Some of the past opportunities:
Most projects in my group are interdisciplinary and involve problems that require strong working knowledge of mathematical modelling tools and the ability to learn quickly from another discipline such as physics, engineering, biophysics or systems biology. As a doctoral student, who will be working in my group, you will have to register in the graduate program of the Guelph-Waterloo Institute of Physics, the University of Toronto (either Mechanical Engineering or Numerical Analysis Group, Computer Science Department), the University of Waterloo (Physics Department) or the University of Guelph (either Mathematics and Statistics Department or Physics Department). Myself (and possibly one of my colleagues from the above institutions) will be your supervisors. Information for prospective Master's students who would like to join my group are given in the end of this message. My main office is located at the Waterloo Campus of the Wilfrid Laurier University. You will be located in the M2NeT Lab is part of the MS2Discovery Interdisciplinary Reserch Institute, based in Waterloo. Waterloo is a dynamic city in Ontario, 50 minutes west of Toronto, the major business and financial centre in Canada. All three Universities, Wilfrid Laurier University, University of Waterloo, and the University of Guelph are located within very close proximity to each other. They have joint library facilities via the TriUniversity Group of Libraries as well as joint computational facilities via the Sharcnet.
My group focuses on the studies of coupled dynamics and complex systems with tools of mathematical modelling and computational experiments. If you plan to join my research group as a Doctoral student, your research project will be centered around one of the following areas
- Mathematical Modelling in Nanosciences, in particular in the analysis of phenomena that involve coupled effects and/or phase transitions, with major focus on mathematical models for (a) quantum dots and other low-dimensional semiconductor nano-structures and (b) novel "smart" materials that exhibit biological patterns of functioning;
Other areas are also possible, subject to student's background and experience. If you would like to work towards your PhD in one of the above areas, you have your Master's degree in Applied Mathematics or a relevant Science or Engineering discipline, you have strong analytical skills and programming experience, and you are most welcome to contact me to inquire further information. In your preliminary inquiry, we will be looking for indications that you have the necessary preparation to complete all PhD course requirements, you will be a productive team member, and you will likely make quick progress towards PhD.
I will also supervise from 1 to 3 Master's students who will be receiving support under my Canada Research Chair. To be eligible for stipends under the CRC Program, the students will have to register in the Graduate Studies at Laurier for the MSc program with the field of specialization in Mathematics for Science and Finance. This MSc program is normally completed in three or four consecutive terms, beginning in the Fall. In addition to the above listed research areas, the students may decide to specialize in the area of
- Stochastic models which may include applications in financial engineering with particular focus on inverse problems.
Preference will be given to students who decide to follow the thesis stream of the program. The minimum admission requirements for these particular positions include an Honours degree in Applied Mathematics or another quantitative discipline such as Physics, Biophysics/Biosciences, or Engineering. An aptitude for mathematical and computational tools, programming skills (e.g., Matlab, C++), as well as knowledge of theoretical and practical aspects of numerical linear algebra and differential equations are required.
The above information about opportunities for graduate studies in my group is directed to both Canadian and international students.
If you have completed 3rd or 4th year of your university studies and you have strong interest in the analysis and applications of mathematical models to problems from one of the following areas
- nano- and bio- sciences/technologies,
- financial engineering,
- parallel computing and visualization tools for computational physics and biosciences
you are welcome to discuss your interests further with Prof. Roderick Melnik (rmelnik at wlu dot ca).
I am affiliated with the University of Waterloo and the University of Guelph, as well with the Guelph-Waterloo Institute of Physics. Students with strong background in applied quantitative disciplines, such as applied mathematics, physics, engineering, biophysics or systems biology, who would like to continue their studies at the Master's or Doctoral level to work on one of the projects in my group should follow this link (at the Doctoral level, there are also opportunities in joint projects with the University of Toronto).
Undergraduate and vacation students working in my group will be located on the Waterloo Campus at Laurier where there is a wealth of opportunities to be involved in research in an interdisciplinary setting. You are stongly encouraged to attend our regular interdisciplinary seminars organized by the researchers at the MS2Discovery Interdisciplinary Research Institute, where you can learn how mathematical models and computational tools are applied in such diverse fields of human endeavour as physics and engineering, biology and medicine, and finance to name just a few.
Honours projects are open to the Laurier students only (mathematics students should register for MA489). Vacation projects may be open also to exceptional students from other Universities. Such projects provide an opportunity for students to complete a meaningful piece of research work in one of the areas of mathematical modelling and computational science, typically at the border between mathematics and another discipline.
Depending on a specific project, you should possess a subset of the following skills: an aptitude for mathematical and computational tools in science, technology, or finance; programming skills (Matlab, C++; or for some projects Maple, Fortran90); visualization programming skills; understanding of numerical methods for solving equations; willingness to learn quickly from areas other than mathematics (e.g., physics and engineering, biology, financial engineering, depending on your interests).
As a result of your project, you will have the opportunity to develop your skills in the design, refinement and implementation of mathematical models, as well as the opportunity to familiarize yourself with tools and methodologies of computational experiments as they applied in science, technology, or finance. You will produce a report describing the model, its analysis, algorithm development and results of your computational experiments whenever applicable. Where practical, the above projects may involve joint supervision with colleagues from biology, physics, or computer science departments.
The information on this page is mainly directed to the students from the Waterloo-Guelph and Greater Toronto area. If you are a student with strong credentials who lives elsewhere in Canada or abroad and you are interested in possible opportunities to work in my group, please consult section on Graduate Studies above.