Very important question for math-

[T.O.E Dream]

Lately, I've been trying to learn as much as mathematics as i can, but i have been also trying to find out what order i should learn it in so that when I'm learning a new thing i won't get stuck because i didn't learn an important part of it. For example, i don't want to be learning calculus but i can't because i don't know enough geometry, or algebra etc. So i need your help by telling me (try to be very specific) what order of math i need to learn by, even from Grade 1 to Grade 12 to a Ph.D in mathematics. If there are any books or website that i can read for more information that would help a lot. and i know someone might come and say "Well, it really depends and it may vary." I know that but any basic outline of branches in math would be great. For example, "You need to know how to add and subtract fractions to learn this and you need to know how to count to do this,,," What I'm trying to say is that i don't want it be to basic, so when you tell me i need to learn something also include what i need to know to learn it. I hope you got the point, and i don't care if your answer is really long because i prefer it to be. I hope you can HELP!

Also, can you tell me any good books that i could use to learn any of the subjects?

 

[DrummingAtom]

http://www.phys.uu.nl/~thooft/theorist.html#list

Check out the Math section.

 

[General_Sax]

If you hope to one day hold a PHD in Math, then find out the pre-requisites for the math program at your university of choice and complete those classes. Study hard and good luck. As for good books on the subject, what's wrong with your class textbook?

 

[T.O.E Dream]

well, really I'm still in grade 7, so that really says everything
and I'm not thinking of getting a ph.d in math i just wanted to get an outline of practically eveything that's all. but thanks anyways

 

[qntty]

IMO, you're trying to rush through subjects way too fast. What classes have you taken in school so far? Even if you're capable of studying calculus in middle school, you should wait until at least sophomore year (this is assuming that you don't take a class in calculus freshmen year, but if you do there's nothing wrong with learning from a high school class as long as you took all the classes before it). There is a lot of math out there and you don't need to rush into calculus to learn it. First you should master the basics of algebra, this is key. Gelfand wrote a good book on the subject if you don't have one already. After that there's no order that you really need to go in. You should get involved in an extracurricular math team that you can. Some middle schools have a MATHCOUNTS program which is good to do.

You won't find too much help from this forum as it's geared toward grad and undergrad students, but you'll probably find a forum like mathlinks very helpful. They have a http://www.mathlinks.ro/Wiki/index.php/Math_books of books which you'll also find useful.

 

[snipez90]

I agree with many of qntty's points. There is no need to rush into more advanced mathematics. This is especially important if you don't have the basics down yet. On the other hand, it wouldn't hurt to go on wikipedia and check out the relevant articles for understanding calculus. You can really learn lot about various mathematical topics just by checking out wikipedia, mathworld, planetmath, etc. Don't worry too much about finding the "right" books.

 

[derek e]

Start with a geometry book. Euclid's elements should be fine and Green Lion Press makes a copy that might be good for you.

Algebra/Trig
Calculus. This will require algebra and trigonometry. Think about it geometrically.

[the next courses can be taken in any order, they require the above]
Multi-variable Calculus (may or may not be a separate course)
Linear Algebra
Differential Equations
[end]

At this point, you should know the above well and may have taken some statistics or finite mathematics somewhere in there. Upper division has some freedom and exploration, but here is a core outline that is usually supplemented with electives.

Linear Algebra
Real Analysis. Formal calculus.
Complex Analysis. Requires real analysis.
Abstract Algebra

[example electives]
Set Theory
Logic
Differentiable Geometry
Partial Differentiable Equations
Numerical Analysis
[end]

Notice some reoccurring words, such as 'differential', 'algebra', 'analysis' and 'geometry'. This is through an undergraduate degree. Your best bet might be to just look at a college catalog. The information about each course will be more precise and it will have a list of requirements for a given course. Reading these catalogs makes it easy to plan and get involved in your education. They also help build up excitement for classes that have taken some investment (satisfying prereqs). Colleges usually have an online catalog. You can also visit a college :), go to the campus bookstore and most will have catalogs available for purchase (call and check, of course).

 

[qntty]

Start with a geometry book. Euclid's elements should be fine

Although it's fine to read after a first geometry course, I'd say that elements isn't a good introduction. A modern book is a better choice, especially for a 7th grader.

 

[derek e]

Although it's fine to read after a first geometry course, I'd say that elements isn't a good introduction. A modern book is a better choice, especially for a 7th grader.

I don't see the harm for self study. An Element's book from Dover may be a little oppressive, but the Green Lion Press copy has a lot of the extra exposition removed. Although, I learned a lot from reading cheap Dover books "before I should have." It is a good skill to be able to translate this type of writing into something one can digest.

 

[T.O.E Dream]

the reason I'm asking what order i should learn it in is because recently I've been learning Algebra that's more advanced than what we do at school and I've done a good job of understanding it. all i want to do is take small steps to learning more advanced stuff so that i still understand what I'm actually doing. that means I'm learning basic stuff than more advanced stuff to really advanced stuff. I don't expect to be learning really advanced stuff until I'm in grade 10 or maybe 11 so i got a few years to go but i still want to draw out a plan of what i need to learn.

By the way just in case you might be wondering I'm doing all this so i actually get to learn the mathematical side of physics. i feel like if you don't know the math you might as well say you don't know anything (though that's not completely true). I've asked this in a few other threads but it seems like the answers are too raw, so can anybody tell me exactly (in detail) what math i need to learn for everything in physics. include how to learn it if you can. THANKS!

 

[T.O.E Dream]

Also, can somebody tell me when you actually learn all of this stuff in school?

 

[owlpride]

Also, can somebody tell me when you actually learn all of this stuff in school?

A typical college-bound high school student might finish algebra and geometry by the end of sophomore year, take pre-calc as a junior and calculus as a senior. Then linear algebra, multivariable calculus and differential equations freshman year in college or spread out over two years freshman and sophomore year. Real analysis, abstract algebra and other higher-level math electives sophomore, junior or senior year in college, depending on how much you want to rush things.

 

[Troponin]

With each new math course, I'm reminded just how important algebra is...

 

[Tiger99]

I think it's great that you're learning mathematics on your own and starting early. :)

The great thing about starting young is that you can take your time and concentrate on whatever interests you. It's hard to answer your question just because once you learn a bit of mathematics, it's hard to remember not knowing it. For example, in grade 7 do you know about trigonometric functions like sine, cosine, etc? and other functions like log? and solving quadratic equations? Maybe I'm asking dumb questions.

Actually when I was in grade 6 I used to take my older siblings' test papers and problem sets that they brought home and work through them to try to learn a bit ahead. They were more interesting than what I was doing in school because they were more advanced (and so mysterious).

I don't remember it doing me any harm that I didn't always know everything. I would just guess and see if my guess fit the answers. You can always fill in the gaps later. I found learning by doing problems was a lot more fun than trying to read textbooks or even trying to learn "ideas". Also, it keeps you grounded. I would recommend just looking at the problem sets in books - if they seem like you can (almost?) do them, then that's probably a good book to look at.

I think it's only a slight over-statement to say everything in mathematics is related to everything else in mathematics. So any knowledge you gain will be useful. Later on, the peculiar things that you learned really carefully and deeply when you were young give you a particular individual view of mathematics that will allow you to see something another person misses.

I don't think there's a wrong way to learn about things like calculus on your own anyway. Sure, it might take you a lot longer to learn the basic things but there's no harm in that. Don't worry too much and have fun.