topics in.

This is because Maths hangs together so you need a bit of one branch to be able to work in another branch.
With that under you belt you can use your new knowledge to expand both branches and perhaps a third, fourth etc.

One word of warning since your ambition is  (astro)physics.

Any course whether at school, college or online will be designed for the questions asked to be solvable using the material taught.

But no course teaches it all so they leave out the exceptions and difficult pieces, and never ask questions about them.

So it is easy for a student to be lulled into a sense of false security, thinking they know enough.

But in real Physics it is often the exception that you need.

Go well in your studies, I look forward to periodic questions from you.

Thanks for the warm welcome  .

I am from Bosnia and Herzegovina in which high school is made out of 4 years. I am currently the second year of high school, and after I finish all four years I will head off to college. In my first year of high school we've done some mathematical tautology, geometry and just a little bit of trigonometry (just some basic introduction though). As I said, right now we've been covering quadratic equations for quite some time. When I mentioned that order, I did not mean some dogmatic branch following, I rather meant what would be the best order of branches to study if I want to leave no blank things about one branch while going into next one which requires things from the previous one, if you understand me. The point of my studies is to learn as much as possible and to start early in life. I just always want to know more and it's like I'm never satisfied. In school, we are given completed results of formulae and equations by our teachers while not being taught where did all those formulae and equations come from. That's what I want to know and that is my point. My two questions are always how and why. Until I get to the rock buttom of questioning something, I will not stop doing it. I wish to explore the way nature works and of course to be ahead of school, learn things that I truly want to. I want to untie some misteries of today world's physics and hopefully discover something one day.

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55 minutes ago, Riba said:

if I want to leave no blank things about one branch while going into next one which requires things from the previous one, if you understand me.

I do understand you and please be clear.

That is just not possible.

There are many branches of maths.

You need a bit of almost each and evry one to study fully any one branch.

That is why Maths in particular is taught in what I call a spiral approach.

At each turn of the spiral (say each year) you learn some more of some or all the branches, based on all that you learned in each branch the precious year.

Mathematicians carry this on through their working lives.

Here is a true story.

When I was in junior high I was pretty good at Geometry.

I thought I knew everthing there was to know about Geometry and could solve any problem.

So when I move up to  senior high (college for you like the american system) I was suprised to find the first thing on the curiculum was   -  Geometry.

But Coordinate Geometry.

I was shocked and blown away by all this new stuff.

But it underlies calculus, applied maths, differential equations, physics and so much more.

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3 hours ago, Riba said:

The point of my studies is to learn as much as possible and to start early in life. I just always want to know more and it's like I'm never satisfied. In school, we are given completed results of formulae and equations by our teachers while not being taught where did all those formulae and equations come from. That's what I want to know and that is my point. My two questions are always how and why. Until I get to the rock buttom of questioning something, I will not stop doing it. I wish to explore the way nature works and of course to be ahead of school, learn things that I truly want to. I want to untie some misteries of today world's physics and hopefully discover something one day.

Gerard ’t Hooft has created this website for you:

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18 hours ago, studiot said:

I do understand you and please be clear.

That is just not possible.

There are many branches of maths.

You need a bit of almost each and evry one to study fully any one branch.

That is why Maths in particular is taught in what I call a spiral approach.

At each turn of the spiral (say each year) you learn some more of some or all the branches, based on all that you learned in each branch the precious year.

Mathematicians carry this on through their working lives.

Here is a true story.

When I was in junior high I was pretty good at Geometry.

I thought I knew everthing there was to know about Geometry and could solve any problem.

So when I move up to  senior high (college for you like the american system) I was suprised to find the first thing on the curiculum was   -  Geometry.

But Coordinate Geometry.

I was shocked and blown away by all this new stuff.

But it underlies calculus, applied maths, differential equations, physics and so much more.

Gerard ’t Hooft has created this website for you:

I appreciate your response, it's a long way in front of me. I'll try to do my best and thanks again!

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27 minutes ago, Riba said:

I appreciate your response, it's a long way in front of me. I'll try to do my best and thanks again!

It sure is. Good luck!

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Hello Riba ,

I have tried to do this on my own too . The good thing is i discovered a lot of new good books .

Whenever i have questions in my head i look at these books .

Once upon a time i was only familiar with my school and college textbooks and internet at my place was very slow .

But now i can recommend these books to you .

Homework Helpers Basic Maths and Pre Algebra

Intermediate Algebra - Terrance Berg

Precalculus 7th Edition by David Cohen/Theodore B. Lee/David ( For trigonometry )

Calculus and its applications. — 10th ed./Marvin L. Bittinger,. David J. Ellenbogen, Scott A. Surgent

I also think most of the mathematics we generally  learn looks like this .

Correct me if i am wrong

Quote

Algebra , Find the unknown x
Differentiation , Find the unknown instantaneous rate of change
Integration , Find the unknown area underneath an instantaneous rate of change
Differential equation , Find the unknown function

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• 1 month later...

Have you seen this ?

Edited by studiot
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On 2/22/2022 at 5:04 PM, studiot said:

Have you seen this ?

Yeah, I have! I watched the video on the youtube too!

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Or send me somebody who passes the vision test first and I'll do their homework. You have a genie a bottle here if you match the part.

The whole 'litany against the senses' thing is being a bit overblown value wise.

It's slim pickin's where I come from.

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