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# Research opportunities

## Postdoctoral fellowships

If you expect to graduate from a doctoral program in the near future or are a recent graduate and are interested in a post-doctoral fellowship, consider contacting our faculty members to make inquiries. There are a number of possible sources of funding for post-doctoral fellowships including Natural Sciences and Engineering Research Council (NSERC), Canadian Institutes of Health Research (CIHR), and Social Sciences and Humanities Research Council (SSHRC). Deadlines for applications for these awards are typically in the fall.

Other sources of support include the Fields Institute which gives competitive awards for fellowships involving a period of time (six months) located at the Fields Institute in Toronto.

If you are interested in getting some experience in research, there are three programs described below to work with faculty members in our department. If you qualify for any of the three programs, please contact Carla Daniels indicating your interest. Please provide the following:

• a resume
• a copy of your unofficial transcript(s)
• the areas of research you are interested in
• the term you are interested in working
• whether you are interested in full or part-time work

### USRA opportunity at the Royal Military College of Canada

The following USRA opportunity is being offered by:
Mohan Chaudhry
Department of Mathematics and Computer Science
Students interested in applying for this project should contact
Dr. Mohan Chaudhry at (613-541-6000/6460)

Project Title:

Inverting transforms that arise in the study of Markov models

Project description:

Many of the analytic solutions in queueing and other stochastic processes are derived in various transforms such as probability generating functions and Laplace transforms. The problems become more complicated if there are unknowns in the transforms. Several complicated algorithms/methods have been proposed to invert such transforms. We have developed a software program which inverts such transforms using the roots of high degree polynomials and transcendental functions. Our method of inverting such transforms is much more efficient and fast when compared with other methods. The inversion of such transforms will make the mathematical models useful for practitioners and others. Recently, some researchers have used heavy-tailed distributions which may not have moments. The applications of such distributions arise in Internet and telecommunication problems. Besides working on various other computational problems, we intend to work on the use of these distributions both in continuous- and discrete-time queueing problems. All the previous students who came to work for me have gone for graduate work and after completing graduate work as Master's and/or Ph. D. students, they are now working at various places.

Student role:

The student's role will be to invert such transforms using mathematical tools such as

MAPLE/MATLAB or MATHEMATICA and QROOT, a software developed by us.

While working for this, they will also do mathematical typing by using Latex and/or MS word. This will be a great learning experience for a student who is wishing to go for graduate work

### President's Scholarship of Distinction (PSD)

Exceptional undergraduate students can also gain experience in research if they received a President's Scholarship of Distinction, awarded on admission, and have completed their first year with an average of at least 80%. The PSD comes with \$1500 in funding for research which can serve as full or partial payment for an on-campus research position with a UWaterloo professor or for a research-based co-op position within the University of Waterloo. Students with a PSD award are encouraged to find a faculty member to work with as a full- or part-time research assistant for a term to conduct research under their supervision. Interested faculty are encouraged to invite an eligible student to gain research experience through this opportunity. This can be done by contacting Carla Daniels for the names of eligible candidates, or by expressing a general interest to Carla who can put prospective students in contact with you.