
Mathematics And Statistics
Faculty
MSc Program
PhD Program
Interdepartmental Programs
Courses
Disclaimer
Chair
O. Brian Allen (539 MaNaughton, Ext. 56556/52155)
(Email: ballen@uoguelph.ca)
Graduate coordinators:
Mathematics
William Langford (544 MacNaughton, Ext. 53289/52155)
(Email: wlangfor@msnet.mathstat.uoguelph.ca)
Statistics
Ed Carter (516 MacNaughton, Ext.53569/52155)
(Email: ecarter@uoguelph.ca)
Graduate secretary
Susan McCormick (535 MacNaughton, Ext. 56553/52155)
smccormi@uoguelph.ca
Graduate Faculty
O. Brian Allen BSc, MSc Guelph, PhD Cornell  Professor and Chair
Heinz H. Bauschke Diploma Goethe, PhD Simon Fraser  Assistant 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  Professor
Joseph Cunsolo BA McMaster, MA Waterloo, PhD Toronto  Associate Professor
Gerda Darlington BSc, MSc Guelph, PhD Waterloo  Assistant Professor
Hermann J. Eberl Dipl. Math (MSc), PhD Munich Univ. of Tech.  Assistant Professor
Anthony F. Desmond BSc, MSc National University of Ireland
(U.C.C.), PhD Waterloo  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
Julie Horrocks BSc Mount Allison, BFA Nova Scotia College of Art & Design, MA, PhD Waterloo  Assistant 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)  Professor
Herb Kunze BA, MA, PhD Waterloo  Assistant Professor
William F. Langford BSc Queen's, PhD California Institute of
Technology  Professor
Anna T. Lawniczak MSc Wroclaw, PhD Southern Illinois  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
Gary J. Umphrey BSc, MSc Guelph, PhD Carleton  Assistant Professor
The objective of the 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 real
world 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 real
world 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; bioassay; and
survival analysis, life testing and reliability.
MSc Program
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; 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 a nondegree 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
fulfils 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, 2.0 of which must be for graduatelevel
courses plus successful completion within two semesters of MSc
Project in Mathematics, MATH*6998, or MSc Project in Statistics,
STAT*6998.
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:
MATH*6011 Dynamical Systems I
MATH*6021 Optimization I
MATH*6400 Numerical Analysis I
MATH*6041 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:
STAT*6801 Advanced Data Analysis I
STAT*6802 Advanced Data Analysis II
STAT*6860 Linear Statistical Models
It is recommended that students take the undergraduate course
Statistical Inference, STAT*4340, if this course or its equivalent has
not previously been taken.
Interdisciplinary Programs
(i) The general course requirements, above, must be met.
(ii) The project or thesis of an interdisciplinary program must directly
integrate the study of mathematics or statistics with another
discipline.
PhD Program
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:
MATH*6012 Dynamical Systems II
MATH*6022 Optimization II
MATH*6410 Numerical Analysis II
MATH*6042 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):
STAT*6802 Advanced Data Analysis II
STAT*6860 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.
Interdepartmental Programs
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.
Courses
Course/(Credit Value) 
Term 
Course Description 
Mathematics 
MATH*6011 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. 
MATH*6012 Dynamical Systems II (0.5)  
The quantitative theory of dynamical systems defined by
differential equations and discrete maps, including: generic
properties; bifurcation theory; the center manifold theorem;
nonlinear oscillations, phase locking and period doubling;
the BirkhoffSmale homoclinic theorem; strange attractors
and deterministic chaos. 
MATH*6021 Optimization I (0.5)  
A study of the basic concepts in: linear programming,
convex programming, nonconvex programming, geometric
programming and related numerical methods. 
MATH*6022 Optimization II (0.5)  
A study of the basic concepts in: calculus of variations,
optimal control theory, dynamic programming and related
numerical methods. 
MATH*6041 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. 
MATH*6042 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. 
MATH*6051 Mathematical Modelling (0.5)  
Selected advanced topics in mathematical modelling,
possibly in conjunction with the departmental Mathematics
and Statistics Clinic. 
MATH*6071 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. 
MATH*6091 Topics in Analysis (0.5)  
Selected topics from topology, real analysis, complex
analysis, and functional analysis. 
MATH*6400 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. 
MATH*6410 Numerical Analysis II (0.5)  
One or more topics selected from those discussed in
Numerical Analysis I, but in greater depth. 
MATH*6990 Mathematics Seminar (0.0)  
Students will review mathematical literature and present a
published paper. 
MATH*6998 MSc Project in Mathematics (1.0)   
Statistics 
STAT*6700 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 using concepts from measure theory and
so familiarity with measures, measurable spaces, etc., will
be assumed. 
STAT*6721 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. 
STAT*6741 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. 
STAT*6761 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. 
STAT*6801 Advanced Data Analysis I (0.5)  
Residual analysis, deletion residuals, influential points,added variable plots, constructed variables, families of
transformations, jackknife and bootstrap methods, local linear regression, regression splines and cubic smoothing splines. 
STAT*6802 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. 
STAT*6821 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. 
STAT*6841 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. 
STAT*6850 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. 
STAT*6860 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; mixed models;
components of variance. 
STAT*6870 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. 
STAT*6880 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. 
STAT*6920 Topics in Statistics (0.5)   
*STAT*6950 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. 
*STAT*6960 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. 
STAT*6970 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. 
STAT*6990 Statistics Seminars by Graduate Students (0.0)   
STAT*6998 MSc Project in Statistics (1.0)   
*STAT*6950 and STAT*6960 are intended for graduate students of
other departments and may not normally be taken for credit by
mathematics and statistics graduate students. 
The Office of Graduate Studies has attempted to ensure the accuracy of this
online Graduate Calendar. However, the publication of information in this document does not
bind the university to the provision of courses, programs, schedules of studies, fees, or facilities as
listed herein. Other limitations apply.

