RE: Math suggestions
January 2, 2016 at 5:42 am
(This post was last modified: January 2, 2016 at 6:08 am by Alex K.)
Problem is that I have only spent my senior year in the US and don't know exactly what all the courses are called there.Americans with science degrees can give you more specific info there.
Basic algebra is a given if course, how to use fractions and all that. The most important things you need in order to study physics and astronomy (which I assume you still intend to) are then linear algebra and calculus, and in particular trigonometry, which kind of becomes a part of calculus. Those are the things you need on a daily basis. In particular
Calculus
-how to simplify expressions
- how limits and derivatives work
- how series and sequences work
- how integration works in principle
- integrals and derivatives of standard functions such as polynomials and trig functions
-tricks for simplifying integrals
in LinA
- how vector spaces work in principle
- representation of vectors in a basis
-scalar products and projections
- multiplication of matrices and vectors and how to use them to write down systems of linear equations and quadratic equations
- determinants and systems of linear equations
- Matrix inversion, diagonalization, eigenvectors and eigenvalues
Other:
Look at the basic trigonometric functions (sin, cos, tan) and their relations to triangles. Do that before you do anything else, or you will be very confused by many things above
Then you are off to a good start and good till a coupla semesters in.
Later you will need ordinary and partial differential equations and calculus of complex variables and functionals, but that is something you can keep in mind but you do not have to worry about in the beginning. Learning how to use complex numbers in basic operations is simple and fun though, so you should just do it on the side.
I took AP level calculus in 12th grade (derivatives, limits, integrals and volume integrals) and that was pretty spot on what I needed later. You do not need worry about too much abstract algebra in the beginning.
So my suggestion is look at introductory college level linear algebra and calculus books, and check whether you think you can understand it and work the problems. If there is too much stuff that you do not get, try to find out where the deficits are. You can ask me, too.
Use a good book. By all means, use websites and youtube tutorials and wikipedia too, but not as your primary guide I would say.
Basic algebra is a given if course, how to use fractions and all that. The most important things you need in order to study physics and astronomy (which I assume you still intend to) are then linear algebra and calculus, and in particular trigonometry, which kind of becomes a part of calculus. Those are the things you need on a daily basis. In particular
Calculus
-how to simplify expressions
- how limits and derivatives work
- how series and sequences work
- how integration works in principle
- integrals and derivatives of standard functions such as polynomials and trig functions
-tricks for simplifying integrals
in LinA
- how vector spaces work in principle
- representation of vectors in a basis
-scalar products and projections
- multiplication of matrices and vectors and how to use them to write down systems of linear equations and quadratic equations
- determinants and systems of linear equations
- Matrix inversion, diagonalization, eigenvectors and eigenvalues
Other:
Look at the basic trigonometric functions (sin, cos, tan) and their relations to triangles. Do that before you do anything else, or you will be very confused by many things above
Then you are off to a good start and good till a coupla semesters in.
Later you will need ordinary and partial differential equations and calculus of complex variables and functionals, but that is something you can keep in mind but you do not have to worry about in the beginning. Learning how to use complex numbers in basic operations is simple and fun though, so you should just do it on the side.
I took AP level calculus in 12th grade (derivatives, limits, integrals and volume integrals) and that was pretty spot on what I needed later. You do not need worry about too much abstract algebra in the beginning.
So my suggestion is look at introductory college level linear algebra and calculus books, and check whether you think you can understand it and work the problems. If there is too much stuff that you do not get, try to find out where the deficits are. You can ask me, too.
Use a good book. By all means, use websites and youtube tutorials and wikipedia too, but not as your primary guide I would say.
The fool hath said in his heart, There is a God. They are corrupt, they have done abominable works, there is none that doeth good.
Psalm 14, KJV revised edition
