Math suggestions

[Heat]

I'll just get to the point

I'm thinking I want to improve my math skills. I'm in 10th grade, basically only experienced with algebra, no geometry, calculus, whatever yet.

First question; what are the different courses of math? Like levels, categories, whatever they're called. I.E: Algebra would be one. Geometry would be another.

Second question; What are some resources you could refer me to that would skip all the useless stuff they do in class. What I mean is like generally in classes they will drag out the subjects, and it will end up being boring because when you could have easily gotten by on information that could be provided in half the time it took, the actual time they took is just unknowingly packing on information in hopes it might be useful to a couple kids in class, or is used for repeating information already learned. 

Do any of you know where I can progress in math, learning the basics of each subject, so I have an understanding that's sufficient in grasping and obtaining the skill in hopes it will benefit me in the future? Things like Khan math, etc. It all just seems incredibly daunting, there's so many different math skills I COULD learn, so much information, I just don't want to waste my time. I really prefer(for many other things as well) when everything is layed out, as if in a check list, like "Do this, that, that, that, done". I don't like the information being scattered all over the place so that i'm not even sure where to start, because it makes me not want to start. 

I just want someone to help me, and simplify it for me, like "Here are the main categories that will be important to learn, __, __, __, __. Now here are the sites that will help __ ,__, __, __. Now here are the things, on those sites, that you can do to get a basic understanding of each category, __, __, __, __, __."


I appreciate it.
Heat

[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.

[robvalue]

Calculus is integral (hah!) to further mathematics. Getting a handle on that will be a great start.

I don't have knowledge of resources I'm afraid, but I can help with many specific questions or subjects.

[vorlon13]

In 'real life', I've found geometry more useful. Also, just doing the problems helps you sharpen your thinking skills across the board.

[robvalue]

Indeed, geometry is exceptionally useful.

Just don't do what my previous students tended to do and write down whatever the calculator tells you without using your brain. If the calculator says the length of wood you need to cut is minus 4cm, you probably hit a wrong button.

[Alex K]

In 'real life', I've found geometry more useful. Also, just doing the problems helps you sharpen your thinking skills across the board.

Certainly. But heat previously said he wanted to become an astronomer so I listed the essential topics needed to get started in college as a physics/astronomy major. Geometry is indispensible as well of course.

[SteelCurtain]

Generally:

Algebra
Geometry
Trigonometry/Precalculus
Calculus
Linear Algebra (aka College Algebra)
Calc II
Statistics
Calc III
Differential Equations

Those will get you through a BS in an Engineering principle. (Calc II/III/DiffEqs will be integral is Statics/Dynamics and physics/chemistry)

For learning on your own, I can't stress how awesome Khan Academy is. From Elementary school through college math, everything you need to learn is right there. It was amazing for me to teach myself Calc II/III again after 10 years for a Calculus based Statistics class. Well thought out problems, all leading toward conceptual understanding.

Very useful.

[Angrboda]

A large part of math is training your brain how to think properly. There is no substitute for doing the work.

I never did the work because I was bright enough to pass the tests without doing the work. I would just absorb the concepts and improvise the supporting bridges.

For example, I never worked through the trigonometric identities. So even in Differential Equations, if I needed a bit of trigonometry, I would invent it on the hoof from sin^2 x + cos^2 x = 1. This basically doomed my later math career.

I suggest you do the work.

[Alex K]

A large part of math is training your brain how to think properly. There is no substitute for doing the work.

I never did the work because I was bright enough to pass the tests without doing the work. I would just absorb the concepts and improvise the supporting bridges.

For example, I never worked through the trigonometric identities. So even in Differential Equations, if I needed a bit of trigonometry, I would invent it on the hoof from sin^2 x + cos^2 x = 1. This basically doomed my later math career.

I suggest you do the work.

Knowing how to derive these things is incredibly important, too, but when push comes to shove, even when you for example do cutting edge research, *anything* you know by heart will allow you to think faster about things. It will make the difference of being able to complete a complicated argument at the blackboard vs. awkwardly scrambling for notes for half a day. Some things you only see in the first place if youhave done the work. I say that as someone who like you tended to be lazy with the rote work, compensating by deriving on the fly.

[brewer]

Remember to use all your fingers and toes. Need more, sit next to a cutie with a pension for one toed shoes! (hehe)