I am currently a senior studying mathematics. My program is heavily focused on pure maths, however, my interests lie in the area of applied mathematics. Specifically, I am interested in the study of complex systems modeling. I am currently interning at a research lab devoted to this field and while they are helpful, I don't view it as their job to teach me the nuts and bolts but rather how to assemble the nuts and bolts. I feel like I am missing out on a potentially great learning experience by not having enough of the fundamentals in place.
What I would like to do is put together a self-study program that will help prepare me for graduate studies in the area of complex systems modeling. To do so, I need to identify the key components and prioritize them. From what I have learned thus far, a competent modeler must be proficient in math skills (ODEs in particular) and scripting/programming (MATLAB, Python, R, etc.).
What I a looking for is what others believe the most relevant skills (mathematical, programming, or others) to complex systems modeling are and what resources they would recommend for self-learning these disciplines. I would like to eventually chart out a defined self-study program and am interested as to where I should start and in what direction I should go. Any help from the community would be greatly appreciated. Thank you!
Edit To clarify, by complex systems modeling I mean the practice of developing a mathematical model (typically using ODEs) to describe a process or event (e.g. financial markets, proliferation of cancer cells, etc.), using data to refine the model's parameters, and then simulating the effects of different inputs (e.g. optimization). Hope this helps, feel free to ask if you need further clarification.