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2010-2011 Academic Year
Arts and Science Departments, Programs and Courses Mathematics and Statistics Courses of Instruction in Mathematics in the Faculty of Arts and Science


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Courses of Instruction in Mathematics in the Faculty of Arts and Science
MATH-006*/0.5 MATH-010*/0.5 MATH-013*/0.5 MATH-014*/0.5 MATH-110/1.0 MATH-111/1.0 MATH-112*/0.5 MATH-120/1.0
MATH-121/1.0 MATH-122/1.0MATH-123*/0.5MATH-124*/0.5 MATH-126/1.0 MATH-210*/0.5MATH-211/1.0 MATH-213*/0.5
MATH-221*/0.5 MATH-228*/0.5 MATH-231*/0.5 MATH-232*/0.5 MATH-272*/0.5 MATH-280*/0.5 MATH-281*/0.5 BIOM-300*/0.5
MATH-310*/0.5MATH-311*/0.5 MATH-312*/0.5 MATH-326*/0.5 MATH-328*/0.5 MATH-334*/0.5 MATH-335*/0.5 MATH-337*/0.5
MATH-339*/0.5MATH-341*/0.5 MATH-381*/0.5 MATH-382*/0.5 MATH-384*/0.5 MATH-385*/0.5 MATH-386*/0.5 MATH-387*/0.5
MATH-391*/0.5 MATH-392*/0.5 MATH-401*/0.5 MATH-402*/0.5 MATH-405*/0.5 MATH-406*/0.5 MATH-411*/0.5MATH-412*/0.5
MATH-413*/0.5MATH 414*/0.5MATH-418*/0.5 MATH-421*/0.5MATH-427*/0.5 MATH-432*/0.5 MATH-434*/0.5 MATH-436*/0.5
MATH-437*/0.5 MATH-439*/0.5 MATH-443*/0.5MATH-474*/0.5 MATH-477*/0.5 MATH-481*/0.5MATH-484*/0.5 MATH-491*/0.5
MATH-492*/0.5 MATH-495*/0.5 MATH-497*/0.5 MATH-498*/0.5 MATH-499*/0.5MATH-500*/0.5 MATH-501*/0.5 MATH-502*/0.5
MATH-503*/0.5
AVAILABILITY
The Department of Mathematics and Statistics does not offer all of the courses listed in the Calendar every year. For the most up-to-date information on the availability of courses offered in the current year, check QCARD or consult with the departmental office, web site, or an academic adviser.

PREREQUISITES
In all cases, stated course prerequisites are suggested guidelines meant to indicate the type and level of background that will be assumed in the course. A student lacking the stated prerequisite or equivalent should consult the instructor before registration. 4U AFIC refers to Advanced Functions and Introductory Calculus; 4U GDM refers to Geometry and Discrete Mathematics.
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MATH-006*/0.5 Introduction to Calculus 3L
Corresponds to 4U AFIC. Functions and their graphs, limits, derivatives.
NOTE    This course may not be included in any concentration in Mathematics or Statistics.
 PREREQUISITE    Ontario Grade 11 Mathematics or equivalent.
EXCLUSION    Students who have received a grade of 75 per cent in 4U AFIC or who have successfully completed a 100 level calculus course in the Department are not normally permitted to take this course for credit.
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MATH-010*/0.5 Fundamental Concepts in Elementary Mathematics for Teachers 3L;1P
A course of interest to prospective teachers. Elementary school mathematics is considered from an enriched point of view. Theoretical and pedagogical questions will be raised throughout the course, and students will be required to teach a one-hour enrichment class, once a week for 10 weeks, to grade 7 or 8 students in a local elementary school.
NOTE    Students may incur transportation costs. These will vary, but are expected to be no more than $50. Students must obtain a criminal record check at their local police prior to the course. A fee will be charged. This course may not be included in any concentration in Mathematics or Statistics.
 PREREQUISITE    Second-year standing.
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MATH-013*/0.5 Elementary Concepts in Discrete Mathematics 3L
Topics in mathematics, emphasizing patterns, problem solving, applications. Connections between contemporary mathematics and society. Emphasis on number systems, arithmetic, combinatorics, graph theory. Of interest to prospective teachers.
NOTE    Does not prepare student for other courses in mathematics or statistics. May not be used as part of any concentration in Mathematics or Statistics.
 PREREQUISITE    Ontario Grade 10 Mathematics or equivalent.
EXCLUSIONS    Not open to students with 2.0 credits or more in university mathematics or statistics courses numbered 100 or above, or to students enrolled in the B.Com. program.
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MATH-014*/0.5 Elementary Concepts in Continuous Mathematics 3L
Topics in mathematics, emphasizing patterns, problem solving, applications. Connections between contemporary mathematics and society. Emphasis on geometry, mathematical models of growth and change. Of interest to prospective teachers.
NOTE    Does not prepare student for other courses in mathematics or statistics. May not be used as part of any concentration in Mathematics or Statistics.
 PREREQUISITE    Ontario Grade 10 Mathematics or equivalent.
EXCLUSIONS    Not open to students with 2.0 credits or more in university mathematics or statistics courses numbered 100 or above, or to students enrolled in the B.Com. program.
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MATH-110/1.0 Linear Algebra 3L;1T
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. PREREQUISITE    At least one 4U mathematics course or equivalent.
EXCLUSIONS    MATH 111, MATH 112*.
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MATH-111/1.0 Linear Algebra 3L;1T
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. PREREQUISITE    At least one 4U mathematics course or equivalent.
EXCLUSIONS    MATH 110, MATH 112*.
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MATH-112*/0.5 Introduction to Linear Algebra 3L
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. PREREQUISITE    At least one 4U mathematics course or equivalent.
EXCLUSIONS    MATH 110, MATH 111.
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MATH-120/1.0 Differential and Integral Calculus 3L;1T
For students intending a medial or major concentration in Mathematics or Statistics. The basic concepts in calculus - limit, continuity, the fundamental theorem - as well as its development as a tool are studied. MATH 121 and MATH 126 cover approximately the same topics in calculus with different emphases. PREREQUISITES    MHF4U and MCV4U or equivalent, or 4U AFIC, or permission of the Department.
EXCLUSIONS    MATH 121, MATH 122, MATH 123*, MATH 124*, MATH 126.
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MATH-121/1.0 Differential and Integral Calculus 3L;1T
Differentiation and integration of the elementary functions, with applications to physical and social sciences; Taylor polynomials; multivariable differential calculus. Intended for students planning to concentrate in subjects other than Biochemistry, Biology, Life Sciences, Mathematics or Statistics.
Also offered at the International Study Centre, Herstmonceux.
PREREQUISITE    MHF4U and MCV4U or equivalent, or 4U AFIC, or MATH 006*, or permission of the Department.
EXCLUSIONS    MATH 120, MATH 122, MATH 123*, MATH 124*, MATH 126.
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MATH-122/1.0 Calculus for Students in Biochemistry, Biology and Life Sciences 3L;1T
Primarily intended for students in Biology, Biochemistry and Life Sciences, this course covers differentiation and integration, Taylor polynomials, multivariable differential calculus, and applications of probability, statistics, and dynamical systems. Material will be presented in the context of biological examples from ecology, behaviour, physiology, evolutionary biology, and other areas of modern biology. PREREQUISITES    MHF4U and MCV4U or equivalent, or 4U AFIC, or permission of the Department.
COREQUISITE    BIOL 102*.
EXCLUSIONS    MATH 120, MATH 121, MATH 123*, MATH 124*, MATH 126.
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MATH-123*/0.5 Differential and Integral Calculus I 3L;1T
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.  Intended for students not concentrating in Mathematics or Statistics. PREREQUISITE    Permission of the Department.   
EXCLUSIONS    MATH 120, MATH 121, MATH 122, MATH 126, APSC 171.
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MATH-124*/0.5 Differential and Integral Calculus II 3L;1T
Numerical integration; differential equations; multivariable differential calculus; optimization. Intended for students who have credit for a one-term calculus course covering the topics in the first term of MATH 121. PREREQUISITE    MATH 123* or permission of the Department.
EXCLUSIONS    MATH 120, MATH 121, MATH 122, MATH 126, APSC172.
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MATH-126/1.0 Differential and Integral Calculus 3L
The content is similar to that of MATH 121 but assumes no knowledge of calculus. BSCH, BCOM, and BCMPH students may not enrol in this course.
EXCLUSIONS    MATH 120, MATH 121, MATH 122, MATH 123*, MATH 124*.
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MATH-210*/0.5 Rings and Fields    3L
Integers, polynomials, modular arithmetic, rings, ideals, homomorphisms, quotient rings, division algorithm, greatest common divisors, Euclidean domains, unique factorization, fields, finite fields. PREREQUISITE    MATH 110, or MATH 111 or MATH 112* with permission of the Department.
EXCLUSIONS    MATH 211, MATH 213*, MATH 217*.   
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MATH-211/1.0 Algebraic Methods 3L
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. PREREQUISITES    A course in calculus and one of MATH 110, MATH 111.
EXCLUSIONS    MATH 210*, MATH 212*, MATH 213*, MATH 217*, MATH 312*.
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MATH-213*/0.5 Methods of Modern Algebra   3L
Algebraic techniques used in mathematics, computer science, and other areas. Factorization, divisibility and congruence for integers and polynomials. Complex numbers. Computational and algorithmic considerations will be stressed, with reference as needed to structures such as rings and fields. MATH 213* is suitable in lieu of MATH 210* or MATH 212* towards a medial or 14.0-credit concentration. PREREQUISITE    One of MATH 110 or MATH 111 or MATH 112*.
EXCLUSIONS    MATH 210*, MATH 211, MATH 212*, MATH 217*.
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MATH-221*/0.5 Vector Calculus 3L
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. PREREQUISITES    One of MATH 120, MATH 121, MATH 122, MATH 124*, or MATH 126; some linear algebra is recommended.
EXCLUSIONS    MATH 227*, MATH 280*.
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MATH-228*/0.5 Complex Analysis 3L;1T
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. PREREQUISITES    MATH 110 or MATH 111 or MATH 112*; MATH 120 or MATH 121 or MATH 122 or MATH 124*.
EXCLUSION    MATH 326*.
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MATH-231*/0.5 Differential Equations 3L;1T
An introduction to ordinary differential equations and their applications. Intended for students concentrating in Mathematics or Statistics. PREREQUISITES    MATH 110 (or MATH 111); MATH 120 (or MATH 121 or MATH 122 or MATH 124*).
EXCLUSIONS    MATH 225*, MATH 226*, MATH 232*, MATH 235*, MATH 237*.
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MATH-232*/0.5 Differential Equations 3L
Introduction to ordinary differential equations and their applications to the physical and social sciences. Topics may include: numerical solutions, power series and series solutions, Laplace transforms. PREREQUISITE    One of MATH 120, MATH 121, MATH 122, MATH 124*, or MATH 126; some knowledge of linear algebra is assumed.
EXCLUSIONS    MATH 225*, MATH 226*, MATH 231*, MATH 235*, MATH 237*.
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MATH-272*/0.5 Applications of Numerical Methods 3L;1T;1P
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. PREREQUISITES    MATH 110 or MATH 111, and CISC 101* or CISC 121*.
COREQUISITE    MATH 232* or equivalent.
EXCLUSIONS    CISC 271*, PHYS 313*.
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MATH-280*/0.5 Advanced Calculus 3L;1T
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. PREREQUISITES    MATH 110 or MATH 111 or MATH 112* or APSC 174; MATH 120 or APSC 172.
EXCLUSIONS    MATH 221*, MATH 227*.
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MATH-281*/0.5 Introduction to Real Analysis 3L;1T
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. PREREQUISITES    MATH 120 or APSC 172 (or MATH 121 or MATH 122 or MATH 124*).
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BIOM-300*/0.5 Modeling Techniques in Biology 3L;2P
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. PREREQUISITE    One of MATH 120, MATH 121, MATH 122, MATH 124*; one of MATH 110, MATH 111 is recommended.
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MATH-310*/0.5 Group Theory    3L
Permutation groups, matrix groups, abstract groups, subgroups, homomorphisms, cosets, quotient groups, group actions, Sylow theorems. PREREQUISITE    MATH 210* or MATH 212* or MATH 217*.
EXCLUSION    MATH 313*.
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MATH-311*/0.5 Elementary Number Theory 3L
Congruences; Euler’s theorem; continued fractions; prime numbers and their distribution; quadratic forms; Pell's equation; quadratic reciprocity; introduction to elliptic curves. PREREQUISITE    One of MATH 210*, MATH 211, MATH 212*.
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MATH-312*/0.5 Linear Algebra 3L;1T
Canonical forms, spectral and other matrix decompositions, quadratic forms, inner product spaces, projection theorem, applications to linear systems and optimization. PREREQUISITE    MATH 110.
EXCLUSION    MATH 211.
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MATH-326*/0.5 Functions of a Complex Variable 3L
Complex numbers, analytic functions, harmonic functions, Cauchy's Theorem, Taylor and Laurent series, calculus of residues, Rouche's Theorem. PREREQUISITE    MATH 281*.
EXCLUSION    MATH 228*.
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MATH-328*/0.5 Real Analysis 3L
Metric spaces, topological spaces, compactness, completeness, contraction mappings, sequences and series of functions, uniform convergence, inverse and implicit function theorems. PREREQUISITE    MATH 281*.
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MATH-334*/0.5 Mathematical Methods for Engineering and Physics 3L;1T
Orthonormal families, Fourier series and convergence. Signal spaces, Fourier transforms, and generalized functions. Solution of boundary value problems, including heat, wave, and potential equations. Applications to mechanical, electrical, and thermal systems. PREREQUISITES    MATH 231* or MATH 237*; MATH 281*.
EXCLUSION    PHYS 312.
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MATH-335*/0.5 Mathematics of Engineering Systems 3L;1T
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. PREREQUISITES    MATH 334*; MATH 326* or MATH 228*.
EXCLUSIONS    MATH 236*, MATH 436*; PHYS 312.
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MATH-337*/0.5 Introduction to Operations Research Models 3L
Some probability distributions, simulation, Markov chains, queuing theory, dynamic programming, inventory theory. PREREQUISITES    One of STAT 251*, STAT 261*, STAT 263*, STAT 267*, STAT 356* or STAT 367*; a course in calculus; a course in linear algebra.
EXCLUSION    COMM 365*.
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MATH-339*/0.5 Evolutionary Game Theory 3L
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. PREREQUISITES    One of MATH 120, MATH 121, MATH 122, MATH 124*; one of MATH 110, MATH 111 is recommended.
EXCLUSION    MATH 239*.
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MATH-341*/0.5 Differential Geometry 3L
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. PREREQUISITE    MATH 110, MATH 280*.
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MATH-381*/0.5 Mathematics with a Historical Perspective 3L
A historical perspective on mathematical ideas focussing on a selection of important and accessible theorems. A project is required. PREREQUISITES    MATH 110 or MATH 111; MATH 121, MATH 126 or MATH 120.
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MATH-382*/0.5 Mathematical Explorations 3L
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. PREREQUISITES    MATH 221* or MATH 231* or MATH 232* or MATH 280*; MATH 210* or MATH 211.
EXCLUSION    IDIS 303* (prior to 2008).
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MATH-384*/0.5 Mathematical Theory of Interest 1P;1T
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. PREREQUISITE    A course in calculus; third-year standing.
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MATH-385*/0.5 Life Contingencies 3T
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. PREREQUISITES    One of MATH 120, MATH 121, MATH 122, MATH 124*; MATH 384*; one of STAT 251*, STAT 268*, STAT 351*; or permission of the Department.
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MATH-386*/0.5 Our Number System - an Advanced Perspective 3L
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. Normally offered in alternate years (alternating with MATH 387*). PREREQUISITE    MATH 281*.
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MATH-387*/0.5 Elementary Geometry - an Advanced Perspective 3L
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. PREREQUISITES    MATH 221* or MATH 280* or MATH 281*; third-year standing or permission of the Department.
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MATH-391*/0.5 Topics in Mathematics I 3L
An important topic in mathematics or statistics not covered in any other courses. PREREQUISITE    Prerequisites vary depending on specific course content; consult instructor or departmental webpage.
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MATH-392*/0.5 Topics in Mathematics II 3L
For a complete description, see MATH 391*. PREREQUISITE    Prerequisites vary depending on specific course content; consult instructor or departmental webpage.
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MATH-401*/0.5 Graph Theory 3L
An introduction to graph theory, one of the central disciplines of discrete mathematics. This course, MATH 402* and MATH 434* constitute a survey of discrete mathematics and its applications. Topics include graphs and subgraphs, trees, bond and cycle spaces, connectivity, Euler tours and Hamiltonian cycles, matchings, independent sets, cliques and networks. Given jointly with MATH 801*. PREREQUISITES     One of MATH 210*, MATH 211, MATH 212*, MATH 217*. Experience with abstract mathematics and mathematical proof, and a good foundation in linear algebra, are recommended.
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MATH-402*/0.5 Combinatorics: Enumeration and Designs 3L
An introduction to two subjects which together with MATH 401* provide an entry into discrete mathematics and its applications. Among the enumeration techniques covered are inclusion-exclusion, recurrence relations, and generating functions. The study of designs includes finite geometries and Latin squares. Given jointly with MATH 802*. PREREQUISITES    One of MATH 210*, MATH 211, MATH 212*, MATH 217*. Experience with abstract mathematics and mathematical proof, and a good foundation in linear algebra, are recommended.
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MATH-405*/0.5 Applications of Matrix Algebra 3L
Similarity and canonical forms. Non-negative matrices: Perron-Frobenius theorem, applications to probability (Markov chains). Matrix differential equations: Stability theory. Estimation of eigenvalues, Gersgorin's theorem, and related inequalities. Given jointly with MATH 805*. PREREQUISITES    One of MATH 210*, MATH 211, MATH 212*, MATH 217*, MATH 312*.
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MATH-406*/0.5 Introduction to Coding Theory 3L
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. PREREQUISITE    MATH 210* or MATH 212*.
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MATH-411*/0.5 Topics in Algebra    3L
Subject matter will vary from year to year. Offered in 2006-2007 and in alternate years. PREREQUISITE    Permission of the Department.
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MATH-412*/0.5 Topics in Number Theory 3L
Subject matter will vary from year to year. PREREQUISITE    Permission of the Department.
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MATH-413*/0.5 Computational Commutative Algebra 3L
Algorithms for solving systems of nonlinear equations; applications in geometry, algebra, and other areas; Gröbner basis methods. A suitable software package (e.g. CoCoA, Macaulay2, Singular, Magma) will be used to explore applications. PREREQUISITE    MATH 210* or MATH 212* or MATH 313*.
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MATH 414*/0.5 Introduction to Galois Theory 3L;1T
An introduction to Galois Theory and some of its applications. PREREQUISITES    MATH 310* or MATH 313*.
EXCLUSION    MATH 314*.
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MATH-418*/0.5 Number Theory and Cryptography 3L
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. PREREQUISITE    MATH 210* or MATH 212* or MATH 217*; or MATH 211 with permission of the Department.
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MATH-421*/0.5 Fourier Series  3L
An exploration of the modern theory of Fourier series: Abel and Cesaro summability; Dirichlet’s and Fejér’s kernels; term by term differentiation and integration; infinite products; Bernoulli numbers; Gibbs’s phenomenon. PREREQUISITE    MATH 281* or permission of the Department.
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MATH-427*/0.5 Introduction to Deterministic Dynamical Systems 3L
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*. PREREQUISITES    MATH 328*; MATH 231* or permission of the Department.
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MATH-432*/0.5 Variational Methods 3L
The classical calculus of variations: the Gateaux variation, necessary conditions, transversality, corner conditions, Euler-Lagrange multiplier theorem; applications to Hamiltonian mechanics and the Maximum Principle. Given jointly with MATH 832*. PREREQUISITES    MATH 280* and MATH 281* and MATH 231*.
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MATH-434*/0.5 Linear and Nonlinear Optimization 3L
Optimization of functions of several variables, restricted by equality and inequality constraints, with applications. Linear programming, including convexity, simplex algorithm, duality, sensitivity analysis. Techniques of unconstrained optimization. Constrained optimization, including Lagrangian, Kuhn-Tucker conditions, convexity, duality, numerical techniques. Given jointly with MATH 834*. PREREQUISITES    MATH 221* or MATH 280*; MATH 110 or MATH 111 or MATH 112*.
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MATH-436*/0.5 Partial Differential Equations 3L
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. PREREQUISITES    MATH 231* or MATH 237*; MATH 280*. One of MATH 328*, MATH 334*, MATH 338*, PHYS 312 is recommended.
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MATH-437*/0.5 Topics in Applied Mathematics 3L
Subject matter to vary from year to year. Given jointly with MATH 837*. PREREQUISITE    Permission of the Department.
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MATH-439*/0.5 Lagrangian Mechanics, Dynamics, and Control 3L;1T
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. PREREQUISITE    MATH 231* or MATH 237*, MATH 280* or MATH 281*; or permission of the Department.
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MATH-443*/0.5 Algebraic Topology 3L
Topological equivalence and topological invariants; homotopy and the fundamental group; covering spaces; homotopy type; Brower’s fixed point theorem; triangularization; homology and cohomology groups. PREREQUISITES    MATH 310* or MATH 313*; MATH 328* (or MATH 326* with permission of the Department).
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MATH-474*/0.5 Information Theory 3L
Fundamental principles of communication theory, information measures, entropy, mutual information, divergence; source encoding, Huffman codes, lossless source coding theorem; channel capacity, noisy channel coding theorem, information transmission theorem; continuous-alphabet channels; capacity of discrete-time and band-limited continuous-time Gaussian channels, channels with memory, rate distortion theory. Given jointly with MATH 874*. PREREQUISITE    STAT 251* or STAT 256* or STAT 356* or equivalent.
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MATH-477*/0.5 Source Coding and Quantization 3L
Theory and practice of quantization and signal compression systems. PREREQUISITE    MATH 474*.
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MATH-481*/0.5 Mathematical Logic 3L
An introduction to mathematical logic, including some of the following topics: syntax of first-order theories, Peano arithmetic, Gödel's first incompleteness theorem, sentences undecidable in Peano arithmetic, Gödel's second incompleteness theorem, and the Hilbert program and philosophical consequences of Gödel's theorems. PREREQUISITES    At least one MATH course at the 100-level or above, and third- or fourth-year standing in a MATH or PHIL honours program.
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MATH-484*/0.5 Data Networks 3L
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.  PREREQUISITE    STAT 455* or permission of the Department.
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MATH-491*/0.5 Topics in Mathematics I 3S
An important topic in mathematics not covered in any other courses. PREREQUISITE    Prerequisites vary depending on specific course content; consult instructor or departmental webpage.
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MATH-492*/0.5 Topics in Mathematics II 3S
For a complete description, see MATH 491*. PREREQUISITE    Prerequisites vary depending on specific course content; consult instructor or departmental webpage.
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MATH-495*/0.5 Topics in Mathematics III 3S
For a complete description, see MATH 491*. PREREQUISITE    Prerequisites vary depending on specific course content; consult instructor or departmental webpage.
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MATH-497*/0.5 Topics in Mathematics IV 3S
For a complete description, see MATH 491*. PREREQUISITE    Prerequisites vary depending on specific course content; consult instructor or departmental webpage.
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MATH-498*/0.5 Topics in Mathematics V 3S
For a complete description, see MATH 491*. PREREQUISITE    Prerequisites vary depending on specific course content; consult instructor or departmental webpage.
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MATH-499*/0.5 Topics in Mathematics VI 3S
For a complete description, see MATH 491*. PREREQUISITE    Prerequisites vary depending on specific course content; consult instructor or departmental webpage.
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MATH-500*/0.5 Readings in Mathematics I
Open to students with a strong interest in some topic not covered in any of the regular courses. The student must find an instructor willing to supervise an agreed upon reading program and evaluation procedure, and also obtain Departmental approval for the reading program prior to registration. PREREQUISITE    Approval of the instructor and the Department.
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MATH-501*/0.5 Readings in Mathematics II
For a complete description, see MATH 500*. PREREQUISITE    Approval of the instructor and the Department.
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MATH-502*/0.5 Readings in Mathematics III
For a complete description, see MATH 500*. PREREQUISITE    Approval of the instructor and the Department.
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MATH-503*/0.5 Readings in Mathematics IV
For a complete description, see MATH 500*. PREREQUISITE    Approval of the instructor and the Department.
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Arts and Science Departments, Programs and Courses Mathematics and Statistics Courses of Instruction in Mathematics in the Faculty of Arts and Science
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