How to self-study mathematics and understand it well?

[icecubebeast]

I am taking AP Calculus BC and I want to self study math so that I can be good at it.
The field of mathematics I want to study is applied mathematics. What methods are good for studying math by myself and becoming good at it? Which topics should I study sequentially after learning AP Calculus BC? By topics I mean topics that are equivalent to university math courses.

Please don't say, "It depends on the university" but say which math courses that YOU took to get your applied math degree (masters 6 year).

 

[jedishrfu]

There's the big three: Calculus, Linear Algebra and Differential Equations...

From there math branches out in many other areas.

 

[icecubebeast]

There's the big three: Calculus, Linear Algebra and Differential Equations...

From there math branches out in many other areas.

Which areas? Can you be specific? How to self-study mathematics and understand it well?

 

[jedishrfu]

Calculus is taught in three parts differential, integral and multivariable. Linear Algebra is a one semester course and so is Differential Equations which usually covers ordinary differential equations not partial differential equations.

Check the site: http://mathispower4u.yolasite.com/

There are videos that that cover these three courses.

 

[icecubebeast]

Calculus is taught in three parts differential, integral and multivariable. Linear Algebra is a one semester course and so is Differential Equations which usually covers ordinary differential equations not partial differential equations.

Check the site: http://mathispower4u.yolasite.com/

There are videos that that cover these three courses.

Can you please give me a course list and specifically which topics are based on and branch out from Calculus, Linear Algebra and Differential Equations? It is because I asked my teacher and there is complex analysis, differential geometry and many other topics that I don't know. So that's why I'm asking you to be specific.

 

[jedishrfu]

I can't answer your question as I don't have an MS or BS in Applied Math. I do have a BS in Physics which is close and I got that decades ago.

From my recollection the courses I took that were related to applied math:

Calculus 1, 2, 3
Linear Algebra
Differential Equations
Advanced Calculus
Boundary Value Problems
Tensor Analysis and Differential Geometry
Abstract Algebra
Topology
Group theory

And these physics courses

Classical Mechanics with Lagrangian and Hamiltonian forms
Electromagnetic Theory used Vector Analysis
Quantum Mechanics used Boundary Value Problems
General Relativity used Tensor Analysis and Differential Geometry

My suggestion to you is to look at the syllabus for Applied Math at several major universities and piece together a list and start studying it.

Be aware though that if you plan to skip some courses to "get ahead" you might regret it because your grades will be lower overall. I know I did this, I came in as a freshman and skipped Calculus 1 because I had learned the mechanics of it over the summer but didn't know the mathematical basis for it. I traveled farther mathematically by skipping a couple of others but then started taking some really tough courses with the proper background for doing proofs and it hurt my grades because I was getting Bs when I could have gotten As with less effort taking those courses I skipped and got no credit for.