Roadmap for Career Transition to Computational Science

Question

What sort of path should I follow to make a the transition from high school physics to computational science?

Context 15 years teaching experience in physics and general science. Maths is currently rusty, but currently I teach college level physics to 14 year old students in China using algebraic approaches and soon to transition to calculus based approaches (AP1 level). My level of computing experience is probably basic level. I can make simple command line scripts using procedural and OOP approaches in C++ and python. Some of my current projects include:-

• Simulating a meandering river using random walks
• Making a small class with methods for basic matrix operations
• Implementing some simple numerical solving techniques such newton-raphson and bisection methods

My current roadmap is as follows

1. Continue to work through simple problems from undergraduate/graduate level books.
2. Enroll on an MSc course for scientific computing or Data Science with a heavy modelling component.

Project Euler whilst appealing to a mathematician, my interest are mainly routed in science and physics. Is there perhaps a version of project euler that has problems related to science in general?

Recently I have just become a little lost. I would like to learn alongside my job, so I can dedicate some time out of work. But since I work internationally, distance learning courses would probably be best.

Answer 1

I think most people who are into computational science start the same way. When they learn the basics and decide which problems they want to solve, they start learning specific computational methods to solve them.

After you brush up on your math (algebra and analysis), you should study a book on numerical analysis. That's pretty much the main starting point from which everything else is built. I recommend this book.

The next thing I would advise you is to study the finite difference method. No matter what physics branch you choose to be in, there is always a chance you can solve your problem quickly using this method. It is a simple method and you will encounter some key concepts that can also be applied to other methods.

At this point, you should choose a physics branch that you would like to study and solve problems in. If you want to deal with fluid mechanics for instance, then you should study the finite volume method. If you want to deal with elastic body mechanics, you should study the finite element method. These methods are pretty much the most popular and applied ones, and there is a good amount of literature on them.

EDIT: I recommend also learning to write code in Matlab or Mathematica. They are quite handy if you want to solve a problem by writing your own algorithm.