PhD Applied Math Finite Element Analysis

Graduate School
1

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. University of Reading The University of Reading is a global university that enjoys a world-class reputation for teaching, research and enterprise. www.reading.ac.uk University of Reading The University of Reading is a global university that enjoys a world-class reputation for teaching, research and enterprise. www.reading.ac.uk

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.

2

Why do you want a Phd? Personal satisfaction? Career opportunities in industry? Pursuing a tenure track position in academia? Depending on your answer, Reading might be totally unsuitable. They only list one completed thesis in their distance learning Maths and Statistics department (on flood inundation modeling) so you should make very sure that their program will meet your needs before enrolling.

3

“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.”

Yes that’s how PhDs work in the UK, you just get on with it. The key thing is finding a supervisor who is interested in you and your work and can offer guidance on what problems to take on (i.e. interesting but not impossible ones) and how to overcome difficulties. So rather than you coming up with ideas, I would tend to go the other direction, find out what the relevant professor(s) are working on and then see which areas might be of interest. Because if you do something your supervisor doesn’t care about then you will be left to your own devices, which is even more of a problem at a distance.

My supervisor essentially abandoned me to go on sabbatical in my third year. Fortunately I already had the problems I was working on so I was fine on my own. Earlier on that wouldn’t have been OK. And my PhD was purely theoretical (I mostly did it in the bath and while rowing). Not sure how things would work remotely if you needed access to high powered computers for any practical implementation.

4

Hello.

Thanks for the reply. Motivations are personal achievement and a career in industry. I have no desire to pursue academia.

5

The good news is that Reading lists several areas of finite element research, so I should be able to find overlapping topics of interest.