Self Studying Advanced Mathematics

Hello, my name is Alex Figueroa and I am currently a high school junior. I am highly motivated to learn math and wish to pursue a PHD in Applied Mathematics.

My question is: Would my hard work and motivation self-studying math be noticed by university admissions? If so, would it increase my chances of admission to Stanford, Princeton, or MIT? I have so much passion for mathematics (I want to learn everything there is to learn about it, and add to the plethora of mankind's mathematical knowledge), yet I fear that universities will fail to notice it.

I have began self studying calculus and am now ahead of my AP Calculus AB class. I plan to finish self studying Calculus II, Calculus III (Multivariable Calculus), and Linear Algebra before the start of my senior year. However, I searched online for opinions and perspectives on how universities would view this. The responses I read we generally along the lines of, " Colleges don't like self study. They want the student to fully grasp the concept, which is "not possible" through self study. They merely think 'This kid had nothing else to do with his time but read 1000s of pages of textbooks.'" However, I strongly disagree because mathematics is my passion. I love learning about it and think about it all the time, even when I'm supposed to be "hanging out" or "relaxing"; it stimulates my mind and is extremely pleasing to learn. I have a deep level of understanding for the mathematics that I have self studied so far and have put my mathematical skills to use by self studying even more intensively than as if I was in the class: assigning difficult exercises from multiple sources, taking notes from textbooks, videos, and online lectures, and occasionally, intuitively, discovering new (new to me) theorems before coming across them in my studies. I also plan on taking higher division classes at my local college. If possible, please contact me

The best advice I can offer to you is to document your interest in advanced mathematics through courses and standardized tests. Understanding advanced mathematics and having a thirst to learn more is admirable, but it will only cross over from being a hobby to being something colleges will take into account if you show what you've learned.

Taking higher level classes at your local college is a great start, especially if the classes are ones that require a certain level of baseline knowledge as a prerequisite (e.g., multivariable calc requires having a solid grasp of calculus beforehand). You might also consider online open course modules like EdX or Coursera, particularly if the schools you're thinking of applying to have courses on there.

A couple of other things you can do to demonstrate your passion for advanced mathematics are to excel at every math standardized test you can (SAT Math 2 Subject Test, AP Calc AB test) and to take part in math-related extracurricular activities like the Math Olympiad.