Computational Science Qualifying Exam Process

The computational science qualifying exam will cover five subareas:

• Parallel algorithms and computing.
• Numerical linear algebra.
• Differential equations.
• Optimization and nonlinear equations.
• Approximation.

During the period February 6-15, you will need to take an oral exam in front of the committee. In the oral exam, basic knowledge on all five subareas will be tested. Here basic knowledge is limited by the topics covered in the CS3414, CS4234, and CS5465 courses. For your reference, please check the corresponding course webpages and the following textbooks:

• Kahaner, Moler, and Nash, Numerical Methods and Software, Prentice-Hall, 1989.
• Ananth Grama, George Karypis, Vipin Kumar, and Anshul Gupta: "Introduction to Parallel Computing". Addison-Wesley, 2003
• E.W. Cheney and D. Kincaid, Numerical Mathematics and Computing, 6th Ed., Brooks/Cole, 2008.

For more advanced knowledge, choose two of the five subareas and carefully read the corresponding papers (and related references) listed. You are not expected to teach a short-course on the details of a particular topic. Instead, we want to see how you begin to explore a particular topic: synthesize the main ideas and issues from the relevant papers; put those subareas in some context (with respect to other papers on the list, perhaps, or with respect to how that topic is evolving); perhaps explore a subtopic a little more, following leads to a few related papers, etc. This exam tests your ability to begin exploring and contributing to a particular research area. That means finding relevant papers, reading those papers carefully, identifying the main issues and developments in a particular area, and pursuing other references to fill in gaps in your understanding. It also means learning to present, in your own words, on a particular subtopic.

The exam will be scheduled for 90 minutes. Prepare 40-50 minutes of material. Assume we will ask questions, including questions to explore the limits of your knowledge and skills. We do not expect you to have memorized the papers. We do expect you to have read them carefully and have a good idea of what's in them. We recommend that you bring your copies of the papers to your presentation, since we may want to look at a section of one of them together.

In preparing your written responses and in preparing for the oral exam, you should do the work yourself. That means not talking to other students. You are welcome to look at any other references that seem useful. And you are welcome to ask any of us questions about the papers too. However, we will only answer specific, narrowly focused questions (e.g., "What does this notation mean?" or "I've stared at this for two hours and I'm pretty sure this is a typo!") We cannot spend a lot of time helping you figure out the paper — that's your job!

Reading List in Subareas

1. Parallel Algorithms & Computing
   • Buttari, A., Langou, J., Kurzak, J., Dongarra, J. A Class of Parallel Tiled Linear Algebra Algorithms for Multicore Architectures, Parallel Computing, 35, pp. 38-53, 2009.
   • Gustafson, J.L., Montry, G.R., and Benner, R.E., Development of parallel methods for a 1024-processor hypercube, SIAM J. Sci. Stat. Comput., 9(4), pp. 609-638, 1988.

2. Numerical Linear Algebra
   • Bowdler, H., Martin, R.S., Reinsch, C., and Wilkinson, J.H., The QR and QL algorithms for symmetric matrices, Numer. Math., 11, pp. 293-306, 1968.
   • Youcef Saad and Martin Schultz, GMRES: A generalized minimal residual algorithm for solving nunsymmetric linear systems, Siam J. Sci. Stat. Comput. 7(3), 1986.

3. Optimization and Nonlinear Equations
   • Dennis., J.E., and More, J.J., Quasi-Newton methods, motivation and theory, SIAM Review, 19(1), pp. 46-89, 1977.
   • Lewis, R.M., Torczon, V., and Trosset, M.W., Direct search methods: then and now, Journal of Computational and Applied Mathematics, 124, pp. 191-207, 1985.

4. Differential Equations
   • Gupta, G. K., Sacks-Davis, R., and Tischer, P. E., A review of recent developments in solving ODES, ACM Computing Surveys, 17(1), pp. 5-47, 1985.
   • J.C. Butcher, A history of Runge-Kutta methods, Applied Numerical Mathematics 20, pp. 247-260, 1996.

5. Approximation
   • Rene Pinnau, Model Reduction via Proper Orthogonal Decomposition, Model order reduction: Theory, research aspects and applications, Mathematics in Industry, 13(II), pp. 95-109, 2008.
   • Sobieszczanski-Sobieski, J., and Haftka, R.T., Multidisciplinary aerospace design optimization: survey of recent developments, Structural Optimization, 14, pp. 1-23, 1996.

   Examining Committee

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   Cal Ribbens (Chair), Adrian Sandu, Layne Watson