I'm a highly determined (and slightly stubborn) high school freshman who wants to learn enough mathematics to conduct mathematics research with a mentor. Looking on the internet, I found a program called MIT Primes, where students can be matched with graduate students/professors at MIT to conduct research over the course of one-year. However, looking at their qualifying test, I am very far from that skill level. A link to their qualifying test can be found here. https://math.mit.edu/research/highschool/primes/usa/index.php The program seems to only accept juniors, so one could say I have plenty of time to prepare, but I know that Junior Year will be extremely stressful and full of college preparations, so I'm aiming to mentally ready for such a program by next fall. I know it's a stretch, but I believe if I work that hard, I'll get somewhere close to where I want to be. If anyone knows any suggestions for reaching such a level of proficiency even after studying and completing the following outline, I would be really, really grateful! Any adjustments or removals to this outline are also gratefully received. How would you train a high schooler with only Algebra II and Honors Geometry under her belt to conduct mathematical research? I'm really interested in Group Theory and Abstract Algebra, as well as Braid Theory, Topology, Number Theory and Combinatorics. PROBLEM SOLVING The Art of Problem Solving, Vol. 1 The Art of Problem Solving, Vol. 2 Introduction to Number Theory, AOPS ALGEBRA Algebra by I.M Gelfand Schaum's Outlines for Algebra GEOMETRY Geometry I: Planimetry by Kiselev Geometry II: Stereometry by Kiselev Geometry by Serge Lang Schaum's Outlines for Geometry TRIGONOMETRY Trigonometry by I.M Gelfand Schaum's Outlines for Trigonometry REFERENCE Basic Mathematics by Serge Lang PRE-CALCULUS Schaum's Outlines for Pre-calculus CALCULUS AP Calculus AB, Thinkwell AP Calculus BC, Thinkwell PROOF-WRITING ??? Mathematics is my favorite thing in the entire world-- I'm not afraid of putting in a ridiculous amount of work, because I am a ridiculous type of student :) Just tell me what I'll have to do! Thanks and have a safe and happy day!