Scientific Computing is a truly interdisciplinary field, which complements the more traditional avenues of the scientific process: theory and experiment. It involves the use of computer hardware, software and algorithms to explore and understand complex problems from Science and Engineering. Mathematical descriptions of physical, social or economic situations are implemented on a computer. The resulting computational tool allows an improved understanding of the problem.
The program is designed to produce effective researchers in Scientific Computing and within the application area of interest. The program’s courses are designed to ensure advanced understanding of core Scientific Computing principles. The flexibility inherent in these course requirements allows students to choose courses from existing offerings in participating departments. A given student’s specific program of study will be tailored by their supervisory committee to meet their needs, ensuring both breadth and an ability to focus on original research culminating in a thesis of publishable quality.
The program is designed with the understanding that graduates in scientific computing may be employed in a wide variety of sectors, including private industry, government, and academia.
Students completing a Scientific Computing PhD will be required to complete courses, a comprehensive examination, a seminar, and a thesis. The exact number and nature of required courses will be decided at the time of admission, and will be based on the student’s background and proposed research area. These courses will be specified in the student’s program of study form.
The comprehensive examination will typically be done upon completion of all course work, no later than the end of the seventh semester of the student’s program. The candidate is required to prepare a paper on the theoretical background of his or her project. The examination will cover material related to this paper as well as fundamental topics in scientific computing.
Candidates will also be required to prepare and present a public seminar on the subject of his/her thesis as part of the thesis defense. The thesis is expected to be an original and substantial contribution to research in the areas of scientific computing and the sciences.
The duration of the program will typically be four years. It will be available on a full-time or part-time basis. The program will primarily be delivered on the St. John’s campus of Memorial University. Courses will be offered by faculty in the participating sub-disciplines. Students will generally be hosted in the home department of the thesis advisor. Supervisory committees, examinations, seminars, and other program meetings will be scheduled as needed.
All students MUST complete at least 2 courses, with higher expectations depending on background. The specific course requirements will be decided by the supervisory committee, in consultation with the board of study and will be noted on the program of study form completed upon admission. Given the interdisciplinary nature of the program, the guiding principle is to ensure both an adequate background in core scientific computing and a sufficient knowledge of the primary application area. Substitutions for courses in the list of core scientific computing courses below are possible, in keeping with these guiding principles. Normally, the following guidelines would be followed:
- Students who have completed an MSc in Scientific Computing or equivalent will be required to complete two courses chosen from the list of core courses or two courses from the application area as appropriate.
- Students who have completed a disciplinary MSc will be required to complete 4 courses. Normally, 3 of these courses would be chosen from the list of core courses to ensure sufficient training in scientific computing.
- Students who transfer to the PhD program from MSc in Scientific Computing will be required to complete 6 courses in total. Normally 3 to 4 of these courses would be from the list of core courses.
- Students holding a BSc (Hons) degree who are accepted into the program will be required to complete 6 courses. Normally 3 to 4 of these courses would be from the list of core courses.
Upon admission a student will be assigned a supervisory committee, which is composed of the student’s supervisor(s) and two other faculty members. An examination committee will be formed at least three months before the comprehensive exam. This committee will be composed of the supervisor and two other faculty members who are qualified to examine the student’s background and their research progress and proposal. Normally at least one member of the examining committee will be distinct from the members of the supervisory committee. Finally, there will be a thesis examination committee formed according to the regulations of the School of Graduate Studies.
Comprehensive Exam requirement
Students must pass a comprehensive exam to ensure that all graduates have an acceptable knowledge of the field of scientific computing and a mastery of those subdisciplines appropriate to his/her research area. The exam must be completed no later than the end of seventh semester of the student’s PhD program.
In the letter initiating the comprehensive exam, the student will be provided with a syllabus and list of texts on which the exam will be based. The candidate will independently prepare a paper of 20 to 25 pages describing the theoretical background, progress to date, and a proposal of their thesis research. This paper must be submitted to the chair of the board of study for dissemination to the comprehensive examination committee at least two weeks before the date of the examination. The student will give a 20 to 30 minute presentation on the contents of the paper. The paper will also serve as the starting point for the oral examination. Examiners may also ask questions related to fundamental aspects of scientific computing or the student’s research. The comprehensive examination procedures will follow those described in General Regulations – Comprehensive Examination (PhD and PsyD Comprehensive Examination) section of the School of Graduate Studies calendar.
During the comprehensive exam the proficiency with basic numerical analysis will be tested. The following is a typical syllabus for that part of the exam:
Text: A first course in Numerical Methods, by Ascher and Greif, SIAM 2011
Floating point arithmetic/round-off (Chapter 2)
Nonlinear equations: bisection, fixed points, Newton’s method (Chapter 3 and Sections 9.1-9.2) Direct Methods (Sections 5.1-5.5)
Linear least squares (Sections 6.1-6.2)
Iterative Methods (Sections 7.1-7.3)
Interpolation (Sections 10.1-10.5, 11.1-11.3, 12.1-12.4)
Differentiation (Sections 14.1-14.4)
Integration (Sections 15.1-15.3)
ODEs (Sections 16.1-16.5)
Each candidate must give at least one public presentation at Memorial on their research. This can take the form of a seminar or by presentation at an approved research colloquium. This requirement is intended to help develop the public speaking skills of students, inform other students enrolled in the program about this area of research, and allow for constructive feedback. Students enrolled in the program are expected to attend all Scientific Computing seminars and seminars in their home departments as identified by their supervisors.
Each candidate must generate original research results and prepare and submit a thesis according to the General Regulations – Theses and Reports of the School of Graduate Studies calendar. Prior to submission for examination, candidates must submit a draft of the thesis to the supervisory committee for feedback and approval. The quality of the thesis would merit publication in a reputable peer-reviewed journal. Scientific computing must be an integral part of the thesis. The thesis is expected to be of a scope and significance that is consistent with the norms of international research universities.
Students will usually complete all requirements and thesis within four years (twelve semesters) of enrolling in the program.
Supervisory Committee Meetings
Students in the PhD program must have an annual meeting of their supervisory committee. The student must prepare a short presentation that describes his/her progress towards completing his/her degree. At this time the supervisory committee will complete an annual progress report, which shall be submitted to the School of Graduate Studies and the board of study.