Hi, I'm going to be going into 12th grade. I have taken (out of applicable classes): Calculus 1-3 Differential Equations AP Physics Statics Physical Chemistry 1 (Classical Thermodynamics) Currently Taking: Linear Algebra Number Theory Thermodynamics Statistical Mechanics (graduate level, chemistry-based, independent study course) Anyways, I went looking for research and a (math) professor changed his mind about allowing me to do the research topic that would be more interesting to me (due to the math prerequisites). So my question is, for research in contact mechanics, what math would be necessary? The professor ended up mentioning it required partial differential equations and operator theory. So, for operator theory, what books would I have to work through to go through for a sufficient knowledge to be able to use for contact mechanics? What topics would I have to work on beforehand before operator theory and any book suggestions? His book is Models and Analysis of Quasistatic Contact Variational Approach in the Springer Lecture Notes on Physics Series (Vol. 655), it would be at a little bit more advanced level then this.