<p>I'm going to be a freshman in college from the next year, and my first math class will be linear algebra, since I got exempted from taking multivariable calculus class. I have studied college-level math and physics since long time ago, and I'm now familiar with the above two topics as well as group theory, elementary number theory, special relativity and analytic mechanics at undergraduate-level. At some colleges, professor's permission can place one at advanced math course even if he/she hasn't taken the prerequisite classes. Is it common in many colleges that the students with strong mathematical background skip some relatively lower-division math classes such as elementary number theory, linear algebra, and differential equations due to professor's permission? Is there any tip for getting such permission or getting an opportunity to take placement tests? </p>
<p>It depends a lot on the university, the math department, and the individual, I think. Since you seem to have your first semester of math classes set, I would wait until you can talk to people in person to figure this out. Once you get to campus in the fall, figure out what the policy is and talk to those responsible for these decisions.</p>
<p>Thanks for your response. I will just wait until the fall as you suggested. </p>