Graduate Program in Mathematics University of British Columbia Okanagan 12

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1 PROGRAM INFORMATION Graduate Program in Mathematics University of British Columbia Okanagan 12 Name of Credential: M.Sc. and Ph.D. Title: Graduate Program in Mathematics Unit Offering the Program: Unit 5, Irving K. Barber School of Arts and Sciences, UBC Okanagan Contact Person: Dr. Shawn Wang Mathematics University of British Columbia Kelowna, B.C. V1V 1V7 CANADA PROGRAM OBJECTIVES The Graduate Program in Mathematics offers the degrees of M.Sc. and Ph.D. The program is designed for students with a background in mathematics. It provides students with opportunities for research in four areas of specialization: Mathematical Biology and Differential Equations; Optimization and Analysis; Number Theory and Algebra; and Statistics and Probability. It prepares graduating students for careers in research and teaching as well as industry and government. 1 Version: October 28, Additional details are provided on the following pages of this document.

2 PROGRAM SUPPORT BY FACULTY MEMBERS Currently, the Mathematics Graduate Program Committee consists of the continuing members Name Rank Area Heinz Bauschke Full Professor Optimization and Analysis John Braun Full Professor Computational Statistics Wayne Broughton Associate Professor Coding Theory Ed Butz Associate Professor Financial Mathematics Sylvie Desjardins Associate Professor Mathematical Biology Sylvia Esterby Associate Professor Environmetrics Paramjit Gill Associate Professor Spatial Statistics Donovan Hare Associate Professor Combinatorics and Optimization Warren Hare Associate Professor Cont. & Numerical Optimization Jason Loeppky Associate Professor Design & Anal. of Experiments Blair Spearman Full Professor Number Theory Javad Tavakoli Associate Professor Queuing Theory and Algebra Rebecca Tyson Associate Professor Mathematical Biology Shawn Wang Full Professor Optimization and Analysis Qiduan Yang Associate Professor Algebra and the following term-limited committee members Winfried Grassmann 3, Adjunct Professor, Computer Science Yves Lucet 4, Associate Professor, Computer Science Yong Gao 5, Associate Professor, Computer Science Faculty members who have research interests with a significant mathematical or statistical component may become term-limited members of the Mathematics Graduate Program Committee and participate in the graduate program in mathematics through cosupervision of graduate students. At least one supervisor of every Graduate student must be a continuing member of the Mathematics Graduate Program. 3 From March 2011 February From January 2008 August From January 2010 April 2017.

3 Research Expertise In view of the relatively small number of faculty members teaching mathematics at UBCO, the UBCO Graduate Program in Mathematics focuses on the following four areas of specialization ( clusters ) for which the faculty members have significant expertise to support research projects. Mathematical Biology and Differential Equations: E. Butz (Mathematical Biology and Financial Mathematics), S. Desjardins (Mathematical Biology and Global Analysis), R. Tyson (Mathematical Biology), and D. Vollick (Mathematical Physics, from Physics); Optimization and Analysis: H. Bauschke (Convex Analysis and Optimization), W. Hare (Continuous and Numerical Optimization), S. Wang (Nonsmooth Analysis and Optimization), Y. Gao (Computer Science and Discrete Optimization, from Computer Science) and Y. Lucet (Computer Science and Numerical Optimization, from Computer Science); Number Theory and Algebra: W. Broughton (Combinatorics), B. Spearman (Algebraic Number Theory), J. Tavakoli (Categorical Algebra), and Q. Yang (Matrix Representations of Finite Groups); Statistics and Probability: J. Braun (Computational Statistics, Environmetrics and Statistical Process Control), S. Esterby (Environmetrics and Ecological Statistics), P. Gill (Spatial Statistics and Applications), J. Loeppky (Design and Analysis of Experiments). For specific training not available at UBCO, students may spend a semester at UBCV. The Western Deans Accord makes it easy for Graduate students to obtain credit for courses taken at other regional institutions.

4 GRADUATE PROGRAM IN MATHEMATICS OVERVIEW The Graduate Program in Mathematics offers both M.Sc. and Ph.D. degrees. The program prepares students for careers in research and teaching as well as industry and government, with specialization in four areas: Mathematical Biology and Differential Equations; Optimization and Analysis; Number Theory and Algebra; and Statistics and Probability. Degrees require course work, research, and a thesis that is defended at an oral examination. ADMISSION REQUIREMENTS General admission requirements stipulated by the College of Graduate Studies must be satisfied. Master of Science (M.Sc.): Applicants are normally required to hold a bachelor s degree in mathematics or a related field with at least a B+ (76% or greater across the last 60 credits 6 taken toward the degree) average. Doctor of Philosophy (Ph.D.): Applicants are normally required to hold a Master of Science or equivalent in mathematics or a related field with at least a B+ (76% or greater) average. COMPLETION REQUIREMENTS Throughout either program, a student is guided by the Student's Advisory Committee that consists of the student's thesis supervisor and at least two graduate program committee members, or consists of two co-supervisors and another graduate program committee member. When beneficial to the student's progress, the student's Advisory Committee may include an additional member who is not a mathematician. The Advisory Committee will form the core of a student's Thesis Proposal Examination Committee. The requirements below represent the normal completion requirements for each program. If the proposed course plan deviates from the requirements below, then it must acquire pre-approval by the Graduate Program Advisory Committee. 6 credit means UBC credit or equivalent.

5 Master of Science (M.Sc.): The student must complete a minimum of 18 credits in coursework and 12 credits for the M.Sc. thesis (MATH 549). The student must complete a minimum of 4 approved graduate course credits in every Winter term (i.e., the terms starting in September and January) until the term in which they will complete their coursework. The Advisory Committee, in consultation with the student, will propose a course plan that will normally conform to the following four requirements. 9 credits through the following list of core courses (choose three out of four core courses): MATH 559 (Mathematical Biology, 3 credits) MATH 563 (Convex Optimization and Nonsmooth Analysis, 3 credits) MATH 538 (Algebraic Number Theory, 3 credits) STATS 560 (Probability and Stochastic Processes, 3 credits) The three core courses chosen have to be approved by the advisory committee of the graduate student. 3 credits from MATH 590 (Mathematics Graduate Seminar, taken thrice) 12 credits from MATH 549 (Master s Thesis) 6 credits from optional courses Doctor of Philosophy (Ph.D.): The student must complete a minimum of 30 graduate course credits approved by the student's advisory committee. Up to 18 course credits from an M.Sc. program may count towards satisfying this requirement. The student is also required to obtain 6 approved graduate course credits per year, until the thesis proposal examination is passed. The normal completion of the Ph.D. program follows three stages. Stage 1 (must be achieved within 16 months): Student passes the written comprehensive examination. At this stage students are still required to take 6 credits per year. Stage 2 (must be achieved within 28 months): Student passes the Thesis proposal examination. Upon passing the thesis proposal examination the students are no longer required to take 6 credits per year. Upon passing the thesis proposal examination the student becomes a Ph.D. Candidate. Stage 3 (completion): Submission and defence of a thesis with a public oral examination.

6 COURSE SELECTION Any of the following courses can be used to fulfill the course requirements without approval of the Graduate Program Advisory Committee. Three out of four core courses must be taken. Course Number Title Credits /Term Max credits counted towards M.Sc. MATH 549 M.Sc. Thesis N/A 12 (required) N/A Max credit counted towards Ph.D. MATH 649 Ph.D. Thesis N/A N/A 0 (required) MATH 590 Math. Grad. Sem. 1 9 (3 required) N/A MATH 523 Comb. Optim MATH 538 Alg. Number. Th. 3 3 (core) 3 MATH 539 Anal. Number Th MATH 546 Meth. & App. PDEs MATH 555 Th. Error-Corr. Codes MATH 559 Math. Biology 3 3 (core) 3 MATH 563 Conv. Optim. 3 3 (core) 3 MATH 570 Optim. & Anal. I MATH 600 Topics in Algebra MATH 601 Topics in Analysis MATH 604 Topics in Optim MATH 605 Topics in Appl. Math MATH 610 Topics in Pure Math MATH 612 Topics in Math. Bio MATH 620 Directed Studies MATH 670 Optim. & Anal. II STAT 560 Prob. & Stoch.. Proce. 3 3 (core) 3 STAT 538 Adv. Stat. Modelling STAT 547 Topics in Statistics Optional courses may also include graduate courses outside mathematics or advanced undergraduate courses (numbered 400 or higher). Any optional course not on the above list requires pre-approval by the Graduate Program Advisory Committee.

7 EXAMINATIONS AND THESIS Examinations will be held in accordance with the policies and guidelines of the College of Graduate Studies. MASTER S STUDENTS The master s students will take the following examinations: Course examinations where applicable; a minimum course grade of 68% must be obtained unless otherwise specified. All master s students are required to defend their theses in a final oral examination, in which the student will demonstrate his/her knowledge of the material in the thesis. The thesis may be submitted at any time of the year, but candidates are advised to allow ample time for revision and examination. As the thesis is being written, the candidate will be in regular communication with the Advisory Committee. The student may request an examination once the Advisory Committee recommends the final draft. Arrangements for the final oral examination are then made. Final oral examinations can be scheduled no sooner than four weeks after submission of the approved thesis. When the final draft of the thesis is submitted to the College of Graduate Studies, an announcement will be made within the Unit/Department that the final draft is publicly available for inspection with the Administrative Assistant. The Examining Committee will include the members of the student s Advisory Committee, one member either from the Mathematics Graduate Program committee who has not served on the student's Advisory Committee or from outside the Unit, and a committee chair appointed in consultation with the Dean of the College of Graduate Studies. As a result of the final oral examination, corrections may be necessary to produce a revised final version of the thesis. DOCTORAL STUDENTS Doctoral students must take and pass the following examinations: A written comprehensive examination held no later than 16 months after initial enrolment in the Ph.D. program. The written comprehensive examination consists of three 3-hour-long written examinations written during a one-week period. The syllabus for this exam is based on advanced undergraduate material, in four areas: Differential Equations and Mathematical Biology; Algebra and Applied Linear Algebra; Analysis and Probability; Mathematical Statistics and Linear Models. The student in PhD program has to take qualifying examinations of three topics out of the four listed above, and those three topics will be determined by the student's advisory committee. The written comprehensive examination may be repeated once (within 6 months of the original examination date). The thesis proposal examination must be taken no later than 3 years. The thesis proposal examination tests the student s overall knowledge of mathematics, with particular emphasis on the student s area of research and the proposed contents of the Ph.D. thesis. It has a written and an oral component. The written component consists of a report prepared by the student outlining the proposed

8 Ph.D. thesis research. The 2 3 hour-long oral component is determined by the student s Ph.D. Advisory Committee. It consists of an in camera presentation by the student outlining the thesis proposal, followed by a question period where the student must demonstrate in-depth knowledge of the proposal and corresponding background material, provided by the student's advisory committee in form of a reading list. The thesis proposal examination may be repeated once (within 6 months of the original examination date, or within 40 months of initial enrolment, whichever comes first). Upon successful completion of these two pass/fail examinations, the doctoral student will be admitted to candidacy. A student who is not admitted to candidacy will be asked to withdraw from the program. Extensions to the completion of the examinations may be granted under exceptional circumstances. All doctoral candidates are required to take a final oral examination (defence) of the thesis. The administration of the oral examination follows the policies and guidelines of the College of Graduate Studies. Ph.D. candidates are advised to allow ample time for revision and examination. As the thesis is being written, the candidate will be in regular communication with the Advisory Committee. When a draft is completed that the Advisory Committee recommends for examination, the student may request the oral examination. A copy of the final draft is then sent to the external examiner. When the final draft of the thesis is submitted to the College of Graduate Studies, an announcement will be made within the Unit/Department that the final draft is publicly available for inspection with the Administrative Assistant. All doctoral theses must be assessed by an examiner external to the University, as well as by internal examiners. The external examiner s written report must be received before the final examination of the thesis can take place. As a result of the final oral examination, corrections may be necessary to produce a final version of the thesis. PROGRESS REQUIREMENTS Once each year, the Graduate Program Advisory Committee will rate the performance of each Graduate student. The three possible ratings are: SATISFACTORY PROGRESS (SP), SATISFACTORY PROGRESS WITH CONDITIONS (SPWC), and UNSATISFACTORY PROGRESS (USP). For a Graduate student, the following conditions will normally result in SATISFACTORY PROGRESS. The student must complete a minimum of 4 approved graduate course credits in every Winter term (i.e., the terms starting in September and January) until the term in which they will complete their coursework. The student passes all courses taken in that term, with a term average of 76%. The student maintains a cumulative average of 80%.

9 The student makes satisfactory progress towards the completion of his/her thesis (as determined by his/her supervisor(s)). A student not meeting the above will normally receive SATISFACTORY PROGRESS WITH CONDITIONS or UNSATISFACTORY PROGRESS unless exceptional circumstances are proven. The student will be notified in writing if progress is rated SPWC or USP with a list of specific requirements for the next semester included in the notification. If a student is rated SPWC or USP in a semester, then the student will be rated either SP or USP in the following semester. The student will be asked to withdraw from the Mathematics graduate program if the student has accumulated two semesters where progress was rated USP. GRADUATE SCHOLARSHIPS An M.Sc. student entering his/her second year who maintains a rating of SATISFACTORY PROGRESS is eligible for a University Graduate Fellowship. A Ph.D. Student entering his/her second, third or fourth year who maintains a rating of SATISFACTORY PROGRESS is eligible for a University Graduate Fellowship. Graduate students not satisfying these requirements should not expect to receive a University Graduate Fellowship.

10 PROGRAM ADMINISTRATION GRADUATE PROGRAM COMMITTEE MEMBERSHIP Besides teaching graduate courses and supervising graduate students, Mathematics Graduate Program Committee members are eligible to serve on the Advisory Committees of individual graduate students, as well as the Graduate Program Advisory Committee (GPAC). Faculty members appointed to Unit 5 as (Assistant, Associate or Full) Professors of Mathematics or Statistics are automatically continuing members of the Graduate Program Committee. Adjunct Professors may be appointed as non-voting term-limited members of the Graduate Program Committee for a term of up to three years or up to the length of their appointment as an adjunct professor, whichever is less. UBC faculty members of other departments or units, and faculty members appointed to Unit 5 in subjects other than Mathematics or Statistics, may also be appointed as non-voting termlimited members for terms of up to three years. In both cases the individual must have a Ph.D. or equivalent and their appointment must be approved by a 2/3-majority vote of the continuing members of the Mathematics Graduate Program Committee. GRADUATE PROGRAM COORDINATOR The Mathematics Graduate Program will be administered by the Graduate Program Coordinator (GPC) in consultation with the Unit Head. The Graduate Program Coordinator is appointed by the Head in consultation with the continuing members of the Mathematics Graduate Program Committee. This individual must be a continuing member of the Mathematics Graduate Program Committee. The GPC chairs the Graduate Program Advisory Committee. In addition, the GPC acts as liaison with the College of Graduate Studies and helps with the following tasks: Arranging the review of applications to the program and notifying applicants of the outcome. Approving the composition of students Advisory Committees. Ensuring that students Advisory Committees conduct annual reviews. Arranging for Ph.D. written and oral comprehensive examinations. Arranging for the oral examination of submitted theses. Ensuring that program standards are maintained. GRADUATE PROGRAM ADVISORY COMMITTEE The Mathematics Graduate Program Advisory Committee (GPAC) consists of the Graduate Program Coordinator (GPC) and three members, one of whom should be the Unit Head. The GPAC should be approved by the MGPC. GPAC is chaired by the GPC. This committee generally advises the GPC on matters pertaining to the program but specifically recommends to the GPC which applicants should be accepted into the program and what credit may be given for previously taken courses. Any changes to the graduate program must be reviewed and approved by this committee. The GPAC will also revisit this document regularly and propose changes as needed. Major changes to the program will be brought before the full program committee.

11 STUDENT ADVISORY COMMITTEES Membership in students Advisory Committees will be determined in accordance with the policies and guidelines of the College of Graduate Studies. A student s Advisory Committee consists of at least three members of the Graduate Program Committee, one of whom is the student s thesis supervisor or co-supervisor. Either the supervisor or at least one co-supervisor must be a continuing member of the Mathematics Graduate Program Committee. The composition of a committee is determined by the GPC in consultation with the student s thesis supervisor. When beneficial to the student s progress, the student's Advisory Committee may include an additional member who is not a mathematician and a statistician. The GPC will endeavour to ensure that at least one of the members of each M.Sc. advisory committee has successfully supervised a student through the completion of a M.Sc. or Ph.D. degree. Similarly, the GPC will arrange, when possible, that at least one of the members of each Ph.D. advisory committee has successfully supervised a student through the completion of a Ph.D. degree. While primary supervision of a student rests with the student s thesis supervisor, the Advisory Committee must conduct an annual review of the student s progress and file a report with the GPC. The report may include recommendations, or require the student take additional courses or seminars above and beyond the program requirements, or request the withdrawal of a student from the program in the case of unsatisfactory progress. The Advisory Committee will also form the core of a student s Thesis Proposal Examination Committee. COMPREHENSIVE AND THESIS PROPOSAL EXAMINATION COMMITTEES These committees administer the written comprehensive examination and the thesis proposal examination of the student. The written comprehensive examination committee is a standing committee appointed by and chaired by the GPC. It consists of the GPC and four members of the Mathematics Graduate Program Committee, and takes care of all the comprehensive exams in the four areas Differential Equations and Mathematical Biology; Algebra and Applied Linear Algebra; Analysis and Probability; Mathematical Statistics and Linear Models. The student's thesis proposal examination committee consists of three members of the student's Advisory Committee plus an at-arm's-length member of the Mathematics Graduate Program Committee who serves as Chair. ORAL EXAMINATION (THESIS DEFENCE) COMMITTEES Membership in these committees will be determined in accordance with the policies and guidelines of the College of Graduate Studies.