Steps to Studying in Math I'm 16 and quite a late-start in math. I was home-schooled for a while and just got interested in math recently. I would like to make a footprint in the field of mathematics when I'm older and would like to know my logical next path for achieving that goal. Currently I am using the Art of Problem Solving's Intro to Algebra and Intermediate Algebra. During my winter break I plan to go on to Counting & Probability and then the Introduction to Number Theory, and when I get the time I will finish their Intro to Geometry. I have no experience prior to Algebra in homeschool as I didn't study much math in homeschool between grades 3-8. My current prior experience includes Algebra 1 and 2, and Intermediate Algebra in college. The reason I am using the AoPS books is because I feel lied to from my school because I thought I was doing well, and then I look onto problems like the IMO, AMC 8, 10,12 and I have no clue where to start. This is why I would like to begin studying math, intensively. Thank you all 
 A: Yup. AOPS is a good start. Their website also has a forum like this one that you can use to ask and answer questions I believe.
Math is a big topic. You may use the texts you reference above to explore Number theory, Probablity, Algebra, etc. But the real issue is that there isn't really a "right" path to learning math. Study the things that you find interesting. Take those interests seriously. When you have a  number theory puzzle you are curious about: document the question. Sit with a few days. Try and solve it. Can't? See if the Aops text on number theory is a rewarding resource. If it is: great. It isn't? Document the question again on the AOPS website. Can they help? No? Ask the question again here. 
Here is the issue: no one can tell you that you should study X then Y then Z. Educators will tell you that but honestly they don't know that studying differential equations will be more relevant to your life than studying discrete structures. My point is you should study the things that make you happy and worry less about "making a footprint" or being confident that you are the same level as students who are taking the AMC 8,10,12. These are quiet enjoyable/challenging puzzles that one can look at. It should be noted that work of mathematics discovery and solving a challenging puzzle on a timed test are connected only in a very superficial way.  
I think your school may be communicating to you that are you doing fine in math... because you are doing fine in math. It is not their job to supply you with all the resources for you to do the things you want to do... Want to study number theory? Go for it. 
