Academic Calendar 2021-2022

Mathematics (MATH)

MATH 110  Linear Algebra  Units: 6.00  

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).

Requirements: Prerequisite None. Exclusion MATH 111; MATH 112; MATH 212. Recommended At least one 4U Mathematics course.  
Offering Faculty: Faculty of Arts and Science  
MATH 111  Linear Algebra  Units: 6.00  

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).

Requirements: Prerequisite None. Exclusion MATH 110; MATH 112. Recommended At least one 4U Mathematics course.  
Offering Faculty: Faculty of Arts and Science  
MATH 112  Introduction to Linear Algebra  Units: 3.00  

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).

Requirements: Prerequisite None. Exclusion MATH 110; MATH 111. Recommended At least one 4U Mathematics course.  
Course Equivalencies: MATH 110B/112 / APSC 174  
Offering Faculty: Faculty of Arts and Science  
MATH 120  Differential and Integral Calculus  Units: 6.00  

A thorough discussion of calculus, including limits, continuity, differentiation, integration, multivariable differential calculus, and sequences and series.
LEARNING HOURS 288 (72L;24T;192P).

Requirements: Prerequisite None. Exclusion MATH 121; MATH 123; MATH 124; MATH 126. Recommended MHF4U and MCV4U or 4U AFIC or permission of the Department. Note This course is intended for students who plan to pursue a Major or Medial Plan in Mathematics, Statistics or Physics.  
Offering Faculty: Faculty of Arts and Science  
MATH 121  Differential and Integral Calculus  Units: 6.00  

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).

Requirements: Prerequisite None. Exclusion MATH 120; MATH 123; MATH 124; MATH 126. Recommended MHF4U and MCV4U or equivalent, or 4U AFIC, or MATH P06, or permission of the Department. Note This course is intended for students who wish to pursue a Major or Medial Plan in a subject other than Mathematics or Statistics.  
Course Equivalencies: MATH121; MATH121B;MATH122B  
Offering Faculty: Faculty of Arts and Science  
MATH 123  Differential and Integral Calculus I  Units: 3.00  

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. 

Requirements: Prerequisite Permission of the Department. Exclusion MATH 120; MATH 121; MATH 126. Note This course is not intended for students pursuing a MATH or STAT Plan.  
Offering Faculty: Faculty of Arts and Science  
MATH 124  Differential and Integral Calculus II  Units: 3.00  

Topics include techniques of integration; differential equations, and multivariable differential calculus.
LEARNING HOURS 126 (36L;12T;78P).

Requirements: Prerequisite MATH 123 or permission of the Department. Exclusion MATH 120; MATH 121; MATH 126. Note For students who have credit for a one-term course in calculus. Topics covered are the same as those in the Winter term of MATH 121.  
Course Equivalencies: APSC172, MATH124  
Offering Faculty: Faculty of Arts and Science  
MATH 126  Differential and Integral Calculus  Units: 6.00  

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).

Requirements: Prerequisite None. Exclusion MATH 120; MATH 121; MATH 123; MATH 124; MATH 126. Note This course is primarily intended for students in the BAH program. Students in the BSCH, BCMPH or BCOM program should not enrol in this course.  
Offering Faculty: Faculty of Arts and Science  
MATH 210  Rings and Fields  Units: 3.00  

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)

Requirements: MATH110  
Offering Faculty: Faculty of Arts and Science  
MATH 211  Algebraic Methods  Units: 6.00  

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)

Requirements: Pre MATH120;121;122;124;126  
Offering Faculty: Faculty of Arts and Science  
MATH 212  Linear Algebra ll  Units: 3.00  

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).

Requirements: Prerequisite MATH 111 or MATH 112 or MTHE 217. Exclusion MATH 110. Equivalency MATH 312.  
Offering Faculty: Faculty of Arts and Science  
MATH 217  Algebraic Structures  Units: 3.50  

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)

Requirements: MATH118 OR APSC174  
Offering Faculty: Faculty of Arts and Science  
MATH 221  Vector Calculus  Units: 3.00  

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.

Requirements: MATH120 OR MATH121 OR MATH126 OR APSC172 OR MATH122 OR MATH124  
Offering Faculty: Faculty of Arts and Science  
MATH 224  Applied Math For Civil Eng.  Units: 4.50  

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)

Requirements: (APSC171 AND APSC172) OR (APSC142 AND APSC172) OR (APSC142 AND APSC174) OR (APSC171 AND APSC174)  
Offering Faculty: Faculty of Arts and Science  
MATH 225  Ordinary Differential Equations  Units: 3.00  

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)

Requirements: (MATH128 AND MATH118) OR (MATH128 AND MATH129) OR (APSC171 AND APSC174) OR (APSC171 AND APSC172) OR (MATH120 AND MATH110) OR (MATH120 AND MATH111) OR (MATH120 AND MATH112)  
Offering Faculty: Faculty of Arts and Science  
MATH 227  Vector Analysis  Units: 3.00  

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)

Requirements: (MATH128 AND MATH118) OR (MATH128 AND MATH129) OR (MATH12## AND MATH11##) OR (APSC171 AND APSC172) OR (APSC171 AND APSC174)  
Offering Faculty: Faculty of Arts and Science  
MATH 228  Complex Analysis  Units: 3.00  

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).

Requirements: Prerequisite (MATH 110 or MATH 111 or MATH 112) and (MATH 120 or MATH 121 or MATH 124). Exclusion MATH 326; PHYS 312; PHYS 317.  
Offering Faculty: Faculty of Arts and Science  
MATH 231  Differential Equations  Units: 3.00  

An introduction to ordinary differential equations and their applications. Intended for students concentrating in Mathematics or Statistics.
LEARNING HOURS 132 (36L;12T;84P).

Requirements: Prerequisite (MATH 110 or MATH 111 or MATH 212) and (MATH 120 or MATH 121 or MATH 124). Exclusion MATH 225; MATH 226; MATH 232.  
Offering Faculty: Faculty of Arts and Science  
MATH 235  Diff Equations For Elec & Comp  Units: 3.00  

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)

Requirements: (MATH128 AND MATH118) OR (MATH128 AND MATH129) OR (APSC171 AND APSC172) OR (APSC171 AND APSC174) OR (MATH120 AND MATH11##)  
Offering Faculty: Faculty of Arts and Science  
MATH 237  Diff Equations & Computer Meth  Units: 3.50  

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)

Requirements: MATH110 or MATH120 or (APSC171  
Offering Faculty: Faculty of Arts and Science  
MATH 239  Applied Math Modeling  Units: 3.00  

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 ~

Requirements: APSC172 OR MATH120 OR MATH121 OR MATH120 OR MATH126 OR MATH121 OR APSC172 OR MATH126  
Course Equivalencies: MATH239, MATH339  
Offering Faculty: Faculty of Arts and Science  
MATH 272  Applications of Numerical Methods  Units: 3.00  

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).

Requirements: Prerequisite (MATH 110 or MATH 111 or MATH 212) and (CISC 101 or CISC 121) Corequisite (MATH 225 or MATH 231 or MATH 232). Exclusion CISC 271; PHYS 213; PHYS 313.  
Offering Faculty: Faculty of Arts and Science  
MATH 280  Advanced Calculus  Units: 3.00  

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)

Requirements: (MATH120 AND MATH110) OR (MATH120 AND MATH111) OR (MATH120 AND APSC174) OR (APSC172 AND MATH110) OR (APSC172 AND MATH111) OR (APSC172 AND APSC174) OR (MATH120 AND MATH112) OR (APSC172 AND MATH112)  
Offering Faculty: Faculty of Arts and Science  
MATH 281  Introduction to Real Analysis  Units: 3.00  

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).

Requirements: Prerequisite MATH 120 or MATH 121 or MATH 124.  
Offering Faculty: Faculty of Arts and Science  
MATH 310  Group Theory  Units: 3.00  

Permutation groups, matrix groups, abstract groups, subgroups, homomorphisms, cosets, quotient groups, group actions, Sylow theorems.
LEARNING HOURS 132 (36L;96P).

Requirements: Prerequisite MATH 210.  
Course Equivalencies: MATH310, MATH313  
Offering Faculty: Faculty of Arts and Science  
MATH 311  Elementary Number Theory  Units: 3.00  

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).

Requirements: Prerequisite MATH 210 or MATH 211.  
Offering Faculty: Faculty of Arts and Science  
MATH 314  Representations of the Symmetric Group  Units: 3.00  

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).

Requirements: Prerequisite MATH 210 or MATH 211.  
Offering Faculty: Faculty of Arts and Science  
MATH 326  Functions of a Complex Variable  Units: 3.00  

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).

Requirements: Prerequisite MATH 281. Exclusion MATH 228; PHYS 312; PHYS 317.  
Offering Faculty: Faculty of Arts and Science  
MATH 328  Real Analysis  Units: 3.00  

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).

Requirements: Prerequisite MATH 281.  
Offering Faculty: Faculty of Arts and Science  
MATH 334  Mathematical Methods for Engineering and Physics  Units: 3.00  

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).

Requirements: Prerequisite (MATH 110 or MATH 111 or MATH 212) and MATH 281. Exclusion PHYS 312; PHYS 316.  
Offering Faculty: Faculty of Arts and Science  
MATH 335  Mathematics of Engineering Systems  Units: 3.00  

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).

Requirements: Prerequisite MATH 334 and (MATH 228 or MATH 326). Exclusion PHYS 312. Equivalency MATH 236.  
Course Equivalencies: MATH236, MATH335  
Offering Faculty: Faculty of Arts and Science  
MATH 337  Stochastic Models in Operations Research  Units: 3.00  

Some probability distributions, simulation, Markov chains, queuing theory, dynamic programming, inventory theory.
LEARNING HOURS 120 (36L;84P).

Requirements: Prerequisite (MATH 120 or MATH 121 or MATH 124) and (MATH 231 or MATH 225).  
Offering Faculty: Faculty of Arts and Science  
MATH 338  Fourier Methods for Boundary Value Problems  Units: 3.00  

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).

Requirements: Prerequisite (MATH 221 or MATH 280) and (MATH 225 or MATH 231 or MATH 232) and (MATH 110 or MATH 111). Exclusion PHYS 312; PHYS 316.  
Offering Faculty: Faculty of Arts and Science  
MATH 339  Evolutionary Game Theory  Units: 3.00  

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).

Requirements: Prerequisite (MATH 120 or MATH 121 or MATH 124) and (MATH 110 or MATH 111 or MATH 112). Equivalency MATH 239. Recommended MATH 110 or MATH 111.  
Course Equivalencies: MATH239, MATH339  
Offering Faculty: Faculty of Arts and Science  
MATH 341  Differential Geometry  Units: 3.00  

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).

Requirements: Prerequisite MATH 110 and MATH 280.  
Offering Faculty: Faculty of Arts and Science  
MATH 381  Mathematics with a Historical Perspective  Units: 3.00  

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).

Requirements: Prerequisite (MATH 110 or MATH 111 or MATH 212) and (MATH 120 or MATH 121 or MATH 126).  
Offering Faculty: Faculty of Arts and Science  
MATH 382  Mathematical Explorations  Units: 3.00  

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)

Requirements: (MATH221 AND MATH210) OR (MATH221 AND MATH211) OR (MATH212 AND MATH280) OR (MATH212 AND MATH281) OR (MATH210 AND MATH280) OR (MATH231 AND MATH210) OR (MATH210 AND MATH281) OR (MATH231 AND MATH211) OR (MATH232 AND MATH210) OR (MATH232 AND MATH211) OR (MATH280 AND MATH210) OR (MATH280 AND MATH211)  
Offering Faculty: Faculty of Arts and Science  
MATH 384  Mathematical Theory of Interest  Units: 3.00  

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).

Requirements: Prerequisite Level 3 or above and (MATH 120 or MATH 121 or MATH 124 or MATH 126).  
Offering Faculty: Faculty of Arts and Science  
MATH 385  Life Contingencies  Units: 3.00  

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).

Requirements: Prerequisite ([MATH 120 or MATH 121 or MATH 124 or MATH 126] and MATH 384 and [STAT 268 or STAT 351]) or permission of the Department.  
Offering Faculty: Faculty of Arts and Science  
MATH 386  Our Number System - an Advanced Perspective  Units: 3.00  

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).

Requirements: Prerequisite MATH 281.  
Offering Faculty: Faculty of Arts and Science  
MATH 387  Elementary Geometry - an Advanced Perspective  Units: 3.00  

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).

Requirements: Prerequisite (Level 3 or above and [MATH 221 or MATH 280 or MATH 281]) or permission of the Department.  
Offering Faculty: Faculty of Arts and Science  
MATH 401  Graph Theory  Units: 3.00  

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).

Requirements: Prerequisite MATH 210 or MATH 211. Recommended Experience with abstract mathematics and mathematical proof, and a good foundation in linear algebra.  
Offering Faculty: Faculty of Arts and Science  
MATH 402  Enumerative Combinatorics  Units: 3.00  

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).

Requirements: Prerequisite MATH 210 or MATH 211. Recommended Experience with abstract mathematics and mathematical proof, and a good foundation in linear algebra.  
Offering Faculty: Faculty of Arts and Science  
MATH 406  Introduction to Coding Theory  Units: 3.00  

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).

Requirements: Prerequisite MATH 210.  
Offering Faculty: Faculty of Arts and Science  
MATH 413  Introduction to Algebraic Geometry  Units: 3.00  

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).

Requirements: Prerequisite MATH 210.  
Offering Faculty: Faculty of Arts and Science  
MATH 414  Introduction to Galois Theory  Units: 3.00  

An introduction to Galois Theory and some of its applications.
LEARNING HOURS 132 (36L;96P).

Requirements: Prerequisite MATH 310.  
Offering Faculty: Faculty of Arts and Science  
MATH 418  Number Theory and Cryptography  Units: 3.00  

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).

Requirements: Prerequisite MATH 210 or (MATH 211 with permission of the Department).  
Offering Faculty: Faculty of Arts and Science  
MATH 421  Fourier Analysis  Units: 3.00  

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).

Requirements: Prerequisite MATH 281 or permission of the Department.  
Offering Faculty: Faculty of Arts and Science  
MATH 427  Introduction to Deterministic Dynamical Systems  Units: 3.00  

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).

Requirements: Prerequisite (MATH 231 and MATH 328) or permission of the Department.  
Offering Faculty: Faculty of Arts and Science  
MATH 429  Functional Analysis and Quantum Mechanics  Units: 3.00  

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).

Requirements: Prerequisite ([MATH 110 or MATH 111 or MATH 112] and MATH 281) or permission of the Department.  
Offering Faculty: Faculty of Arts and Science  
MATH 433  Continuum Mechanics with Applications  Units: 3.00  

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).

Requirements: Prerequisite (MATH 231 and MATH 280) or permission of the Instructor.  
Offering Faculty: Faculty of Arts and Science  
MATH 434  Optimization Theory with Applications to Machine Learning  Units: 3.00  

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.

Requirements: Prerequisite (MATH 110 or MATH 111 or MATH 212) and MATH 281.  
Offering Faculty: Faculty of Arts and Science  
MATH 436  Partial Differential Equations  Units: 3.00  

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).

Requirements: Prerequisite MATH 231 and MATH 280. Recommended MATH 328 or MATH 334 or MATH 338 or PHYS 312.  
Offering Faculty: Faculty of Arts and Science  
MATH 437  Topics in Applied Mathematics  Units: 3.00  

Subject matter to vary from year to year. Given jointly with MATH 837.
LEARNING HOURS 132 (36L;96P).

Requirements: Prerequisite Permission of the Department.  
Offering Faculty: Faculty of Arts and Science  
MATH 439  Lagrangian Mechanics, Dynamics, and Control  Units: 3.00  

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).

Requirements: Prerequisite (MATH 231 and [MATH 280 or MATH 281]) or permission of the Department.  
Offering Faculty: Faculty of Arts and Science  
MATH 474  Information Theory  Units: 3.00  

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).

Requirements: Prerequisite STAT 268 or STAT 351. Recommended STAT 353.  
Offering Faculty: Faculty of Arts and Science  
MATH 477  Data Compression and Source Coding  Units: 3.00  

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).

Requirements: Prerequisite MATH 474. Recommended STAT 353.  
Offering Faculty: Faculty of Arts and Science  
MATH 497  Topics in Mathematics IV  Units: 3.00  

An important topic in mathematics not covered in any other courses.

Requirements: Note The prerequisite can vary depending on specific course content, please consult the Instructor or visit the Department of Mathematics and Statistics webpage for more information.  
Offering Faculty: Faculty of Arts and Science  
MATH 498  Topics in Mathematics V  Units: 3.00  

An important topic in mathematics not covered in any other courses.

Requirements: Note The prerequisite can vary depending on specific course content, please consult the Instructor or visit the Department of Mathematics and Statistics webpage for more information.  
Offering Faculty: Faculty of Arts and Science  
MATH 499  Topics In Mathematics  Units: 3.00  

Important topics in mathematics not covered in any other courses.

Requirements: Prerequisite Permission of the Department.  
Offering Faculty: Faculty of Arts and Science  
MATH 594  Independent Study  Units: 3.00  

Offering Faculty: Faculty of Arts and Science  
MATH 595  Independent Study  Units: 6.00  

Offering Faculty: Faculty of Arts and Science  
MATH 603  Mathematics  Units: 6.00  

Offering Faculty: Faculty of Arts and Science  
MATH 620  Diff. & Int. Calculus  Units: 6.00  

Offering Faculty: Faculty of Arts and Science  
MATH 800  Seminar  Units: 3.00  

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.

Offering Faculty: Faculty of Arts and Science  
MATH 801  Graph Theory  Units: 3.00  

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*.)

Offering Faculty: Faculty of Arts and Science  
MATH 802  Enumerative Combinatorics  Units: 3.00  

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.

Offering Faculty: Faculty of Arts and Science  
MATH 806  Introduction To Coding Theory  Units: 3.00  

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.

Offering Faculty: Faculty of Arts and Science  
MATH 812  Topics In Number Theory  Units: 3.00  

Subject matter may vary from year to year. Three term-hours, fall or winter; lectures.

Offering Faculty: Faculty of Arts and Science  
MATH 813  Introduction to Algebraic Geometry  Units: 3.00  

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).

Offering Faculty: Faculty of Arts and Science  
MATH 818  Number Theory & Cryptography  Units: 3.00  

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.

Offering Faculty: Faculty of Arts and Science  
MATH 823  Ordinary Diff. Equations  Units: 3.00  

Offering Faculty: Faculty of Arts and Science  
MATH 827  Deterministic Dynamical System  Units: 3.00  

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.

Offering Faculty: Faculty of Arts and Science  
MATH 829  Functional Analysis  Units: 3.00  

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

Offering Faculty: Faculty of Arts and Science  
MATH 830  Modern Control Theory  Units: 3.00  

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.

Offering Faculty: Faculty of Arts and Science  
MATH 833  Continuum Mechanics  Units: 3.00  

Offering Faculty: Faculty of Arts and Science  
MATH 834  Optimization Theory with Applications to Machine Learning  Units: 3.00  

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

Offering Faculty: Faculty of Arts and Science  
MATH 835  Mathematical Biology  Units: 3.00  

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.

Offering Faculty: Faculty of Arts and Science  
MATH 836  Lagrangian Mechanics. Dynamics & Control  Units: 3.00  

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.

Offering Faculty: Faculty of Arts and Science  
MATH 837  Topics In Applied Mathematics  Units: 3.00  

Subject matter may vary from year to year. Three term-hours, fall or winter; lectures.

Offering Faculty: Faculty of Arts and Science  
MATH 838  Topics In Mathematical Biology  Units: 3.00  

Subject matter may vary from year to year. Three term-hours, fall or winter; lectures.

Offering Faculty: Faculty of Arts and Science  
MATH 844  Differentiable Manifolds  Units: 3.00  

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.

Offering Faculty: Faculty of Arts and Science  
MATH 845  Differential Geometry  Units: 6.00  

Offering Faculty: Faculty of Arts and Science  
MATH 848  Topics In Graph Theory  Units: 3.00  

Offering Faculty: Faculty of Arts and Science  
MATH 860  Probability Theory  Units: 6.00  

Offering Faculty: Faculty of Arts and Science  
MATH 862  Stochastic Processes  Units: 6.00  

Offering Faculty: Faculty of Arts and Science  
MATH 865  Stochastic Processes  Units: 3.00  

Offering Faculty: Faculty of Arts and Science  
MATH 872  Control Of Stochastic Systems  Units: 3.00  

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.

Offering Faculty: Faculty of Arts and Science  
MATH 873  Num. Lin. & Nonlin. Algebra II  Units: 3.00  

Offering Faculty: Faculty of Arts and Science  
MATH 874  Information Theory  Units: 3.00  

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.

Offering Faculty: Faculty of Arts and Science  
MATH 877  Data Compression And Source Co  Units: 3.00  

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*).

Offering Faculty: Faculty of Arts and Science  
MATH 880  Foundations Of Mathematics I  Units: 3.00  

Offering Faculty: Faculty of Arts and Science  
MATH 883  Mathematical Logic  Units: 6.00  

Offering Faculty: Faculty of Arts and Science  
MATH 884  Data Networks  Units: 3.00  

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.

Offering Faculty: Faculty of Arts and Science  
MATH 891  Core Course In Analysis I  Units: 3.00  

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.

Offering Faculty: Faculty of Arts and Science  
MATH 892  Core Course In Analysis II  Units: 3.00  

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.

Offering Faculty: Faculty of Arts and Science  
MATH 893  Core Course In Algebra I  Units: 3.00  

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.

Offering Faculty: Faculty of Arts and Science  
MATH 894  Core Course In Algebra II  Units: 3.00  

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.

Offering Faculty: Faculty of Arts and Science  
MATH 895  Core Course In Prob. Theory  Units: 3.00  

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.

Offering Faculty: Faculty of Arts and Science  
MATH 896  Core Mathematical Statistics I  Units: 3.00  

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.

Offering Faculty: Faculty of Arts and Science  
MATH 897  Core Mathematical Statistics II  Units: 3.00  

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.

Offering Faculty: Faculty of Arts and Science  
MATH 898  Master's Project  Units: 6.00  

Offering Faculty: Faculty of Arts and Science  
MATH 899  Master's Thesis Research  Units: 6.00  

Offering Faculty: Faculty of Arts and Science  
MATH 901  Research Institute Course  Units: 3.00  

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.

Offering Faculty: Faculty of Arts and Science  
MATH 902  Topics In Algebra  Units: 3.00  

Subject matter will vary from year to year. Three term-hours, Fall or winter; Seminar or reading course.

Offering Faculty: Faculty of Arts and Science  
MATH 903  Topics in Algebra  Units: 3.00  

Subject matter will vary from year to year. Three term-hours, Fall or winter; Seminar or reading course.

Offering Faculty: Faculty of Arts and Science  
MATH 905  Topics In Algebra  Units: 3.00  

Subject matter will vary from year to year. Three term-hours, Fall or winter; Seminar or reading course.

Offering Faculty: Faculty of Arts and Science  
MATH 912  Topics In Number Theory  Units: 3.00  

Subject matter will vary from year to year. Three term-hours, Fall or winter; seminar or reading course.

Offering Faculty: Faculty of Arts and Science  
MATH 913  Topics In Number Theory  Units: 3.00  

Subject matter will vary from year to year. Three term-hours, Fall or winter; Seminar or reading course.

Offering Faculty: Faculty of Arts and Science  
MATH 915  Topics in Number Theory  Units: 3.00  

Subject matter will vary from year to year. Three term-hours, Fall or winter; Seminar or reading course.

Offering Faculty: Faculty of Arts and Science  
MATH 916  Group Representations IIb  Units: 3.00  

Offering Faculty: Faculty of Arts and Science  
MATH 920  Topological Vector Spaces  Units: 3.00  

Offering Faculty: Faculty of Arts and Science  
MATH 921  Vector Lattices & Integration  Units: 3.00  

Offering Faculty: Faculty of Arts and Science  
MATH 922  Topics In Analysis  Units: 3.00  

Subject matter will vary from year to year. Three term-hours, Fall or winter; Seminar or reading course.

Offering Faculty: Faculty of Arts and Science  
MATH 923  Topics In Analysis  Units: 3.00  

Subject matter will vary from year to year. Three term-hours, Fall or winter; Seminar or reading course.

Offering Faculty: Faculty of Arts and Science  
MATH 925  Topics In Analysis  Units: 3.00  

Subject matter will vary from year to year. Three term-hours, Fall or winter; Seminar or reading course.

Offering Faculty: Faculty of Arts and Science  
MATH 926  Measure & Integration  Units: 3.00  

Offering Faculty: Faculty of Arts and Science  
MATH 928  Abstract Harmonic Analysis  Units: 3.00  

Offering Faculty: Faculty of Arts and Science  
MATH 930  Quantum Mechanics  Units: 3.00  

Offering Faculty: Faculty of Arts and Science  
MATH 932  Topics In Applied Mathematics  Units: 3.00  

Subject matter will vary from year to year. Three term-hours, Fall or winter; Seminar or reading course.

Offering Faculty: Faculty of Arts and Science  
MATH 933  Topics In Applied Mathematics  Units: 3.00  

Subject matter will vary from year to year. Three term-hours, Fall or winter; Seminar or reading course.

Offering Faculty: Faculty of Arts and Science  
MATH 935  Topics In Applied Mathematics  Units: 3.00  

Subject matter will vary from year to year. Three term-hours, Fall or winter; Seminar or reading course.

Offering Faculty: Faculty of Arts and Science  
MATH 936  Topics In Control Theory  Units: 3.00  

Subject matter will vary from year to year. Three term-hours, Fall or winter; Seminar or reading course.

Offering Faculty: Faculty of Arts and Science  
MATH 937  Topics In Control Theory  Units: 3.00  

Subject matter will vary from year to year. Three term-hours, Fall or winter; Seminar or reading course.

Offering Faculty: Faculty of Arts and Science  
MATH 939  Topics In Control Theory  Units: 3.00  

Subject matter will vary from year to year. Three term-hours, Fall or winter; Seminar or reading course.

Offering Faculty: Faculty of Arts and Science  
MATH 942  Topics In Topology & Geometry  Units: 3.00  

Subject matter will vary from year to year. Three term-hours, Fall or winter; Seminar or reading course.

Offering Faculty: Faculty of Arts and Science  
MATH 943  Topics In Topology & Geometry  Units: 3.00  

Subject matter will vary from year to year. Three term-hours, Fall or winter; Seminar or reading course.

Offering Faculty: Faculty of Arts and Science  
MATH 945  Topics In Topology & Geometry  Units: 3.00  

Subject matter will vary from year to year. Three term-hours, Fall or winter; Seminar or reading course.

Offering Faculty: Faculty of Arts and Science  
MATH 950  Pontragin's Maximum Principle  Units: 3.00  

Offering Faculty: Faculty of Arts and Science  
MATH 972  Topics In Communication Theory  Units: 3.00  

Subject matter will vary from year to year. Three term-hours, Fall or winter; Seminar or reading course.

Offering Faculty: Faculty of Arts and Science  
MATH 973  Topics In Communication Theory  Units: 3.00  

Offering Faculty: Faculty of Arts and Science  
MATH 975  Topics In Communication Theory  Units: 3.00  

Subject matter will vary from year to year. Three term-hours, Fall or winter; Seminar or reading course.

Offering Faculty: Faculty of Arts and Science  
MATH 986  Philosophy Of Mathematics  Units: 3.00  

Offering Faculty: Faculty of Arts and Science  
MATH 999  Ph. D. Thesis Research  Units: 6.00  

Offering Faculty: Faculty of Arts and Science