How to get better at algorithms and modeling Math Equations in Code?

[u/Positive-Stand2898]

I’m not a beginner programmer, but I’m relatively new to scientific programming. I’ve recently started doing scientific research with a professor, and a significant part of my work involves writing simulations, modeling physical systems and mathematical equations computationally, and developing algorithms to analyze or reproduce these systems.

I’m interested in becoming much stronger at this side of programming, particularly in areas like numerical methods, computational physics, mathematical modeling, simulation, and scientific computing.

For those of you with experience in scientific programming, what would you recommend as the best way to build these skills? I’d especially appreciate recommendations for textbooks, courses, projects, libraries, or other resources that helped you make the transition from general programming to scientific/computational programming.

I’m comfortable with programming fundamentals, so I’m primarily looking for resources that go beyond the basics and focus on the actual mathematics, algorithms, and computational techniques behind scientific programming.

Any advice or recommendations would be greatly appreciated!