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PhD Applied Mathematics - Finite Element Analysis

My background is BS Math with Physics minor (3.5) and MA Math (3.7) from the University of Houston. My current plan is to explore the necessary background for doing research in finite element analysis. Over the next few semesters, I plan to take Numerical Methods for PDEs, Statistical Computing, Numerical Analysis, Partial Differential Equations, and Functional Analysis at UT RGV. Fortunately, this university offers these courses online.

The University of Reading offers the possibility of doing a PhD at a distance. Assuming that I do well in the above courses and genuinely find interest in the mathematics, then I'll consider approaching Reading about doing a self-funded research PhD. They offer a discounted rate for distance students. I do take advantage of tuition reimbursement offered at my employer.

However, I am 34 years old, married, and we will probably have our first child next year. I would likely finish the above courses in two to three years, taking one each fall and spring semesters. In my mind, what makes this even remotely possible is the difference between the US and UK programs. In some respects, the US programs are more rigorous and thorough. As far as I know, the program at Reading does not have coursework requirements, comprehensive and qualifying exams, or residency requirements. I assume that they would simply (not simply) expect original research to be completed and presented in the dissertation. If I cannot do that, then I will not be award a degree.

BS Math courses include Calculus I-III, Ordinary Differential Equations, Vector Analysis, Probability, Advanced Linear Algebra I & II, Intermediate Analysis, Discrete Mathematics, Abstract Algebra, Intermediate Mechanics, Thermal Physics, Modern Physics I & II

MA Math courses include Analysis, Differential Equations, Statistics, Regression and Linear Models, Numerical Computing with Python, Complex Analysis, Introduction to Differential Geometry, Number Theory

Other courses include Fourier Analysis, Seismic Wave and Ray Theory

My question is what textbooks do you recommend that would introduce me to the mathematics of finite element analysis, to a practical understanding of its implementation, to understanding the current research, and then to enabling me to ponder novel efforts for research? Thanks for any input.
it depends on your specific research, but a classic FEM book is this one from Ziekiewicz and Taylor:
and this one from Strang and Fix:
Depending on your interests you can look up specific papers on the topic.

I also recommend programming some finite element methods and playing with different classic differential equations. Hope this helps.

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