Syllabus for Ph. D. Preliminary Examination
in High Performance Computing
within Computational Science Cluster
of Mathematical Computer Science
The written preliminary exam for High Performance Computing usually
consists of a total of 9 (6 formerly) questions, 3 (2 formerly) questions
each, depending on recent offerings, from the following courses:
MCS 571 Numerical Methods for Partial Differential Equations
MCS 572 Introduction to Supercomputing
MCS 575 Computer Performance Evaluation
Students are required to answer 5 questions.
Your five best answers determine your score.
A nearly complete answer carries more weight than several partial answers
adding to the same numerical score.
Syllabi for each of the areas:
Numerical Methods for PDEs and Related Numerical Analysis
Normal Preparation: MCS 571 Numerical Methods for Partial
Differential Equations.
J. M. Ortega, Introduction to Parallel and Vector Solution of Linear
Systems, Plenum, 1988.
Quinn, Designing Efficient Algorithms for Parallel Computers,
McGraw-Hill, 1987.
P. J. Hatcher and M. J. Quinn, Data-Parallel Programming on
MIMD Computers, MIT Press, 1991.
Dongarra et al, Implementing linear algebra algorithms for dense
matrices on a vector pipeline machine, SIAM Review 26(1984) 91-112.
Queueing Theory and Computer Performance Evaluation.
Normal Preparation: MCS 575 Computer Performance Evaluation.
Other Background: working knowledge of probability and
statistics is required (e.g., Stat 401 Introduction to Probability )
along with an introduction to stochastic processes (Stat 461-462
Applied Probability Models I-II). This should include Markov processes
and birth-death processes.
Topics:
Operational Analysis - Little's Theorem, Utilization Law, forced flow
law. Application of these results to computer systems (bottleneck
analysis, etc.)
Basic Queueing Theory - state variables - number in system and
unfinished work (virtual waiting time), stationary solutions.