Question

Hi. I'm currently a middle schooler, about to enroll in high school by the end of the year. I've decided to major in theoretical physics and pure mathematics. Now, because I really enjoy math and science, I'm studying math from high school and beyond. Does anyone know the order of studying math?
(Like Pre-Algebra, Algebra I, Geometry, Algebra II...)

Answer 1

What is your current level of mathematical and physical understanding?

Answer 2

For math, I have studied Pre-Algebra~Calculus I and parts of Calculus II, Linear Algebra, Statistics.

Answer 3

For physics, I'm currently studying Systems of Particles/Rotation

Answer 4

With maths, something that is really important to grasp early on in your studies is aiming for a fundamental understanding of the material. To what degree have you studied those subjects you listed?

Answer 5

I'm confident that I have mastered Pre-Algebra~Trigonometry/Precalculus. (I'm currently reviewing by solving hard problems) I'm also confident to say that I mastered 90~95% of Calculus I.

Answer 6

For physics, I can understand/grasp all of the concepts I've learned so far.
However, I have to constantly solve problems because I'm having a bit of a problem to apply them to actual problems.

Answer 7

Also, adding to math, I know the basics/techniques of Integration, but still learning.

Answer 8

That's all very impressive, especially considering your age. So your question is, what is the general order of math education?

Answer 9

Yes.

Answer 10

Up to major level, like topology and tensors, abstract algebra...etc

Answer 11

Well, I'll try my best. For k-12, its early math, arithmetic, pre-algebra, basic geometry, algebra 1, geometry, probability, statistics, algebra 2, trigonometry, pre-calculus, differential calculus, integral calculus and basic differential equations.

Answer 12

How about in college?

Answer 13

In university, students usually take calculus 1, then linear algebra, then calculus 2, then linear differential equations, then multivariable calculus. Beyond that it branches off into numerical analysis, complex analysis, higher order differential equations, topology and a bunch of other obscure topics that you can't put in an order because they are studied concurrently in graduate school.

Answer 14

How much Calculus would you learn in high school?
Like do they go into Taylor Series or is it much easier than what I think?

Answer 15

No, the likes of Taylor and Mclaurin are saved for college.

Answer 16

How about areas under polar or parametric equations?

Answer 17

Or something like cylindrical/spherical coordinate system

Answer 18

All of those are saved for college?

Answer 19

Areas under polar and parametric yes, but cylindrical and spherical co-ordinate systems are saved for later.

Answer 20

Because I'm in Korea, I have no idea how things work there.
How deep do you go for geometry and probability/statistics?

Answer 21

The deepest in geometry is difficult trigonometry problems and a lot of co-ordinate geometry. As for probability and statistics, it is deep enough to apply calculus.

Answer 22

Finally, as I said, I'm currently studying Calc II/ reviewing Pre-Calc. Also, I'm reviewing some stuff that I forgot such as Epsilon-Delta Definition of Limit, Hyperbolic Trig...etc.
Generally, how long does it take to master Calculus?

Answer 23

Considering what I've studies so far...

Answer 24

Depends on what you mean by master?

Answer 25

Like fully understand all the way up to Calculus III so that I have no problem in later courses like differential geometry, topology, or even theoretical physics.

Answer 26

I don't know you, but from what you have told me so far it seems you have a deep interest in mathematics, which is fantastic. It appears that you have a decent comprehension of certain topics but since you teach yourself and haven't been tested, there is no objective way to view your abilities. To put it simply, calculus is started in the last two years of high school, and calculus 1 and 2 take up several years of college. Calculus 3 is a whole other beast and differential equations can be hell. Differential geometry, topology and theoretical physics are all topics that people spend the rest of their lives studying. Basically, for most people, they need to take the long root. Lets say you're 14 right now; if you were to dedicate a lot of your free time to really mastering these topics, you could be doing advanced topics in something like two years maybe. But that's only if you really master every stepping stone on the way.

Answer 27

http://tutorial.math.lamar.edu/ This is a good learning resource for most of what you are looking for.

Answer 28

It's all under the class notes tab.

Answer 29

That's exactly what I used to study Calculus I/ parts of II

Answer 30

If I really don't get a concept, I use www.khanacademy.com

Answer 31

But it is important to remember to test yourself. Otherwise you just think you know the material without being sure of it.

Answer 32

Also, I have been tested on differential calculus/integral calculus, and it seems like I just have to work out few more concepts such as Cauchy Mean Value Theorem or L'Hopital's Rule..., and I think I'll be good to go with differential calculus

Answer 33

You've got all your techniques down?

Answer 34

What do you mean?

Answer 35

Differentiating techniques.

Answer 36

Like do I know every techniques of differentiating?

Answer 37

Yeah. Pretty much.

Answer 38

sum, product, constant, composite, logarithmic...etc.

Answer 39

I just have to learn stuff like differentiating polar/parametric/hyperbolic...etc. those kinds of functions.

Answer 40

It's good you know what to work on.

Answer 41

To @ilr1
Thank you very much for sticking with my question for more than an hour!
You helped me a tons!
Now I know how to continue my studies to become a pure mathematician!
Thank you, again!