What skills should I learn before going for a PhD in numerical analysis, numerical linear algebra and scientific computing? I have two years in my hand after which I would be applying for graduate school most probably in the US. I already have a masters degree in pure mathematics and have very limited computer skills. For some reason, eventually I got interested in applied mathematics. So, now I am going for a second masters (which has not yet started because of the pandemic) in applied mathematics which is heavy on the above-mentioned topics. As of computer skills, I have started learning C++ but I don't know what else should I learn. It would be very helpful if someone can give a roadmap which would prepare me to finally embark for a PhD in one of these areas i.e., in and around numerical analysis. What math and computer science courses should I take? What software should I learn? Any general advice you would like to give is also welcome. Book recommendations would also be very helpful for me.
Thanks!
PS- Sorry for my bad English (not a native speaker).
 A: I'll list some books I like. When I recommend a book, I don't necessarily mean that you should read the whole thing. You can just focus on the parts that seem most interesting.
For numerical linear algebra, I recommend reading Trefethen's book (called Numerical Linear Algebra).
For general applied math background, I'm a fan of Introduction to Applied Mathematics as well as Computational Science and Engineering, both by Gilbert Strang.
Burden and Faires is a standard undergrad numerical analysis book and is worth reading. Bulirsch and Stoer is a classic numerical analysis textbook at the advanced undergrad / beginning graduate level.
For optimization, I'm a fan of Convex Optimization by Boyd and Vandenberghe as well as Numerical Optimization by Nocedal and Wright (in particular I like chapter 12, "Theory of Constrained Optimization").
These days you should probably learn about machine learning even if it's not your research area, just because so many other people are working on it (and it's easy to learn the basics). For machine learning I recommend reading: 1) The Hundred-Page Machine Learning Book by Burkov; 2) Deep Learning with Python by Francois Chollet; 3) An Introduction to Statistical Learning by James et al.
For an introduction to the Bayesian approach to statistics, I like Doing Bayesian Data Analysis by Kruschke.
