I am currently a freshman in high school in the United States. I am very interested in mathematical and theoretical physics. For about the past year or two I have been studying on my own. Over the last summer I spent most of July and August reading Calculus by James Stewart and feel that I have a firm understanding of the information presented in the text. I have also read several other books and am currently working on An introduction to Quantum Mechanics with Applications to Chemistry by Linus Pauling and E. Bright Willson Jr., as well as The Road to Reality by Roger Penrose. Last year my high school physics teacher gave me Physics by Giancoli to study from, and I am currently taking Physics concurrently with AP Physics B, the highest physics course offered at my school. In math I am taking an independent study of Algebra 2 for the first semester and an online Advanced Trig. course the second semester. I understand that many of the topics covered in these courses are important in higher mathematics, but I do not believe that I need this long to learn them. If I follow my current school schedule I will be taking AP Calculus BC, the most advanced mathematics course at my high school, my senior year. I have already learned most of the information covered in this section and would only need a brief refresher to get a firm grasp on the subject. In any spare time I can find outside of school I have continued to study independently. Currently I am learning about Complex Analysis and related mathematical concepts. I have looked into it and found that a few boarding schools offer classes that are this advanced, but I am not enthusiastic about attending one of these. My school is a small public school and has, in the past, offered some support to students that are excelling in their classes. I have been wondering if there was any way that I could take these advanced courses, such as Complex Analysis or possibly Quantum Mechanics, in high school. I have been told that I can take AP tests without actually taking the AP courses, but don't want to risk missing some important concept that is not covered in the books that I read and I am not sure how this looks on a college application. I have also been wondering if there were any specific books that anyone would recommend for someone who is trying to learn through an independent study. Currently I am scavenging most of my books through resale shops. I found one store that has a large selection of Dover books and was wondering if these would be suitable for my studies. Is there any place I can purchase good text books for low prices? I would really appreciate any advice that anyone could give me. I am open to any advice or criticism. Thanks for any advice.