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!

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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&#039;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!

Amy Daniels · Accepted Answer

I&#039;ll list some books I like. When I recommend a book, I don&#039;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&#039;s book (called Numerical Linear Algebra).For general applied math background, I&#039;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&#039;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, &quot;Theory of Constrained Optimization&quot;).These days you should probably learn about machine learning even if it&#039;s not your research area, just because so many other people are working on it (and it&#039;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.

What skills should I learn before going for a PhD in numerical analysis, numerical linear algebra an

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