<p>Hey Guys, So i'm a sophomore in high school and I decided that I wanted to pursue the AMC competition path which is as follows:</p>
<p>AMC 12 - American Mathematics Competition
AIME - American Invitational Mathematics Examinatin (Need to score well on the aforementioned test)
USAMO - U.S.A. Mathematical Olympiad (Need to score excellent on the previous test)
MOSP - Mathematical Olympiad Summer Program (Need to Wreck the previous test)
IMO - Internation Mathematics Olympiad (Total Mathematical Course Anhilation?)</p>
<p>So as many of you can figure out, I'm not going to stress if I don't make it past round 1 as it is quite difficult (and I realize that!) however here is the deal...</p>
<p>My Mathematics Background is quite simply extremely-advanced-in-analysis... I've studied Differential Equations, Tensor Calculus, and other subjects but it comes with one sad drawback...</p>
<p>My Discrete Mathematics is terrible... As in I only know as much probability as can be solved with algebra (and integrals... if you're given the density function), I truly don't understand any number theory, have a very weak background in set theory etc... (Because you don't have to use much of the above to pursue analysis)</p>
<p>So I'm requesting any advice on studying up for the test which is on February... Right now what I have lined up:</p>
<p>Online Set Theory Book (from boistate.edu just google "free set theory textbook to find it")
AoPS - Introduction to Counting and Probability
Khan Academy Probability
AoPS - Intermediate Counting and Probability (once Intro is all done)
AoPS - Introduction to Number Theory
AoPS - Volume 1 & 2
AoPS - Group Theory Course</p>
<p>I generally can work out of books but I prefer self paced online material like Khan Academy... Is this a good amount of stuff for test preparation or should I do more? Should I drop certain things if they are unecessary. I'm going to start tutoring additional students to get the money to fund the whole operation... You can call me immature/arrogant/naive whatever but I have a dream of reaching the MOSP camp this year despite my weak background in discrete through this two month steroid-study that i'm embarking on so any advice on how to streamline it for competition math would be looked favorably upon.</p>
<p>Assuming you read that all I have one more thing: How much does this benefit college admissions? Could you pursue full-time amateur research if you do well on the USAMO/IMO? As in would the academic community take you seriously? Because not only for the thrill of competition but I am doing this more for a job within the next year as opposed to college admission (and then 3-4 years of study, follwed by masters for a job)</p>