Doctor of Philosophy in Applied Mathematics (Water)
The University of Waterloo offers a unique research-based Masters and Doctor of Philosophy (PhD) collaborative program in Water. This program, jointly offered by ten departments across the Faculties of Arts, Engineering, Environment, Mathematics and Science, is intended to promote multi- and inter-disciplinary perspectives related to water. The goal of the program is to supplement disciplinary (specialist) training offered in individual departments with perspectives from a variety of water-related disciplines. Students graduating from the collaborative program will be better equipped to work in multidisciplinary teams to solve increasingly complex water issues.
The over 130 faculty members involved in water research at the University of Waterloo represent international excellence and leadership in the field. The faculty cohort includes a Canada Excellence Research Chair, eight Canada Research Chairs, two NSERC Industrial Research Chairs and several University Chairs. The University’s water programs are diverse and collectively comprehensive, creating a dynamic research and learning environment. Core disciplinary expertise includes:
- Hydrological (groundwater, surface water) science and engineering;
- Water/wastewater treatment and technology;
- Ecohydrology;
- Aquatic ecology and ecotoxicology;
- Water management, policy and governance.
The collaborative program in Water represents tremendous opportunity for graduate students to train within their chosen disciplines while being exposed to perspectives of water research, innovation and management from other fields.
Admissions Requirements
Interested students should apply to the collaborative program in Water in one of the following departments via the regular university application process:
The collaborative program is available to students who are applying to thesis or major paper-based research programs in the home department and whose program of study will have a substantial focus on water. Admission requirements are the same as home department programs, who must approve the application. Students will be required to submit a brief statement of their research interests in water with their application.
Degree Requirements
Students must fulfill all of the requirements of their home department, including any specific courses, thesis or seminar milestones, and all of the requirements of the Water program. Whether or not collaborative program courses can be used as electives in the home department will be determined by the department, and may differ from department to department. It is therefore possible that students will need to take additional courses beyond those prescribed by the home department in order to meet the specific requirements of the Water program.
The requirements for the Doctor of Philosophy in Applied Mathematics (Water) degree are:
- four one-term (0.50 unit) graduate courses after the Master's degree, with a breadth requirement and completion of both WATER 601 and WATER 602, or eight one-term (0.50 unit) graduate courses after the Bachelor's degree, with a breadth requirement,
- the successful completion of the PhD Comprehensive Examination,
- the PhD Lecturing Requirement,
- the presentation and defence of a PhD thesis which contains the results of original research.
PhD students are allowed to take at most one 600-level course (including similar cross-listed courses offered by other departments) for credit.
Breadth Requirement
All Doctoral students are required to take one Computation course, one Differential Equations course, and one Techniques course, from the following list:
If a PhD student has taken an equivalent course during a Master's program, this can be counted, upon approval from the graduate officer, towards completion of the breadth requirement but does not reduce the number of courses required.
The program of studies of a PhD student is directed by an Advisory Committee consisting of the research supervisor and two other faculty members who may be from outside the Applied Mathematics Department. The supervisor, who has the primary responsibility for directing a PhD student's research, must be an Approved Doctoral Dissertation Supervisor (ADDS). "ADDS" status is granted by the Mathematics Faculty Graduate Committee.
The course work of a PhD student's program is approved by the supervisor. In the spirit of the interdisciplinary nature of Applied Mathematics, students are encouraged to take a broad spectrum of courses which are not necessarily restricted to Applied Mathematics Departmental courses. For example, our students often take relevant courses from the departments of Pure Mathematics, Physics, the David R. Cheriton School of Computer Science, and the various departments in the Faculty of Engineering.
Core Courses
Core courses are designed to provide fundamental multidisciplinary knowledge and experience to complement the student’s specialist courses and water-related research in the home department.
The two required core courses are:
- WATER 601: Integrated Water Management (0.50 credit)
- WATER 602: Integrated Water Management Project (0.50 credit)
PhD Comprehensive Examination
The PhD Advisory Committee should be approved within 12 months of enrolment in the PhD program. It shall consist of the supervisor(s) and two others who will normally be in the department. This committee will ultimately be part of the PhD Examination Committee.
In the fourth term of enrolment in the program, the candidate will give a seminar of at most 30 - 45 minutes on the proposed area of research, emphasizing the background material. Shortly thereafter the Advisory Committee shall meet to decide on which areas relevant to the research the candidate will be examined and who will be responsible for each area. The candidate will be informed of the areas of examination 3 - 4 months prior to the Comprehensive Examination.
The candidate will submit a typed research proposal (normally 25 - 30 pages in length) to the Advisory Committee at least two weeks prior to the Comprehensive Examination, which will normally be taken in the fifth term of the PhD program. The proposal will contain a statement of the research problem, together with appropriate background information and motivation, references to related work in the literature, an indication of the methods that might be used to solve the problem, and any progress made to date. The examination will consist of a presentation by the candidate of the proposed research, 20 - 25 minutes in length, followed by two rounds of questions. The first will be on the background material and the second on the formulation of the research proposal and on the relevant research literature. Each examiner shall question the candidate for approximately 15 - 20 minutes in each round. If there is more than one supervisor, the candidate will normally be questioned by only one supervisor in each round in order not to diminish the time allotted to each questioner. The Comprehensive Examination should normally be completed in two hours.
If the Committee finds that the candidate's performance is unsatisfactory in some aspect, they will specify what further requirements the candidate has to fulfil, e.g., to resubmit the research proposal, suitably modified, or to take an oral examination on a specific subject area at a later date.
The Comprehensive Examination is normally taken within the fifth term of admission to the PhD program. Students who have not satisfactorily completed this requirement by the end of the fifth term will have their progress reviewed by the Departmental Graduate Committee.
PhD Lecturing Requirement
Students normally satisfy this requirement by teaching a one-term undergraduate course, usually at the first or second year level, under the supervision of a faculty member. Students will satisfy this requirement after completing the PhD Comprehensive Examination and after obtaining experience as a teaching assistant. If the Department is unable to provide the student with a suitable undergraduate course to teach, the requirement may be met by giving a series of lectures of an introductory nature concerning their field of research.
Research Seminar
Students will make a formal presentation on their research at an annual symposium or other designated event. This will be an opportunity to interact with a very broad multidisciplinary audience that crosses all areas of research in the collaborative programs.
PhD Thesis Examination
It is required that a PhD thesis contain original results of a student that would warrant publication in the research literature. Indeed, candidates are encouraged to publish papers based on their research either before or after submitting their theses. Moreover, the Department expects a PhD thesis to be a scholarly work that is broad in scope. As such, it should contain a discussion of the history of the research problem and an analysis of the relevant literature.
The candidate shall defend the thesis in an oral examination before an Examining Committee, which shall consist of the supervisor, two faculty members in the Department, one faculty member from outside the Department, and an external examiner familiar with the student's research field. The committee is approved by the Faculty Graduate Committee.
Other opportunities
Students enrolled in the collaborative program will be offered other learning opportunities, such as participation in seminars and workshops and access to visiting fellows and scholars, which will enhance the learning experience.
Applying for the collaborative program in Water
For more information about the collaborative Water graduate programs, please contact the Graduate Studies Coordinator of a participating department or:
Dr. Mark Servos
Program Director
Phone: 519-888-4567 x36034
Email: mservos@uwaterloo.ca
Interested students should visit the Graduate Studies Office website.