This is an archived copy of the 2021-2022 calendar. To access the most recent version of the calendar, please visit https://queensu-ca-public.courseleaf.com.
Departmental Notes
Subject Code for Biomathematics: BIOM
Subject Code for Mathematics: MATH
Subject Code for Statistics: STAT
World Wide Web Address: www.queensu.ca/mathstat
Head of Department: Troy Day
Associate Head of Department: Andrew D. Lewis
Department Manager: Jeananne Vickery
Departmental Office: Jeffery Hall, Room 310
Departmental Telephone: 613-533-2390
Departmental Fax: 613-533-2964
Chair of Undergraduate Studies: Peter Taylor
Undergraduate Office E-Mail Address: mathstat@queensu.ca
Coordinator of Graduate Studies: Mike Roth
Chair for Engineering Mathematics: Serdar Yüskel
Overview
The Department of Mathematics and Statistics offers degree Plans designed to appeal to a broad range of students, including those interested in pure mathematics, applied mathematics, the physical and the biological sciences, teaching, actuarial studies (science), probability, and statistics. Our instructors include leading researchers and many winners of national and university teaching awards. The Department offers various plans in Mathematics and in Statistics, leading to either a B.A., B.A.(Hons.), B.Sc. or B.Sc.(Hons.) degree. A Plan in Mathematics and Engineering is also offered through the Faculty of Engineering and Applied Science. For full details of this program, see the Calendar of the Faculty of Engineering and Applied Science.
Advice to Students
Actuarial Science
Students interested in actuarial science should refer to the Actuarial Focus described in the Mathematics Major Plan. Examinations set by the Society of Actuaries are each intended to cover a range of topics in an integrated fashion. The first few of these examinations deal mainly with mathematics and statistics, plus some topics from economics and business. The Queen’s courses listed in the Actuarial Focus will give students background in specific areas needed to prepare students for the Society of Actuaries examinations. Information about the examinations can be obtained from the Society of Actuaries.
Supporting Statistics Courses for Students in Other Disciplines
Students wishing to use statistics in their area of study should include in their degree plan at least 3.0 units beyond the introductory level.
Special Study Opportunities
Applied Mathematics Courses
Some applied mathematics (MTHE) courses designed for students in the Faculty of Engineering and Applied Science may also be open to students in the Faculty of Arts and Science. See the Department for details on registration in these courses.
Courses of Instruction in the School of Graduate Studies and Research
With the permission of the instructor, the Department and the Registrar of the School of Graduate Studies and Research, undergraduate students may take for credit graduate courses in MATH or STAT for which they have the prerequisite background. This permission will require a minimum GPA of 3.50 in the mathematics and statistics courses of the first three years of their programs. Course descriptions are given in the Calendar of the School of Graduate Studies and Research.
Faculty
Selim G. Akl, Fady Alajaji, Thomas Barthelmé, Gunnar Blohm, Steven D. Blostein, Oleg I. Bogoyavlenskij, Francesco Cellarosi, Bingshu E. Chen, Troy Day, Ivan Dimitrov, Bahman Gharesifard, Mark F. Green, Martin Guay, Wenyu Jiang, Ernst Kani, Boris Levit, Andrew D. Lewis, Ping Li, Chunfang Devon Lin, Tamás Linder, Brian Ling, Felicia Magpantay, Abdol-Reza Mansouri, Giusy Mazzone, James McLellan, James A. Mingo, Charles Molson, M. Ram Murty, Dan Offin, Charles Paquette, Paul Y. Peng, Catherine Pfaff, Brad Rodgers, Mike Roth, Gregory G. Smith, Yanglei Song, Glen Takahara, Peter Taylor, Claude Tardif, Dongsheng Tu, David Wehlau, Noriko Yui, Serdar Yüksel, Imed Zaguia
Programs
- Biology and Mathematics – Specialization (Science) – Bachelor of Science (Honours)
- Computing, Mathematics and Analytics – Specialization (Computing) – Bachelor of Computing (Honours)
- Mathematical Physics – Specialization (Science) – Bachelor of Science (Honours)
- Mathematics – Major (Science) – Bachelor of Science (Honours)
- Mathematics – Medial (Arts) – Bachelor of Arts (Honours)
- Mathematics – General (Arts) – Bachelor of Arts
- Mathematics – General (Science) – Bachelor of Science
- Mathematics – Minor (Arts)
- Mathematics – Minor (Science)
- Statistics – Major (Science) – Bachelor of Science (Honours)
- Statistics – Medial (Arts) – Bachelor of Arts (Honours)
- Statistics – General (Arts) – Bachelor of Arts
- Statistics – General (Science) – Bachelor of Science
- Statistics – Minor (Arts)
- Statistics – Minor (Science)
Courses
For students intending a medial or major concentration in Mathematics or Statistics. Provides a thorough introduction to linear algebra up to and including eigenvalues and eigenvectors.
LEARNING HOURS 264 (72L;24T;168P).
An introduction to matrices and linear algebra. Emphasis on applications to biological and economic systems and to computer applications. Topics covered will include systems of equations, eigenvalues, recursions, orthogonality, regression analysis, and geometric transformations.
LEARNING HOURS 240 (72L;168P).
A brief introduction to matrix algebra, linear algebra, and applications. Topics include systems of linear equations, matrix algebra, determinants, the vector spaces Rn and their subspaces, bases, co-ordinates, orthogonalization, linear transformations, eigenvectors, diagonalization of symmetric matrices, quadratic forms.
LEARNING HOURS 120 (36L;84P).
A thorough discussion of calculus, including limits, continuity, differentiation, integration, multivariable differential calculus, and sequences and series.
LEARNING HOURS 288 (72L;24T;192P).
Differentiation and integration with applications to biology, physics, chemistry, economics, and social sciences; differential equations; multivariable differential calculus.
NOTE Also offered online. Consult Arts and Science Online. Learning Hours may vary.
NOTE Also offered at the Bader International Study Centre. Learning Hours may vary.
LEARNING HOURS 262 (48L;11G;72O).
Differentiation and integration of elementary functions, with applications to physical and social sciences. Topics include limits, related rates, Taylor polynomials, and introductory techniques and applications of integration.
Topics include techniques of integration; differential equations, and multivariable differential calculus.
LEARNING HOURS 126 (36L;12T;78P).
Differentiation and integration of the elementary functions with applications to the social sciences and economics; Taylor polynomials; multivariable differential calculus.
LEARNING HOURS 240 (72L;24T;144P).
Integers, polynomials, modular arithmetic, rings, ideals, homomorphisms, quotient rings, division algorithm, greatest common divisors, Euclidean domains, unique factorization, fields, finite fields.
NOTE Students with MATH 112/3.0 may ask for admission with the permissions of the Department.
LEARNING HOURS 132 (36L;12T;84P)
Algebraic techniques used in applied mathematics, statistics, computer science and other areas. Polynomials, complex numbers; least squares approximations; discrete linear systems; eigenvalue estimation; non-negative matrices - Markov chains; permutation groups; linear Diophantine equations; introduction to algebraic structures.
LEARNING HOURS 240 (72L;168P)
Vector spaces, direct sums, linear transformations, eigenvalues, eigenvectors, inner product spaces, self-adjoint operators, positive operators, singular-value decomposition, minimal polynomials, Jordan canonical form, the projection theorem, applications to approximation and optimization problems.
LEARNING HOURS 120 (36L;12T;72P).
The purpose of the course is to provide an introduction to abstract algebraic systems, and to illustrate the concepts with applications to communication engineering. Topics covered are: symbolic logic, switching and logic circuits; set theory and mappings; equivalence relations; the integers; introduction to Boolean algebras; group theory, groups, subgroups, cyclic groups, cosets and Lagrange's theorem, quotient groups, homomorphisms and isomorphisms; applications to error-control codes, binary block codes for noisy communication channels, nearest neighbor decoding, code error detection/correction capabilities, group (linear) codes, coset decoding, generator and parity check matrices, syndrome decoding; basic properties of rings and fields. (30/0/0/12/0)
Double and triple integrals, including polar and spherical coordinates. Parameterized curves and line integrals. Gradient, divergence, and curl. Green's theorem. Parameterized surfaces and surface integrals. Stokes' and Gauss' Theorems.
LEARNING HOURS 120 (36L;84P)
RECOMMENDATION Some linear algebra.
The course will discuss the application of linear differential equations with constant coefficients, and systems of linear equations within the realm of civil engineering. Additionally, the course will explore relevant data analysis techniques including: graphical and statistical analysis and presentation of experimental data, random sampling, estimation using confidence intervals, linear regression, residuals and correlation. (54/0/0/0/0)
An introduction to solving ordinary differential equations. Topics include first order differential equations, linear differential equations with constant coefficients, Laplace transforms, and systems of linear equations.
NOTE Some knowledge of linear algebra is assumed.
LEARNING HOURS 120 (36L;12T;72P)
Review of multiple integrals. Differentiation and integration of vectors; line, surface and volume integrals; gradient, divergence and curl; conservative fields and potential. Spherical and cylindrical coordinates, solid angle. Green's and Stokes' theorems, the divergence theorem. (36/0/0/0/0)
Complex arithmetic, complex plane. Differentiation, analytic functions. Elementary functions. Contour integration, Cauchy's Theorem, and Integral Formula. Taylor and Laurent series, residues with applications to evaluation of integrals.
LEARNING HOURS 120 (36L;12T;72P).
An introduction to ordinary differential equations and their applications. Intended for students concentrating in Mathematics or Statistics.
LEARNING HOURS 132 (36L;12T;84P).
First order differential equations, linear differential equations with constant coefficients. Laplace transforms. Systems of linear differential equations. Examples involving the use of differential equations in solving circuits will be presented. (30/0/0/6/0)
Topics include Newton's Law, conservative and central force fields; linear systems with constant coefficients; matrix exponentials and the variation of constants formula; Euler's method; separable and exact differential equations; Laplace Transforms, transfer functions and convolution; introduction to Fourier Series and boundary value problems: the heat equation, the wave equation. Computer methods (symbolic and numerical) are introduced in the laboratory component of the course. (20/7/0/15/0)
A survey of important mathematical techniques used to model processes in a variety of fields. Topics include multivariable calculus and optimization, game theory, discrete-time dynamical systems, and dynamic optimization. Examples will be drawn from several areas including biology, economics, and medicine. (18/9/5/4/0) ~ COURSE DELETED IN 2008/09 ~
An introductory course on the use of computers in science. Topics include: solving linear and nonlinear equations, interpolation, integration, and numerical solutions of ordinary differential equations. Extensive use is made of MATLAB, a high level interactive numerical package.
LEARNING HOURS 120 (36L;12Lb;12T;60P).
Limits, continuity, C1 and linear approximations of functions of several variables. Multiple integrals and Jacobians. Line and surface integrals. The theorems of Green, Stokes, and Gauss.
LEARNING HOURS 132 (36L;12T;84P)
Taylor's theorem, optimization, implicit and inverse function theorems. Elementary topology of Euclidean spaces. Sequences and series of numbers and functions. Pointwise and uniform convergence. Power series.
LEARNING HOURS 132 (36L;12T;84P).
Permutation groups, matrix groups, abstract groups, subgroups, homomorphisms, cosets, quotient groups, group actions, Sylow theorems.
LEARNING HOURS 132 (36L;96P).
Congruences; Euler's theorem; continued fractions; prime numbers and their distribution; quadratic forms; Pell's equation; quadratic reciprocity; introduction to elliptic curves.
LEARNING HOURS 120 (36L;84P).
The symmetric group consists of all permutations of a finite set or equivalently all the bijections from the set to itself. This course explores how to map the symmetric group into a collection of invertible matrices. To handle, count, and manipulate these objects, appropriate combinatorial tools are introduced.
LEARNING HOURS 132 (36L;96L).
Complex numbers, analytic functions, harmonic functions, Cauchy's Theorem, Taylor and Laurent series, calculus of residues, Rouche's Theorem.
LEARNING HOURS 120 (36L;12T;72P).
Metric spaces, topological spaces, compactness, completeness, contraction mappings, sequences and series of functions, uniform convergence, normed linear spaces, Hibert space.
LEARNING HOURS 132 (36L;96P).
Banach and Hilbert spaces of continuous- and discrete-time signals; spaces of continuous and not necessarily continuous signals; continuous-discrete Fourier transform; continuous-continuous Fourier transform; discrete-continuous Fourier transform; discrete-discrete Fourier transform; transform inversion using Fourier series and Fourier integrals.
LEARNING HOURS 132 (36L;12T;84P).
Linear input/output systems and their stability. Frequency-domain and time-domain analysis. Continuous and discrete time-modeling. Fourier, Laplace, and Z-transforms. Sampling and the discrete-time Fourier transform. Application to modulation of communications signals, filter design, and digital sampling.
LEARNING HOURS 132 (36L;12T;84P).
Some probability distributions, simulation, Markov chains, queuing theory, dynamic programming, inventory theory.
LEARNING HOURS 120 (36L;84P).
Methods and theory for ordinary and partial differential equations; separation of variables in rectangular and cylindrical coordinate systems; sinusoidal and Bessel orthogonal functions; the wave, diffusion, and Laplace's equation; Sturm-Liouville theory; Fourier transform.
LEARNING HOURS 118 (36L;12T;70P).
This course highlights the usefulness of game theoretical approaches in solving problems in the natural sciences and economics. Basic ideas of game theory, including Nash equilibrium and mixed strategies; stability using approaches developed for the study of dynamical systems, including evolutionary stability and replicator dynamics; the emergence of co-operative behaviour; limitations of applying the theory to human behaviour.
LEARNING HOURS 120 (36L;84P).
Introductory geometry of curves/surfaces: directional/covariant derivative; differential forms; Frenet formulas; congruent curves; surfaces in R3: mappings, topology, intrinsic geometry; manifolds; Gaussian/mean curvature; geodesics, exponential map; Gauss-Bonnet Theorem; conjugate points; constant curvature surfaces.
LEARNING HOURS 132 (36L;96P).
A historical perspective on mathematical ideas focusing on a selection of important and accessible theorems. A project is required.
LEARNING HOURS 120 (36L;12G;72P).
Elementary mathematical material will be used to explore different ways of discovering results and mastering concepts. Topics will come from number theory, geometry, analysis, probability theory, and linear algebra. Much class time will be used for problem solving and presentations by students.
LEARNING HOURS 120 (36L;84P)
Interest accumulation factors, annuities, amortization, sinking funds, bonds, yield rates, capital budgeting, contingent payments. Students will work mostly on their own; there will be a total of six survey lectures and six tests throughout the term, plus opportunity for individual help.
LEARNING HOURS 102 (12L;84P).
Measurement of mortality, life annuities, life insurance, premiums, reserves, cash values, population theory, multi-life functions, multiple-decrement functions. The classroom meetings will be primarily problem-solving sessions, based on assigned readings and problems.
LEARNING HOURS 108 (36L;72P).
Integers and rationals from the natural numbers; completing the rationals to the reals; consequences of completeness for sequences and calculus; extensions beyond rational numbers, real numbers, and complex numbers.
LEARNING HOURS 120 (36L;84P).
In-depth follow-up to high school geometry: striking new results/connections; analysis/proof of new/familiar results from various perspectives; extensions (projective geometry, e.g.); relation of classical unsolvable constructions to modern algebra; models/technology for geometric exploration.
LEARNING HOURS 120 (36L;84P).
An introduction to graph theory, one of the central disciplines of discrete mathematics. Topics include graphs, subgraphs, trees, connectivity, Euler tours, Hamiltonian cycles, matchings, independent sets, cliques, colourings, and planarity. Given jointly with MATH 801.
LEARNING HOURS 120 (36L;84P).
Enumerative combinatorics is concerned with counting the number of elements of a finite set. The techniques covered include inclusion-exclusion, bijective proofs, double-counting arguments, recurrence relations, and generating functions. Given jointly with MATH 802.
LEARNING HOURS 120 (36L;84P).
Construction and properties of finite fields. Polynomials, vector spaces, block codes over finite fields. Hamming distance and other code parameters. Bounds relating code parameters. Cyclic codes and their structure as ideals. Weight distribution. Special codes and their relation to designs and projective planes. Decoding algorithms.
LEARNING HOURS 120 (36L;84P).
An introduction to the study of systems of polynomial equations in one or many variables. Topics covered include the Hilbert basis theorem, the Nullstellenstaz, the dictionary between ideals and affine varieties, and projective geometry.
LEARNING HOURS 132 (36L;96P).
An introduction to Galois Theory and some of its applications.
LEARNING HOURS 132 (36L;96P).
Time estimates for arithmetic and elementary number theory algorithms (division algorithm, Euclidean algorithm, congruences), modular arithmetic, finite fields, quadratic residues. Simple cryptographic systems; public key, RSA. Primality and factoring: pseudoprimes, Pollard's rho-method, index calculus. Elliptic curve cryptography.
LEARNING HOURS 120 (36L;84P).
An exploration of the modern theory of Fourier series: Abel and Cesàro summability; Dirichlet's and Fejér's kernels; term by term differentiation and integration; infinite products; Bernoulli numbers; the Fourier transform; the inversion theorem; convolution of functions; the Plancherel theorem; and the Poisson summation theorem.
LEARNING HOURS 132 (36L;96P).
Topics include: global properties of flows and diffeomorphisms, Invariant sets and dynamics, Bifurcations of fixed and periodic points; stability and chaos. Examples will be selected by the instructor. Given jointly with MATH 827.
LEARNING HOURS 120 (36L;84P).
A generalization of linear algebra and calculus to infinite dimensional spaces. Now questions about continuity and completeness become crucial, and algebraic, topological, and analytical arguments need to be combined. We focus mainly on Hilbert spaces and the need for Functional Analysis will be motivated by its application to Quantum Mechanics.
LEARNING HOURS 132 (36L;12G;84P).
Continuum mechanics lays the foundations for the study of the mechanical behavior of materials. After a review of vector and tensor analysis, the kinematics of continua are introduced. Conservation of mass, balance of momenta and energy are presented with the constitutive models. Applications are given in elasticity theory and fluid dynamics.
NOTE This is the MATH version of MTHE 433 in FEAS.
LEARNING HOURS 120 (36L;84P).
Theory of convex sets and functions; separation theorems; primal-duel properties; geometric treatment of optimization problems; algorithmic procedures for solving constrained optimization programs; engineering and economic applications.
Quasilinear equations: Cauchy problems, method of characteristics; Cauchy-Kovalevski theorem; generalized solutions; wave equation, Huygens' principle, conservation of energy, domain of dependence; Laplace equation, boundary value problems, potential theory, Green's functions; heat equation, maximum principle.
LEARNING HOURS 132 (36L;96P).
Subject matter to vary from year to year. Given jointly with MATH 837.
LEARNING HOURS 132 (36L;96P).
Geometric modeling, including configuration space, tangent bundle, kinetic energy, inertia, and force. Euler-Lagrange equations using affine connections. The last part of the course develops one of the following three applications: mechanical systems with nonholonomic constraints; control theory for mechanical systems; equilibria and stability.
LEARNING HOURS 132 (36L;12T;84P).
Topics include: information measures, entropy, mutual information, modeling of information sources, lossless data compression, block encoding, variable-length encoding, Kraft inequality, fundamentals of channel coding, channel capacity, rate-distortion theory, lossy data compression, rate-distortion theorem. Given jointly with MATH 874.
LEARNING HOURS 140 (36L;104P).
Topics include: arithmetic coding, universal lossless coding, Lempel-Ziv and related dictionary based methods, rate distortion theory, scalar and vector quantization, predictive and transform coding, applications to speech and image coding.
LEARNING HOURS 120 (36L;12O;72P).
An important topic in mathematics not covered in any other courses.
An important topic in mathematics not covered in any other courses.
Important topics in mathematics not covered in any other courses.
Students are expected to participate in a weekly seminar in which they are required to present material on a topic that relates to their research.
An introduction to graph theory, one of the central disciplines of discrete mathematics. Topics include: graphs,subgraphs, trees, connectivity, Euler tours, Hamiltonian cycles, matchings, independent sets, cliques, colourings, and planarity.(Offered jointly with MATH-401*.)
Enumerative combinatorics is concerned with counting the number of elements of finite sets with prescribed conditions. The techniques covered include inclusion-exclusion, bijective proofs, double-counting arguments, recurrence relations, and generating functions. (Offered jointly with MATH-402.) Three term hours; lectures.
Construction and properties of finite fields. Polynomials, vector spaces, block codes over finite fields. Hamming distance and other code parameters. Bounds relating code parameters. Cyclic codes and their structure as ideals. Weight distribution. Special codes and their relation to designs and projective planes. Decoding algorithms. (Offered jointly with MATH 406*.) Three term-hours, fall or winter; lectures.
Subject matter may vary from year to year. Three term-hours, fall or winter; lectures.
An introduction to the study of systems of polynomial equations in one or more variables. Topics covered include the Hilbert basis theorem, the Nullstellenstaz, the dictionary between ideals and affine varieties, and projective geometry (Offered jointly with MATH 413).
Time estimates for arithmetic and elementary number theory algorithms (division algorithm, Euclidean algorithm, congruences), modular arithmetic, finite fields, quadratic residues. Design of simple cryptographic systems; public key, RSA systems. Primality and factoring: pseudoprimes, Pollard's rho-method, index calculus. Elliptic curve cryptography. Offered jointly with MATH-418. Three term hours, fall or winter; lectures.
Topics include: global properties of flows and diffeomorphisms; invariant sets and dynamics; bifurcations of fixed and periodic points; stability and chaos. (Offered jointly with MATH-427*.) Three term-hours, fall or winter; lectures.
A generalization of linear algebra and calculus to infinite dimensional spaces. Now questions about continuity and completeness become crucial, and algebraic, topological, and analytical arguments need to be combined. We focus mainly on Hilbert spaces and the need for Functional Analysis will be motivated by its application to Quantum Mechanics. (Offered jointly with MATH 429.) Three term hours; lectures.
EXCLUSION: MATH -429
This course covers core topics in discrete and continuous time modern control theory: controllability, observability and minimal realizations; Lyapunov stability; the linear quadradic regulator and design of robust controllers; state estimation via Luenberger and deterministic Kalman-Bucy filters. Laboratory experiments illustrate design considerations in implementing the lecture material. Students are required to identify a high order under-actuated torsion disc system; perform model verification experiments; design and implement robust linear feedback controllers; design and implement nonlinear sliding mode controllers; study implementation issues for observers and Kalman-Bucy filters; depending on instructor, some nonlinear control strategies may be implemented. (Offered jointly with MATH-430*.) Three term hours, fall; lectures.
Theory of convex sets and functions; separation theorems; primal-dual properties; geometric treatment of optimization problems; algorithmic procedures for solving constrained optimization programs; applications of optimization theory to machine learning. (Offered jointly with MATH/MTHE 434.)
EXCLUSIONS: MTHE/MATH 434
This is a course in advanced mathematical methods used to construct models of biological phenomena in ecology, epidemiology, and evolutionary biology. The course will focus on population models, starting with individual-based models based on assumptions on the distribution of individual traits, then scaling up to stochastic models for small populations and deterministic models for large populations.
Configuration space, generalized coordinates, Euler-Lagrange equations. Forces: dissipative, potential. Simple mechanical control systems: modeling, linearization about equilibrium points, linear controllability tests; equivalence with kinematic systems and trajectory generation. (Offered jointly with MATH 439). Three term hours, fall or winter; lectures.
Subject matter may vary from year to year. Three term-hours, fall or winter; lectures.
Subject matter may vary from year to year. Three term-hours, fall or winter; lectures.
Calculus on manifolds; transversality; Sard's Theorem; immersions and submersions; intersection theory; Jordan curve theorem; Lefschetz fixed point theorem; Poincaré-Hopf Theorem. (Offered jointly with MATH-444*.) Three term-hours, winter; lectures.
Stabilization and optimization of controlled dynamical systems under probabilistic uncertainty. Topics include: review of probability, controlled Markov chains, martingale and Lyapunov methods for stochastic stability, dynamic programming, partially observed models and non-linear filtering, the Kalman Filter, average cost problems, learning and computational methods, decentralized stochastic control, and stochastic control in continuous-time. (Offered jointly with MTHE- 472.) Three term hours, fall or winter; lectures.
An introduction to the fundamental principles of the theory of communication. Topics include: information measures, entropy, mutual information, divergence; modeling of information sources, discrete memoryless sources, Markov sources, entropy rate, source redundancy; fundamentals of lossless data compression, block encoding, variable-length encoding, Kraft inequality, design of Shannon-Fano and Huffman codes; fundamentals of channel coding, channel capacity, noisy channel coding theorem, channels with memory, lossless information transmission theorem; continuous-alphabet sources and channels, differential entropy, capacity of discrete-time and band-limited continuous-time Gaussian channels; rate-distortion theory, lossy data compression, rate-distortion theorem, lossy information transmission theorem. Offered jointly with MATH-474). Three term hours, fall; lectures.
Fundamentals of the theoretical and practical (algorithmic) aspects of lossless and lossy data compression. Topics include: adaptive Huffman coding, arithmetic coding, the fundamental performance limits of universal lossless coding, Lempel-Ziv and related dictionary based methods, the Burrows-Wheeler transform, elements of Kolmogorov complexity theory, rate-distortion theory, scalar and vector quantization, applications to speech and image coding. Offered jointly with MATH-477*).
This course covers performance models for data networking, delay models and loss models; analysis of multiple access systems, routing, and flow control; multiplexing; priority systems; satellite multiple access, wireless networking, wireless sensor networks. Knowledge of networking protocols is not required. (Offered jointly with MATH 484.) Three term hours, winter; lectures.
This course provides basic knowledge in real and complex analysis at the graduate level on the following topics: Lebesgue measure and integration theory; elementary Hilbert space theory; examples of Banach space techniques. Three term-hours, fall; lectures.
This course provides basic knowledge in real and complex analysis at the graduate level on the following topics: basic theory of Fourier transforms; basic elements of spectral theory and Banach algebras; complex analysis. Three term-hours, winter; lectures.
This course provides basic knowledge in algebra at the graduate level on the following topics: elementary theory of groups; elementary theory of rings and modules; Galois theory. Three term-hours, fall; lectures.
This course provides basic knowledge in algebra at the graduate level on the following topics: representation theory of finite groups through characters; advanced theory of modules; advanced theory of rings. Three term-hours, winter; lectures.
This course provides basic knowledge in probability at the graduate level. Topics will include: basic notions and concepts of Probability Theory; characteristic functions; law of large numbers and central limit theorem; martingales; stochastic processes. Three term-hours, fall; lectures.
This course provides basic knowledge in mathematical statistics at the graduate level. Topics will include: Classical and Bayesian inference, Multivariate Gaussian distribution and its applications in Statistics; decision theory; basic techniques of non-parametric estimation. Three term-hours, winter; lectures.
This course provides basic knowledge in mathematical statistics at the graduate level. Topics will include: Weak convergence in metric spaces; Delta method; Method of moments; M-estimation; Asymptotic normality and efficiency; Likelihood ratio test; U statistics; Bootstrap; Applications in statistics.
Advanced topics course, normally offered in the summer term, by a research institute in Canada or abroad can be taken for credit with the permission of the Supervisor and Coordinator of Graduate Studies and in cooperation with Institute organizers. Grades are assigned on a PASS - FAIL basis.
Subject matter will vary from year to year. Three term-hours, Fall or winter; Seminar or reading course.
Subject matter will vary from year to year. Three term-hours, Fall or winter; Seminar or reading course.
Subject matter will vary from year to year. Three term-hours, Fall or winter; Seminar or reading course.
Subject matter will vary from year to year. Three term-hours, Fall or winter; seminar or reading course.
Subject matter will vary from year to year. Three term-hours, Fall or winter; Seminar or reading course.
Subject matter will vary from year to year. Three term-hours, Fall or winter; Seminar or reading course.
Subject matter will vary from year to year. Three term-hours, Fall or winter; Seminar or reading course.
Subject matter will vary from year to year. Three term-hours, Fall or winter; Seminar or reading course.
Subject matter will vary from year to year. Three term-hours, Fall or winter; Seminar or reading course.
Subject matter will vary from year to year. Three term-hours, Fall or winter; Seminar or reading course.
Subject matter will vary from year to year. Three term-hours, Fall or winter; Seminar or reading course.
Subject matter will vary from year to year. Three term-hours, Fall or winter; Seminar or reading course.
Subject matter will vary from year to year. Three term-hours, Fall or winter; Seminar or reading course.
Subject matter will vary from year to year. Three term-hours, Fall or winter; Seminar or reading course.
Subject matter will vary from year to year. Three term-hours, Fall or winter; Seminar or reading course.
Subject matter will vary from year to year. Three term-hours, Fall or winter; Seminar or reading course.
Subject matter will vary from year to year. Three term-hours, Fall or winter; Seminar or reading course.
Subject matter will vary from year to year. Three term-hours, Fall or winter; Seminar or reading course.
Subject matter will vary from year to year. Three term-hours, Fall or winter; Seminar or reading course.
Subject matter will vary from year to year. Three term-hours, Fall or winter; Seminar or reading course.
Basics of probability. Counting principle, binomial expansion. Conditional probability and Bayes' Theorem. Random variables, mean and variance. Bernoulli, binomial, geometric, hypergeometric and exponential distributions. Poisson approximation. Distribution, frequency and density functions. Normal distribution and central limit theorem.
NOTE STAT 252 is a new course for STAT Minors and Medials.
LEARNING HOURS 120 (36L;84P).
A basic course in statistical methods with the necessary probability included. Topics include probability models, random variables, distributions, estimation, hypothesis testing, elementary nonparametric methods.
NOTE Also offered online, consult Arts and Science Online (Learning Hours may vary).
LEARNING HOURS 120 (36L;84P).
Basic ideas of probability theory such as random experiments, probabilities, random variables, expected values, independent events, joint distributions, conditional expectations, moment generating functions. Main results of probability theory including Chebyshev's inequality, law of large numbers, central limit theorem. Introduction to statistical computing.
LEARNING HOURS 120 (36L;84P).
Basic techniques of statistical estimation such as best unbiased estimates, moment estimates, maximum likelihood. Bayesian methods. Hypotheses testing. Classical distributions such as the t-distribution, F-distribution, beta distribution. These methods will be illustrated by simple linear regression. Statistical computing.
LEARNING HOURS 120 (36L;84P).
Probability theory; probability models; random variables; jointly distributed random variables; transformations and generating functions. Inequalities and limit laws. Distributions: binomial, Poisson, exponential, gamma, normal. Applications: elementary stochastic processes, time-to-failure models, binary communication channels with Gaussian noise.
LEARNING HOURS 120 (36L;12T;72P).
Intermediate probability theory as a basis for further study in mathematical statistics and stochastic processes; probability measures, expectations; modes of convergence of sequences of random variables; conditional expectations; independent systems of random variables; Gaussian systems; characteristic functions; Law of large numbers, Central limit theory; some notions of dependence.
LEARNING HOURS 120 (36L;84P).
A detailed study of simple and multiple linear regression, residuals and model adequacy. The least squares solution for the general linear regression model. Analysis of variance for regression and simple designed experiments; analysis of categorical data.
LEARNING HOURS 120 (36L;84P).
Introduction to R, data creation and manipulation, data import and export, scripts and functions, control flow, debugging and profiling, data visualization, statistical inference, Monte Carlo methods, decision trees, support vector machines, neural network, numerical methods.
LEARNING HOURS 118 (36L;12G;70P).
Exploratory data analysis -- graphical and statistical analysis and presentation of experimental data. Random sampling. Probability and probability models for discrete and continuous random variables. Process capability. Normal probability graphs. Sampling distribution of means and proportions. Statistical Quality Control and Statistical Process Control. Estimation using confidence intervals. Testing of hypothesis procedures for means, variances and proportions -- one and two samples cases. Liner regression, residuals and correlation. ANOVA. Use of statistical software. (44/0/0/4/0)
Many systems evolve with an inherent amount of randomness in time and/or space. The focus of this course is on developing and analyzing methods for analyzing time series. Because most of the common time--domain methods are unreliable, the emphasis is on frequency--domain methods, i.e. methods that work and expose the bias that plagues most time--domain techniques. Slepian sequences (discrete prolate spheroidal sequences) and multi--taper methods of spectrum estimation are covered in detail. (12/0/0/12/12)~ COURSE NOT OFFERED IN 2010-2011 ~
Markov chains, birth and death processes, random walk problems, elementary renewal theory, Markov processes, Brownian motion and Poisson processes, queuing theory, branching processes. Given jointly with STAT 855.
LEARNING HOURS 120 (36L;12T;72P).
An introduction to Bayesian analysis and decision theory; elements of decision theory; Bayesian point estimation, set estimation, and hypothesis testing; special priors; computations for Bayesian analysis. Given Jointly with STAT 856.
LEARNING HOURS 120 (36L;84P).
Introduction to the theory and application of statistical algorithms. Topics include classification, smoothing, model selection, optimization, sampling, supervised and unsupervised learning. Given jointly with STAT 857.
LEARNING HOURS 120 (36L;84P).
A working knowledge of the statistical software R is assumed. Classification; spline and smoothing spline; regularization, ridge regression, and Lasso; model selection; treed-based methods; resampling methods; importance sampling; Markov chain Monte Carlo; Metropolis-Hasting algorithm; Gibbs sampling; optimization. Given jointly with STAT 862.
LEARNING HOURS 120 (36L;84P).
Decision theory and Bayesian inference; principles of optimal statistical procedures; maximum likelihood principle; large sample theory for maximum likelihood estimates; principles of hypotheses testing and the Neyman-Pearson theory; generalized likelihood ratio tests; the chi-square, t, F and other distributions.
LEARNING HOURS 132 (36L;96P).
Autocorrelation and autocovariance, stationarity; ARIMA models; model identification and forecasting; spectral analysis. Applications to biological, physical and economic data.
LEARNING HOURS 120 (36L;84P).
An overview of the statistical and lean manufacturing tools and techniques used in the measurement and improvement of quality in business, government and industry today. Topics include management and planning tools, Six Sigma approach, statistical process charting, process capability analysis, measurement system analysis and factorial and fractional factorial design of experiments.
LEARNING HOURS 120 (36L;84P).
Introduction to the basic knowledge in programming, data management, and exploratory data analysis using SAS software: data manipulation and management; output delivery system; advanced text file generation, statistical procedures and data analysis, macro language, structure query language, and SAS applications in clinical trial, administrative financial data.
LEARNING HOURS 120 (36L;84P).
Simple random sampling; Unequal probability sampling; Stratified sampling; Cluster sampling; Multi-stage sampling; Analysis of variance and covariance; Block designs; Fractional factorial designs; Split-plot designs; Response surface methodology; Robust parameter designs for products and process improvement. Offered jointly with STAT 871.
LEARNING HOURS 120 (36L;84P).
An introduction to advanced regression methods for binary, categorical, and count data. Major topics include maximum-likelihood method, binomial and Poisson regression, contingency tables, log linear models, and random effect models. The generalized linear models will be discussed both in theory and in applications to real data from a variety of sources. Given jointly with STAT 873.
LEARNING HOURS 120 (36L;84P).
Introduces the theory and application of survival analysis: survival distributions and their applications, parametric and nonparametric methods, proportional hazards models, counting process and proportional hazards regression, planning and designing clinical trials. Given jointly with STAT 886.
LEARNING HOURS 120 (36L;84P).
An important topic in statistics not covered in any other courses.
An important topic in probability or statistics not covered in any other course.
LEARNING HOURS 132 (24I;108P).
Decision theory and Bayesian inference; principles of optimal statistical procedures; maximum likelihood principle; large sample theory for maximum likelihood estimates; principles of hypotheses testing and the Neyman-Pearson theory; generalized likelihood ratio tests; the chi-square, t, F and other distributions. (Offered jointly with STAT 463.) Three term hours, winter; lectures.
Many systems evolve with an inherent amount of randomness in time and/or space. The focus of this course is on developing and analyzing methods for analyzing time series. Because most of the common time--domain methods are unreliable, the emphasis is on frequency--domain methods, i.e. methods that work and expose the bias that plagues most time--domain techniques. Slepian sequences (discrete prolate spheroidal sequences) and multi--taper methods of spectrum estimation are covered in detail. (Offered jointly with STAT 454*.)Three term-hours, fall; lectures.
A review of probability models and introduction to applied stochastic processes. Topics may include Markov chains, birth and death processes, random walk problems, elementary renewal theory, Markov processes, Brownian motion and Poisson processes, queuing theory. (Offered jointly with STAT-455*.) Three term-hours, fall or winter; lectures.
This course is an introduction to Bayesian analysis and decision theory. Topics covered will include: elements of decision theory; Bayesian point estimation, set estimation, and hypothesis testing; special priors; computations for Bayesian analysis. Offered jointly with STAT-456. Exclusion: STAT-456
Introduction to the theory and application of statistical algorithms. Topics may include classification, smoothing, model selection, optimization, sampling, supervised and unsupervised learning. Offered jointly with STAT-457. Exclusion: STAT-457
Introduction to the statistical packages SAS and R; classification; spline and smoothing spline; regularization, ridge regression and Lasso; model selection; resampling methods; importance sampling; Markov chain Monte Carlo; Metropolis-Hasting algorithm; Gibbs sampling; optimization. (Offered jointly with STAT-462.) Three term hours; lectures.
Autocorrelation and autocovariance, stationarity; ARIMA models; model identification and forecasting; spectral analysis. Applications to biological, physical and economic data. (Offered jointly with STAT-464.) Three term-hours, fall; lectures.
An overview of the tools used in the measurement and improvement of quality in business, government and industry today. About a third of the course will be concerned with the design of experiments, particularly factorial and fractional factorial designs. Includes a project. Three term-hours, fall or winter; lectures.
Introduction to the basic knowledge in programming, data management, and exploratory data analysis using SAS software: data manipulation and management; output delivery system; advanced text file generation, statistical procedures and data analysis, macro language, structure query language, and SAS applications in clinical trial, administrative financial data. Offered jointly with STAT 466.
EXCLUSION: STAT 466
Simple random sampling; Unequal probability sampling; Stratified sampling; Cluster sampling; Multi-stage sampling; Analysis of variance and covariance; Block designs; Fractional factorial designs; Split-plot designs; Response surface methodology; Robust parameter designs for products and process improvement. (Offered jointly with STAT-471.) Three term hours; lectures.
An introduction to advanced regression methods for binary, categorical, and count data. Major topics include maximum-likelihood method, binomial and Poisson regression, contingency tables, log linear models, and random effect models. The generalized linear models will be discussed both in theory and in applications to real data from a variety of sources.(Offered jointly with STAT-473*.)
Introduces the theory and application of survival analysis: survival distributions and their applications, parametric and nonparametric methods, proportional hazards models, counting process and proportional hazards regression, planning and designing clinical trials. (Offered jointly with STAT-486*.) Three term-hours, winter; lectures.
Under the guidance of the supervisor, students will carry out a practicum project in a health research group/site and practise biostatistical methods and data analysis, or conduct methodology research in a biostatistical project. Students will summarize the results of the project in a written report that will be reviewed and orally defended.
Subject matter will vary from year to year. Three term-hours, Fall or winter; Seminar or reading course.
Subject matter will vary from year to year. Three term-hours, Fall or winter; Seminar or reading course.
Subject matter will vary from year to year. Three term-hours, Fall or winter; Seminar or reading course.
Subject matter will vary from year to year. Three term-hours, Fall or winter; Seminar or reading course.
Subject matter will vary from year to year. Three term-hours, Fall or winter; Seminar or reading course.
Subject matter will vary from year to year. Three term-hours, Fall or winter; Seminar or reading course.
Modeling will be presented in the context of biological examples drawn from ecology and evolution, including life history evolution, sexual selection, evolutionary epidemiology and medicine, and ecological interactions. Techniques will be drawn from dynamical systems, probability, optimization, and game theory with emphasis put on how to formulate and analyze models.
LEARNING HOURS 120 (36L;84P)
Modeling will be presented in the context of biological examples drawn from ecology and evolution, including life history evolution, sexual selection, evolutionary epidemiology and medicine, and ecological interactions. Techniques will be drawn from dynamical systems, probability, optimization, and game theory with emphasis put on how to formulate and analyze models.Three term hours; winter. T.B.A.