Mathematics And Statistics
Faculty  MSc  PhD  Shared  Courses

Chair  Joseph P. Mokanski (539 MaNaughton, Ext. 6556/2155)
(Email: jmokansk@msnet.mathstat.uoguelph.ca)
Graduate coordinators:
 Mathematics  Pal Fischer (524 MacNaughton, Ext. 2607/2155) (Email: pfischer@msnet.mathstat.uoguelph.ca)
 Statistics  Edward M. Carter (516 MacNaughton, Ext. 3569/2155) (Email: ecarter@msnet.mathstat.uoguelph.ca)
Graduate secretary  Susan McCormick (535 MacNaughton, Ext. 6553/2155) (Email: smccormi@msnet.mathstat.uoguelph.ca)

O. Brian Allen BSc, MSc Guelph, PhD Cornell  Professor
Edward M. Carter BSc, MSc, PhD Toronto  Professor
G. Robert Chapman BSc, PhD Liverpool  Professor
Eleanor Chu BSc National Taiwan, BSc, MSc Acadia, M. Math, PhD Waterloo  Associate Professor
Murray J. Code BSc Queen's, BSc London, MSc Queen's, PhD London  Associate Professor
Joseph Cunsolo BA McMaster, MA Waterloo, PhD Toronto  Associate Professor
Anthony F. Desmond BSc, MSc National University of Ireland (U.C.C.), PhD Waterloo  Associate Professor
David Fieldhouse BSc Queen's, PhD McGill  Associate Professor
Pal Fischer dip, Dr Univ Eotvos Lorand  Professor
Rodney D. Gentry BA, MA Western Washington State, PhD California (Davis)  Professor
W. Gordon S. Hines BSc Toronto, MSc, PhD Queen's  Professor
John A.R. Holbrook BSc, MSc Queen's, PhD California Institute of Technology  Professor
John D. Holt BSc, MA Toronto, PhD Waterloo  Associate Professor
Jin S. Huang BA National Taiwan, MBA Georgia, PhD Michigan State  Professor
John J. Hubert BSc Windsor, MSc Alberta, PhD State U. of New York  Professor
Peter T. Kim BA Toronto, MA Southern California, PhD California (San Diego)  Associate Professor
William F. Langford BSc Queen's, PhD California Institute of Technology  Professor
Anna T. Lawniczak MSc Wroclaw, PhD Southern Illinois  Associate Professor
George Leibbrandt BSc McMaster, MSc, PhD McGill  Professor
Henrick J. Malik MA Punjab, MSc, PhD CaseWestern  Professor
Joseph P. Mokanski BSc, MSc Windsor, PhD Waterloo  Associate Professor
Hosh Pesotan BSc, MSc, PhD McMaster  Professor
Radhey S. Singh BA, MA Banaras, MS, PhD Michigan State  Professor
William R. Smith BASc, MASc Toronto, MSc, PhD Waterloo  Professor
Gary R. Spoar BSc, MSc, PhD McMaster  Associate Professor
From the Department of Animal and Poultry Science:
Ian McMillan BSc, MSc, PhD Toronto  Professor
From the Department of Computing and Information Science:
Mary D. McLeish BSc Queen's, MSc, PhD McMaster  Professor
David A. Swayne BSc Waterloo, MA York, PhD Waterloo  Professor
From the Department of Population Medicine:
Mohamed M. Shoukri MSc Egypt, MSc, PhD Calgary  Professor
From the Department of Zoology:
Peter Yodzis BSc Duke, PhD New Mexico  Professor
From the School of Engineering:
Otman A. Basir BSc AlFateh, MSc Queen's, PhD Waterloo  Assistant Professor
Associated Graduate Faculty
Ross E. Cressman BSc Toronto, PhD British Columbia Department of Mathematics, Wilfrid Laurier University, Waterloo
Raymond E. Kapral BSc King's College, PhD Princeton  Department of Chemistry, University of Toronto
R. Jeanette O'Hara Hines BA New Brunswick, MA Queen's, MM, PhD Waterloo  Department of Statistics and Actuarial Science, University of Waterloo
The objective of this graduate program is to offer opportunities for advanced studies and research in the fields of applied mathematics and applied statistics, including the interface between the two. Although the two fields within the program have different requirements in terms of specific courses and qualifying examination areas, there is a considerable degree of interaction and commonality between them, from both philosophical and practical viewpoints. Philosophically, this commonality relates to the methodology of constructing and validating models of specific realworld situations. The major areas of specialization in applied mathematics are dynamical systems, mathematical biology, numerical analysis and operations research. Applied statistics encompasses the study and application of statistical procedures to data arising from realworld problems. Much of the emphasis in this field concerns problems originally arising in a biological setting. The major areas of specialization include linear and nonlinear models; bioassays; and survival analysis, life testing and reliability.

The department offers an MSc degree with several options. Students choose between either mathematics or statistics fields and complete their program either by thesis or project. The two main program types are regular and interdisciplinary.
Interdisciplinary programs involve faculty members of this and other university departments and focus on problems of common interest to both departments. Examples include joint studies in quantitative genetics involving faculty in the Department of Animal and Poultry Science; studies of economic management of renewable resources involving faculty from the economics departments; modeling of physiological processes involving faculty from the Ontario Veterinary College or the College of Biological Science; and toxicological modeling or risk assessment in collaboration with faculty involved in the Toxicology Research Centre.
Admission Requirements
A candidate for the MSc Degree Program must possess at least one of the following:
 a specialized honours degree (BSc or BA) in the intended area of specialization
 an honours degree with an equivalent to a major in the intended area of specialization
 an honours degree with the equivalent of a minor in mathematics or in statistics as defined in the University of Guelph Undergraduate Calendar. The student must take sufficient courses to satisfy the requirements (or their equivalents) of a major in the intended area of specialization, normally during the first two semesters of the program. These courses must be taken in addition to those described below. Students are generally not expected to undertake graduate courses before effectively completing the requirements of the undergraduate major.
An applicant who does not meet one of these requirements must register as an unclassified undergraduate student and take courses to achieve an equivalent to one of the above. Such students are encouraged to consult the departmental graduate officers or the chair of the department. The department's diploma in applied statistics fulfills the requirement of a minor equivalent in statistics.
Degree Requirements
For both regular and interdisciplinary programs, the degree requirements may be met by taking either:
 an MSc by thesis which requires at least 2.0 credits (four courses) plus a thesis; or
 an MSc without thesis (by project) which requires at least six courses; i.e., 3.0 credits, 12 of which must be for graduatelevel courses plus successful completion, within two semesters, of MSc Project in Mathematics, 6306998, or MSc Project in Statistics, 8906998.
All programs of study must include the appropriate core courses (see below). Students who have obtained prior credit for a core course or its equivalent will normally substitute a departmental graduate course at the same or higher level, with the approval of the graduate coordinator. The remaining prescribed courses are to be selected from either graduate courses or 400level undergraduate courses. Courses taken outside of this department must have the prior approval of the graduate program committee.
Mathematical Area of Emphasis
All candidates for the MSc with a mathematical area of emphasis are required to include in their program of study at least three of the following core courses:
 6306011 Dynamical Systems I
 6306021 Optimization I
 6306400 Numerical Analysis I
 6306041 Partial Differential Equations I
Statistical Area of Emphasis
All candidates for the MSc with a statistical area of emphasis are required to include in their program of study the following core courses:
 8906801 Advanced Data Analysis I
 8906802 Advanced Data Analysis II
 8906860 Linear Statistical Models
It is recommended that students take the undergraduate course
Statistical Inference, 8904340, if this course or its equivalent has not previously been taken.
Interdisciplinary Programs
 The general course requirements, above, must be met.
 The project or thesis of an interdisciplinary program must directly integrate the study of mathematics or statistics with another discipline.

Admission Requirements
A candidate for the PhD degree program must possess a recognized master's degree obtained with high academic standing. Also, a member of the department's graduate faculty must agree to act as an advisor to the student.
Degree Requirements
The PhD degree is primarily a research degree. For that reason, course work commonly comprises a smaller proportion of the student's effort than in the master's program. Course requirements are as follows:
Applied Mathematics
Students must successfully complete 2.0 graduatecourse credits. Depending upon the student's academic background, further courses may be prescribed. The required four courses must include at least two core courses selected from:
 6306012 Dynamical Systems II
 6306022 Optimization II
 6306410 Numerical Analysis II
 6306042 Partial Differential Equations II
All courses are chosen in consultation with the advisory committee. Additional courses may be required at the discretion of the advisory committee and/or the departmental graduate committee. With departmental approval, some courses given by other universities may be taken for credit. In addition to the courses, the student will be required to participate in the graduate seminar and make one oral presentation in each year of fulltime enrolment.
Applied Statistics
Students must successfully complete 2.0 graduatecourse credits. Depending upon the student's academic background, further courses may be prescribed. Students must take the following courses as part of the four required courses (providing that these courses were not taken as part of the student's master'sdegree program):
 8906802 Advanced Data Analysis II
 8906860 Linear Statistical Models
All courses are chosen in consultation with the student's advisory committee. Additional courses may be required at the discretion of the advisory committee and/or the departmental graduate committee. With departmental approval, some courses given by other universities may be taken for credit. In addition to the courses, the student will be required to participate in the graduate seminar and make one oral presentation in each year of fulltime enrolment.

Biophysics MSc/PhD Program
The Department of Mathematics and Statistics participates in the MSc/PhD programs in biophysics. Professors Gentry, Hines and Smith are members of the Biophysics Interdepartmental Group (BIG). These faculty members' research and teaching expertise includes aspects of biophysics; they may serve as advisors for MSc and PhD students in biophysics. Please consult the Biophysics listing for a detailed description of the graduate programs offered by the Biophysics Interdepartmental Group.
Toxicology MSc/PhD Collaborative Program
The Department of Mathematics and Statistics participates in the MSc/PhD programs in toxicology. Professor Hubert is a member of the Toxicology Interdepartmental Group. This faculty member's research and teaching expertise includes aspects of toxicology; he may serve as advisor for MSc and PhD students in toxicology. Please consult the Toxicology listing for a detailed description of the MSc/PhD collaborative program.

Mathematics
 6306011 Dynamical Systems I (0.5)
 Basic theorems on existence, uniqueness and differentiability; phase space, flows, dynamical systems; review of linear systems, Floquet theory; Hopf bifurcation; perturbation theory and structural stability; differential equations on manifolds. Applications drawn from the biological, physical, and social sciences.
 6306012 Dynamical Systems II (0.5)
 The quantitative theory of dynamical systems defined by differential equations and discrete maps, including: generic properties; bifurcation theory; the centre manifold theorem; nonlinear oscillations, phase locking and period doubling; the BirkhoffSmale homoclinic theorem; strange attractors and deterministic chaos.
 6306021 Optimization I (0.5)
 A study of the basic concepts in: linear programming, convex programming, nonconvex programming, geometric programming, and related numerical methods.
 6306022 Optimization II (0.5)
 A study of the basic concepts in: calculus of variations, optimal control theory, dynamic programming and related numerical methods.
 6306041 Partial Differential Equations I (0.5)
 Classification of partial differential equations. The Hyperbolic type, the Cauchy problem, range of influence, well and illposed problems, successive approximation, the Riemann function. The elliptic type: fundamental solutions, Dirichlet and Neumann problems. The parabolic type: boundary conditions, Green's functions and separation of variables. Introduction to certain nonlinear equations and transformations methods.
 6306042 Partial Differential Equations II (0.5)
 A continuation of some of the topics of Partial Differential Equations I. Also, systems of partial differential equations, equations of mixed type and nonlinear equations.
 6306051 Mathematical Modelling (0.5)
 Selected advanced topics in mathematical modelling, possibly in conjunction with the departmental Mathematics and Statistics Clinic.
 6306071 Biomathematics (0.5)
 The application of mathematics to model and analyze biological systems. Specific models to illustrate the different mathematical approaches employed when considering different levels of biological function.
 6306091 Topics in Analysis (0.5)
 Selected topics from topology, real analysis, complex analysis, and functional analysis.
 6306400 Numerical Analysis I (0.5)
 Topics selected from numerical problems in: matrix operations, interpolation, approximation theory, quadrature, ordinary differential equations, partial differential equations, integral equations, nonlinear algebraic and transcendental equations.
 6306410 Numerical Analysis II (0.5)
 One or more topics selected from those discussed in Numerical Analysis I, but in greater depth.
 6306990 Mathematics Seminar (0.0)
 Students will review mathematical literature and present a published paper.
 6306998 MSc Project in Mathematics (1.0)
Statistics
 8906700 Stochastic Processes (0.5)
 The content of this course is to introduce Brownian motion leading to the development of stochastic integrals thus providing a stochastic calculus. The content of this course will be delivered in the language of measure theory and so familiarity with measures, measurable spaces, etc., will be assumed.
 8906721 Applied Probability Theory (0.5)
 Topics selected from branching process, Markov chains, Markov processes, renewal processes, point processes, harmonic analysis of time series, and spatial distributions.
 8906741 Statistical Analysis for Reliability and Life Testing (0.5)
 Statistical failure models, order statistics, point and interval estimation procedures for life time distributions, testing reliability hypotheses, Bayes methods in reliability, system reliability.
 8906761 Survival Analysis (0.5)
 Statistical modeling and analysis of censored data arising from followup studies in human or animal populations. Topics covered include KaplanMeier estimates, lifetable methods, parametric and semiparametric models, clinical trial designs, and longitudinal study methods for the study of competing risks and disease progression.
 8906801 Advanced Data Analysis I (0.5)
 Residual analysis, deletion residuals, influential points, added variable plots, constructed variables, families of transformations, jackknife and bootstrap methods.
 8906802 Advanced Data Analysis II (0.5)
 Likelihood, quasilikelihood methods, generalized estimating equations for poisson and multinomial data. The inclusion of random effects in generalized linear models.
 8906821 Multivariate Analysis (0.5)
 This is an advanced course in multivariate analysis and one of the primary emphases will be on the derivation of some of the fundamental classical results of multivariate analysis. In addition, topics that are more current to the field will also be discussed such as: multivariate adaptive regression splines; projection pursuit regression; and wavelets.
 8906841 Statistical Inference (0.5)
 Maximum likelihood estimate, minimum variance, unbiased estimate, consistency, sufficiency, asymptotic properties, NeymanPearson lemma, RaoBlackwell theorem, uniformly most powerful test, likelihood ratio test, Bayes estimate, minimax estimate, admissibility.
 8906850 Advanced Biometry (0.5)
 Topics on advanced techniques for analyzing data from biological systems. In particular, univariate discrete models, stochastic processes as it relates to population dynamics and growth models with time dependencies, generalized discrete models for spatial patterns in wildlife, the theoretical foundation and recent results in aquatic bioassays, and other topics relating to the student's research interest.
 8906860 Linear Statistical Models (0.5)
 Generalized inverses of matrices; distribution of quadratic and linear forms; regression or full rank model; models not of full rank; hypothesis testing and estimation for full and nonfull rank cases; estimability and testability; reduction sums of squares; balanced and unbalanced data; components of variance.
 8906870 Experimental Design (0.5)
 This is an advanced course in experimental design which emphasizes proofs of some of the fundamental results in the topic. The topics will include: design principles; design linear models; designs with several factors; confounding in symmetrical factorials; fractional factorials.
 8906880 Sampling Theory (0.5)
 Theory of equal and unequal probability sampling. Topics in: simple random, systematic, and stratified sampling; ratio and regression estimates; cluster sampling and subsampling; double sampling procedure and repetitive surveys; nonsampling errors.
 8906920 Topics in Statistics (0.5)
 *8906950 Statistical Methods for the Life Sciences (0.5) F
 Analysis of variance, completely randomized, randomized complete block and latin square designs; planned and unplanned treatment comparisons; random and fixed effects; factorial treatment arrangements; simple and multiple linear regression; analysis of covariance with emphasis on the life sciences.
 *8906960 Design of Experiments and Data Analysis for the Life Sciences (0.5) W
 Principles of design; randomized complete block; latin square and extensions the split plot and extension; incomplete block designs; confounding and fractional replication of factorial arrangements; response surfaces the analysis of series of experiments; the general linear model; multiple regression and data analytic techniques.
 8906970 Statistical Consulting Internship (0.25)
 This course provides experience in statistical consulting in a laboratory and seminar environment. The student will participate in providing statistical advice and/or statistical analyses and participate in seminar discussions of problems arising from research projects in various disciplines.
 8906990 Statistics Seminars by Graduate Students (0.0)
 8906998 MSc Project in Statistics (1.0)
*8906950 and 8906960 are intended for graduate students of other departments and may not normally be taken for credit by mathematics and statistics graduate students.