Students must check to ensure that prerequisites are met. Students may be deregistered, at the request of the instructor, from any course for which prerequisites and/or restrictions have not been met.
MATHEMATICS COURSES
MATH 1F92
Introductory Statistics
Describing and comparing data sets, linear regression analysis, basic probability theory, discrete probability distributions, binomial and normal distributions, Central Limit Theorem, confidence intervals and hypothesis tests on means and proportions, properties of t, F and chisquared distributions, analysis of variance, inference on regression. Emphasis on interpretation of numerical results for all topics. Use of Minitab.
Lectures, 3 hours per week.
Prerequisite(s): one grade 11 mathematics credit.
Note: designed for nonscience majors. Not open to students with credit in any university mathematics or statistics course. Major credit will not be granted to Mathematics majors.
MATH 1P01
Calculus Concepts I
Differential calculus emphasizing on concepts and the use of both theory and computers to solve problems. Precalculus topics, limits, continuity and the intermediate value theorem, derivatives and differentiability, implicit differentiation, linear approximation, mean value theorem with proof and applications, max and min, related rates, curve sketching, l'Hospital's rule, antiderivatives, Riemann sums, FTC with proof, integration by substitution. Use of Maple.
Lectures, 4 hours per week; lab/tutorial, 1 hour per week.
Prerequisite(s): two grade 12 mathematics credits including MCV4U or permission of the instructor.
Note: intended for mathematics majors and/or future teachers. Students must successfully complete the Mathematics Skills Test.
Completion of this course will replace previous assigned grade and credit obtained in MATH 1P05.
MATH 1P02
Calculus Concepts II
Integral calculus emphasizing concepts, theory and computers to solve problems. Further integration techniques. Applications to areas between curves, volumes, arc length and probabilities. Multivariable calculus: partial derivatives, optimization of functions of two variables. Sequences and series: convergence tests, Taylor and Maclaurin series and applications. Differential Equations: direction fields, separable equations, growth and decay, the logistic equation, linear equations. Use of Maple.
Lectures, 4 hours per week; lab/tutorial, 1 hour per week.
Prerequisite(s): MATH 1P01, 1P05 or permission of instructor.
Note: intended for mathematics majors and/or future teachers.
Completion of this course will replace previous assigned grade and credit obtained in MATH 1P06.
MATH 1P05
Applied Calculus I
Differential calculus emphasizing problem solving, calculation and applications. Precalculus topics, limits and asymptotic analysis, continuity, derivatives and differentiability, implicit differentiation, linear approximation. Applications: slope, rates of change, maximum and minimum, convexity, curve sketching, L'Hospital's rule. Antiderivatives, integrals, fundamental theorem of calculus, integration by substitution. Use of a computer algebra system.
Lectures, 4 hours per week; lab/tutorial, 1 hour per week.
Prerequisite(s): two grade 12 mathematics credits including MCV4U or permission of the instructor.
Note: designed for students in the sciences, computer science, and future teachers. Students must successfully complete the Mathematics Skills Test.
Completion of this course will replace previous assigned grade and credit obtained in MATH 1P01.
MATH 1P06
Applied Calculus II
Integral calculus emphasizing problem solving, calculations and applications. Further techniques of integration. Areas between curves, volumes, arc length and probabilities. 1st order differential equations. Sequences and series: convergence tests, Taylor and Maclaurin series and applications. Use of computer algebra system.
Lectures, 4 hours per week; lab/tutorial, 1 hour per week.
Prerequisite(s): MATH 1P01 or 1P05.
Note: designed for students in the sciences, computer science, and future teachers.
Completion of this course will replace previous assigned grade and credit obtained in MATH 1P02.
MATH 1P11
Linear Algebra I
Review of linear systems and matrix algebra. General determinants and applications. Complex numbers. Vector geometry in R^{2} to R^{3}. Dot product, norm and projections, cross product, lines and planes. Finitedimensional vector spaces (real and complex). Linear transformations from R^{n} to R^{m}; rank and kernels. Eigenvalues. Use of a computer algebra system.
Lectures, 3 hours per week; lab/tutorial, 1 hour per week.
Prerequisite(s): two grade 12 mathematics credits including MCV4U.
MATH 1P12
Applied Linear Algebra
Systems of linear equations with applications. Matrix algebra. Determinants. Vector geometry in R^{2} and R^{3} dot product, norm and projections, cross product, lines and planes. Complex numbers. Euclidean nspace. Linear transformations from R^{n} to R^{m}. Focus on applications of linear algebra to sciences and integrated use of a computer algebra system.
Lectures, 3 hours per week; lab/tutorial, 1 hour per week.
Prerequisite(s): one grade 12 mathematics credit or permission of instructor.
Students will not receive earned credit for MATH 1P12 if MATH 1P11 has been successfully completed.
MATH 1P20
Introduction to Mathematics
Essential mathematics skills required for university mathematics courses. Sets, real and complex numbers, solutions of inequalities and equations, functions, inverse functions, composition of functions, polynomial functions, rational functions, trigonometry, trigonometric functions, trigonometric identities, exponential functions, logarithmic functions, mathematical induction, binomial theorem, vectors and matrices.
Lectures, 3 hours per week; lab/tutorial, 1 hour per week.
Prerequisite(s): one grade 11 mathematics credit.
Note: not open to students with credit in any university calculus course. Cannot be used toward a Mathematics teachable subject at Brock.
MATH 1P40
Mathematics Integrated with Computers and Applications I
Exploration of ideas and problems in algebra, differential equations, and dynamical systems using computers. Topics include number theory, integers mod p, roots of equations, fractals, predatorprey models and the discrete logistic equation for population growth.
Lectures, 2 hours per week; lab, 2 hours per week.
Restriction: open to MATH (single or combined), MATH (Honours)/BEd (Intermediate/Senior) majors and minors until date specified in Registration guide.
Prerequisite(s): MATH 1P01 or 1P05.
MATH 1P66
Mathematical Reasoning
Introduction to mathematical INDGraction, logic and proofs including mathematical induction.
Lectures, 3 hours per week.
Prerequisite(s): MATH 1P20 or one grade 12 mathematics credit.
Note: MCB4U recommended.
MATH 1P67
Mathematics for Computer Science
Development and analysis of algorithms, complexity of algorithms, recursion solving recurrence relations and relations and functions.
Lectures, 3 hours per week.
Prerequisite(s): MATH 1P66.
Corequisite(s): COSC 1P03.
MATH 1P70
Mathematics in Culture
Role of mathematics in past and contemporary cultures including applications to science, society and the arts. Topics may include the stock market, social media, cryptography, history of numbers, statistics in newspapers, game theory, music, epidemics, and mathematics in movies and television.
Lectures, 3 hours per week.
Restriction: not open to Mathematics (single or combined) majors.
Note: major credit will not be granted to Mathematics majors. Cannot be used toward a Mathematics teachable subject for programs at Brock.
MATH 1P97
Calculus With Applications
Lines, polynomials, logarithms and exponential functions; twosided limits; rates of change using derivatives; max and min of functions using derivatives; higher derivatives and concavity; area under a curve using integrals; optimization of functions of two variables using partial derivatives; growth and decay using differential equations; applications to many different disciplines; use of computer algebra systems.
Lectures, 4 hours per week.
Restriction: not open to Mathematics (single or combined) majors.
Prerequisite(s): MATH 1P20 or one grade 12 mathematics credit.
Note: may be available on site, online or blended. Designed for students in Biological Sciences, Biotechnology, Business, Earth Sciences, Economics, Environmental Geoscience, Geography and Medical Sciences. Not open to students with credit in any university calculus course. Major credit will not be granted to Mathematics majors.
MATH 1P98
Practical Statistics
Descriptive statistics; probability of events; counting rules; discrete and continuous probability distributions: binomial, Poisson and normal distributions; Central Limit Theorem; confidence intervals and hypothesis testing; analysis of variance; contingency tables; correlation and regression; emphasis on realworld applications throughout; use of statistical computer software.
Lectures, 3 hours per week.
Restriction: not open to Mathematics (single or combined) majors.
Prerequisite(s): MATH 1P20 or one grade 12 mathematics credit.
Note: designed for students in Biological Sciences, Biotechnology, Business, Earth Sciences, Economics, Environmental Geoscience and Medical Sciences. Not open to students with credit in any university statistics course. Major credit will not be granted to Mathematics majors.
MATH 1P99
Applied Statistics for Life Sciences
Visualizing and interpreting life science data using histograms, frequency tables, correlation and regression, and a variety of statistical measures; basic concepts ofprobability; applications of the binomial, Poisson and normal distributions; confidence intervals for proportions and means; hypothesis testing; contingency tables; introduction to ANOVA; emphasis on interpretation and use of Microsoft Excel software throughout.
Lectures, 3 hours per week.
Prerequisite(s): MATH 1P20 or one grade 12 mathematics credit
Note: designed for students in the Life and Applied Health Sciences. Not open to students with credit in any university statistics course.
MATH 2P03
Multivariable Calculus
Functions of two and three variables, partial derivatives, gradient, critical points, maxima and minima, Taylor expansion, inverse and implicit function theorems. Cartesian, polar, cylindrical and spherical coordinates. Curves and surfaces, parametric representation, tangent space. Two and threedimensional integration, line and surface integrals.
Lectures, 3 hours per week; lab/tutorial, 1 hour per week.
Prerequisite(s): MATH 1P02, 1P06 or permission of the instructor.
MATH 2P04
Basic Concepts of Analysis
Sets; mappings, countability; properties of the real number system; inner product, norm, and the CauchySchwarz inequality; compactness and basic compactness theorems (Cantor's theorem, the BolzanoWeierstrass theorem, the HeineBorel theorem); connectedness; convergence of sequences; Cauchy sequences; continuous and uniformly continuous functions.
Lectures, 3 hours per week; lab/tutorial, 1 hour per week.
Prerequisite(s): MATH 2P03.
MATH 2P08
Ordinary Differential Equations
Linear and nonlinear differential equations. Basic existence and uniqueness theory. Analytical and numerical solution methods; asymptotic behaviour. Qualitative analysis of autonomous systems including periodic cycles and steadystates. Examples of conservative systems and dissipative systems. Modelling and applications of differential equations. Use of Maple.
Lectures, 3 hours per week; lab/tutorial, 1 hour per week.
Prerequisite(s): MATH 1P02, 1P06 or permission of the instructor.
MATH 2P12
Linear Algebra II
General vector spaces. Basis and dimension. Row and column spaces. Rank and nullity; the dimension theorem. Real inner product spaces. Angles and orthogonality. Orthonormal bases. GramSchmidt process. Eigenvalues, eigenvectors and diagonalization. Linear transformations. Applications to differential equations and least square fitting. Use of a computer algebra system.
Lectures, 3 hours per week; lab/tutorial, 1 hour per week.
Prerequisite(s): MATH 1P11 or 1P12.
MATH 2P13
Linear Algebra III  Advanced
Review and further study of vector spaces over arbitrary fields. General linear transformations. Kernel and range. Invertibility. Matrices of linear transformations. Similarity. Isomorphism. Complex vector spaces and inner product spaces. Unitary, normal, symmetric, skewsymmetric and Hermitian operators. Orthogonal projections and the spectral theorem. Bilinear and quadratic forms. Jordan canonical form.
Lectures, 3 hours per week; lab/tutorial, 1 hour per week.
Prerequisite(s): MATH 2P12.
MATH 2P40
Mathematics Integrated with Computers and Applications II
Theory and applications of mathematical modelling and simulation. Topics may include discrete dynamical systems, MonteCarlo methods, stochastic models, the stock market, epidemics, analysis of DNA, chaotic dynamical systems, cellular automata and predatorprey.
Lectures, lab, 4 hours per week.
Prerequisite(s): MATH 1P02 or 1P06; MATH 1P40 or permission of the instructor.
Completion of this course will replace previous assigned grade and credit obtained in MATH 2F40.
MATH 2P52
Principles of Mathematics for Primary and Junior Teachers
Mathematical concepts and ideas in number systems; geometry and probability arising in the Primary and Junior school curriculum.
Lectures, seminar, 4 hours per week.
Restriction: students must have a minimum of 5.0 overall credits.
Note: designed to meet the mathematics admission requirement for the Primary/Junior Preservice program of the Faculty of Education at Brock University. Not open to students holding credit in any grade 12 or university mathematics course.
MATH 2P75
Introductory Financial Mathematics
Mathematical models arising in finance and insurance. Compound interest, the timevalue of money, annuities, mortgages, insurance, measures of risk. Introduction to stocks, bonds and options.
Lectures, lab, 4 hours per week.
Prerequisite(s): one of MATH 1P01, 1P05, 1P97 and 1P98.
MATH 2P81
Probability
Probability, events, algebra of sets, independence, conditional probability, Bayes' theorem; random variables and their univariate, multivariate, marginal and conditional distributions. Expected value of a random variable, the mean, variance and higher moments, moment generating function, Chebyshev's theorem. Some common discrete and continuous distributions: Binomial, Poisson, hypergeometric, normal, uniform and exponential. Use of SAS, Maple or other statistical packages.
Lectures, 3 hours per week; lab/tutorial, 1 hour per week.
Prerequisite(s): MATH 2P03 or permission of the instructor.
Note: may be taken concurrently with MATH 2P03.
MATH 2P82
Mathematical Statistics I
Random sampling, descriptive statistics, Central Limit Theorem, sampling distributions related to normality; point estimation: measurements for estimation performance, methods of moments, maximum likelihood, ordinary/weighted least squares; confidence intervals, testing procedures, and their relation for population means, difference between means, variances, ratio of variances, proportions and difference between proportions.
Lectures, 3 hours per week; lab/tutorial, 1 hour per week.
Prerequisite(s): MATH 2P81.
MATH 2P90
Euclidean and NonEuclidean Geometry I
Development of Euclidean and nonEuclidean geometry from Euclid to the 19th century. Deductive nature of plane Euclidean geometry as an axiomatic system, central role of the parallel postulate and general consideration of axiomatic systems for geometry in general and nonEuclidean geometry in particular. Introduction to transformation geometry. Use of Geometer's Sketchpad.
Lectures, 3 hours per week; lab/tutorial, 1 hour per week.
Prerequisite(s): one MATH credit.
MATH 2P91
Discrete Optimization
Problems and methods in discrete optimization. Linear programming: problem formulation, the simplex method, software, and applications. Network models: assignment problems, maxflow problem. Directed graphs: topological sorting, dynamic programming and path problems, and the travelling salesman's problem. General graphs: Eulerian and Hamiltonian paths and circuits, and matchings.
Lectures, 3 hours per week; lab, 1 hour per week.
Prerequisite(s): MATH 1P11 or 1P12
Completion of this course will replace previous assigned grade and credit obtained in MATH 2P72.
MATH 2P92
Introduction to Combinatorics
Counting, inclusion and exclusion, pigeonhole principle, permutations and combinations, derangements, binomial expansions. Introduction to discrete probability and graph theory, Eulerian graphs, Hamilton Cycles, colouring, planarity, and trees.
Lectures, 3 hours per week; tutorial, 1 hour per week.
Prerequisite(s): two 4U mathematics credits or permission of the instructor.
Completion of this course will replace previous assigned grade and credit obtained in MATH 2P71.
MATH 2P94
Introduction to Network Analysis
Complex networks and their properties, random graphs, network formation models. Webgraph: models, search engines, pageranking algorithms. Community clustering, community structure. Opinion formation, online social networks.
Lectures, 3 hours per week; lab/tutorial, 1 hour per week.
Prerequisite(s): two 4U mathematics credits or permission of the instructor.
Completion of this course will replace previous assigned grade and credit obtained in MATH 2P77.
MATH 2P95
Mathematics and Music
Scales and temperaments, history of the connections between mathematics and music, set theory in atonal music, group theory applied to composition and analysis, enumeration of rhythmic canons, measurement of melodic similarity using metrics, topics in mathematical music theory, applications of statistics to composition and analysis.
Lectures, 3 hours per week; lab/tutorial 1 hour per week.
Prerequisite(s): one of MATH 1P01, 1P02, 1P05, 1P06, 1P97; MATH 1P11 or 1P12 or permission of the instructor.
MATH 2P97
Problem Solving
Solving mathematical problems using insight and creative thinking. Topics may include pigeonhole principle, finite and countable sets, probability theory, congruences and divisibility, polynomials, generating functions, inequalities, limits, geometry, and mathematical games.
Lectures, 3 hours per week; lab/tutorial, 1 hour per week.
Prerequisite(s): MATH 1P01 or 1P05; MATH 1P11 or 1P12; MATH 2P92 (2P71) or 2P81 or permission of instructor.
Note: recommended to students wishing to participate in mathematical problem solving competitions.
MATH 2P98
Applied Statistics
Singlefactor and factorial experimental design methods; nestedfactorial experiments. Simple and multiple linear regression methods, correlation analysis, indicator regression; regression model building and transformations. Contingency tables, binomial tests, nonparametric rank tests. Simple random and stratified sampling techniques, estimation of sample size and related topics. Use of SAS, Maple or other statistical packages.
Lectures, 3 hours per week; lab/tutorial, 1 hour per week.
Prerequisite(s): MATH 1F92 or 1P98.
Note: major credit will not be granted to Mathematics majors.
MATH 3P03
Real Analysis
Approximation of functions by algebraic and trigonometric polynomials (Taylor and Fourier series); Weierstrass approximation theorem; Riemann integral of functions on R^{n}, the RiemannStieltjes integral on R; improper integrals; Fourier transforms.
Lectures, 3 hours per week; tutorial, 1 hour per week.
Prerequisite(s): MATH 2P04.
MATH 3P04
Complex Analysis
Algebra and geometry of complex numbers, complex functions and their derivatives; analytic functions; harmonic functions; complex exponential and trigonometric functions and their inverses; contour integration; Cauchy's theorem and its consequences; Taylor and Laurent series; residues.
Lectures, 3 hours per week; tutorial, 1 hour per week.
Prerequisite(s): MATH 2P03.
MATH 3P06
Vector Calculus and Differential Geometry
Vector fields, vector algebra, vector calculus; gradient, curl and divergence. Polar, cylindrical and spherical coordinates. Green’s, Stokes’ and divergence theorems. Introduction to differential geometry of surfaces. Topics may include differential forms, exterior calculus, frames, GaussBonnet theorem.
Lectures, 3 hours per week; lab/tutorial, 1 hour per week.
Prerequisite(s): MATH 2P03.
MATH 3P08
Advanced Differential Equations
Linear secondorder differential equations and special functions. Introduction to SturmLiouville theory and series expansions by orthogonal functions. Boundary value problems for the heat equation, wave equation and Laplace equation. Green's functions. Emphasis on applications to physical sciences. Use of Maple.
Lectures, 3 hours per week; lab/tutorial, 1 hour per week.
Prerequisite(s): MATH 2P08.
MATH 3P09
Partial Differential Equations
Survey of linear and nonlinear partial differential equations. Analytical solution methods. Existence and uniqueness theorems, variational principles, symmetries, and conservation laws. Emphasis on applications to physical sciences. Use of Maple.
Lectures, 3 hours per week; lab/tutorial, 1 hour per week.
Prerequisite(s): MATH 2P08.
MATH 3P12
Applied Algebra
Group theory with applications. Topics include modular arithmetic, symmetry groups and the dihedral groups, subgroups, cyclic groups, permutation groups, group isomorphism, Burnside's theorem, cosets and Lagrange's theorem, direct products and cryptography, normal subgroups and factor groups.
Lectures, 3 hours per week; lab/tutorial, 1 hour per week.
Prerequisite(s): MATH 2P12 or permission of the instructor.
MATH 3P13
Abstract Algebra
Further topics in group theory: homomorphisms and isomorphism theorems, structure of finite abelian groups. Rings and ideals; polynomial rings; quotient rings. Division rings and fields; field extensions; finite fields; constructability.
Lectures, 3 hours per week; lab/tutorial 1 hour per week.
Prerequisite(s): MATH 3P12.
MATH 3P23
Great Moments in Mathematics I
Triumphs in mathematical thinking emphasizing many cultures up to 1000 AD. Analytical understanding of mathematical problems from the past, referencing the stories and times behind the people who solved them. Matching wits with great mathematicians by solving problems and developing activities related to their discoveries.
Lectures, 4 hours per week.
Prerequisite(s): one MATH credit.
Completion of this course will replace previous assigned grade and credit obtained in MATH 2P93.
MATH 3P40
Mathematics Integrated with Computers and Applications III
Concepts and programming of contemporary models and simulations used in mathematics and sciences.
Lectures, lab, 4 hours per week.
Prerequisite(s): MATH 1P11 or 1P12; MATH 2P03 and COSC 2P95.
Note: students will develop a final project in their own discipline.
Completion of this course will replace previous assigned grade and credit obtained in MATH 2F40.
MATH 3P41
Visual and Interactive Mathematics
Techniques in the visual representation of mathematical data and the interactive presentation of mathematical ideas. Topics may include modelling and simulation, visualization of real world data, interactive learning environments, and interactive websites.
Lectures, lab, 4 hours per week.
Prerequisite(s): MATH 1P02 or 1P06; MATH 1P11 or 1P12; MATH 2P40 or permission of the instructor.
Completion of this course will replace previous assigned grade and credit obtained in MATH 2F40.
MATH 3P51
Applied Mathematics with Maple
Blending mathematical concepts with computations and visualization in Maple. Modelling of physical flows, waves and vibrations. Animation of the heat equation and wave equation; applications including vibrations of rectangular and circular drums, heat flow and diffusion, sound waves. Eigenfunctions and convergence theorems for Fourier eigenfunction series. Approximations, Gibbs phenomena, and asymptotic error analysis using Maple.
Lectures, lab, 4 hours per week.
Prerequisite(s): MATH 2P03 and 2P12; MATH 2P08 or 2P40.
MATH 3P52
Partial Differential Equations in C++
Analytic solution of first order PDEs (characteristic ODE systems and their analytic solution) and the numerical solution of first and second order PDEs (discretization, derivation and comparison of different finite difference equations, stability analysis, boundary conditions), the syntax of the C++ programming language, projects in C++ solving PDEs numerically.
Lectures, lab, 4 hours per week.
Prerequisite(s): MATH 2P03 and 2P12; MATH 2P08 or 2P40.
MATH 3P60
Numerical Methods
Survey of computational methods and algorithms; basic concepts (algorithm, computational cost, convergence, stability); roots of functions; linear systems; numerical integration and differentiation; RungeKutta method for ordinary differential equations; finitedifference method for partial differential equations; fast Fourier transform; Monte Carlo methods. Implementation of numerical algorithms in a scientific programming language.
Lectures, 3 hours per week; lab, 1 hour per week.
Prerequisite(s): MATH 1P02 or 1P06; MATH 1P11 or 1P12; MATH 2P12 or permission of the instructor.
MATH 3P72
Continuous Optimization
Problems and methods in nonlinear optimization. Classical optimization in R^{n}: inequality constraints, Lagrangian, duality, convexity. Nonlinear programming. Search methods for unconstrained optimization. Gradient methods for unconstrained optimization. Constrained optimization. Dynamic programming.
Lectures, 3 hours per week; lab/tutorial, 1 hour per week.
Prerequisite(s): MATH 2P03 and 2P91 (2P72).
*MATH 3P73
Game Theory
(also offered as ECON 3P73)
Representation of Games. Strategies and payoff functions. Static and dynamic games of complete or incomplete information. Equilibria concepts: Nash, Bayesian Nash and Perfect Bayesian Nash equilibria. Convexity concepts, fixed points for correspondences and minimax. Core and Shapley value of a game. Refinements and Applications.
Lectures, 3 hours per week; lab/tutorial, 1 hour per week.
Prerequisite(s): one of MATH 2P91 (2P72), ECON 2P30, 3P91.
MATH 3P75
Theory of Financial Mathematics
Mathematical models arising in modern investment practices. Compound interest, annuities, the timevalue of money, Markowitz portfolio theory, efficient frontier, random walks, Brownian processes, future contracts, European and American options, and putcall parity. Introduction to BlackScholes.
Lectures, lab, 4 hours per week.
Prerequisite(s): MATH 2P82.
MATH 3P81
Experimental Design
Analysis of variance; singlefactor experiments; randomized block designs; Latin squares designs; factorial designs; 2^{f} and 3^{f} factorial experiments; fixed, random and mixed models; nested and nestedfactorial experiments; Taguchi experiments; splitplot and confounded in blocks factorial designs; factorial replication; regression models; computational techniques and use of SAS, Maple or other statistical packages; related topics.
Lectures, 3 hours per week; lab, 1 hour per week.
Prerequisite(s): MATH 2P82.
MATH 3P82
Regression Analysis
Simple and multiple linear regression and correlation, measures of model adequacy, residual analysis, weighted least squares, polynomial regression, indicator variables, variable selection and model building, multicollinearity, time series, selected topics. Use of SAS, Maple or other statistical packages.
Lectures, 3 hours per week; lab/tutorial, 1 hour per week.
Prerequisite(s): MATH 1P11 or 1P12; MATH 2P82 or permission of the instructor.
Note: MATH 3P82 has been approved by VEE (Validation by Education Experience) Administration Committee of the Society of Actuaries. To receive VEE credit, candidates will need a minimum grade of 70 percent.
MATH 3P85
Mathematical Statistics II
Multivariate, marginal and conditional distributions, independence, expectation, covariance, conditional expectation. Functions of random variables, transformation techniques, order statistics. Some special and limiting distributions. Proof of central limit theorem. Point estimation: efficiency, consistency, law of large numbers, sufficiency, RaoBlackwell theorem MVUE. Interval estimation. Hypothesis testing: NeymanPearson theory, likelihood ratio test, Bayesian inference.
Lectures, 3 hours per week; lab/tutorial, 1 hour per week.
Prerequisite(s): MATH 2P82.
MATH 3P86
Applied Multivariate Statistics
Matrix algebra and random vector, sample geometry and random sampling, multivariate normal distribution, inference about mean, comparison of several multivariate means, multivariate linear regression model, principle components, factor analysis, covariance analysis, canonical correlation analysis, discrimination and classification, cluster analysis, computational techniques and use of SAS, Maple or other statistical packages and related topics.
Lectures, 3 hours per week; lab 1 hour per week.
Prerequisite(s): MATH 1P11 or 1P12; MATH 2P82 or permission of the instructor.
MATH 3P91
Mathematics at the Junior/Intermediate/Senior Level
A treatment of mathematics and its teaching and learning at the junior, intermediate and senior levels. A major portion of the course will involve directed projects.
Lectures, seminar, 4 hours per week.
Restriction: open to MATH (Honours) BSc/BEd (Intermediate/Senior) majors, Elementary and Secondary Teaching Mathematics minors with a minimum of 9.0 overall credits.
Prerequisite(s): three MATH credits.
Note: Mathematics Integrated with Computers and Applications with a Concentration in Mathematics Education may register. Contact Department. Students in other programs will require permission of the Department.
MATH 3P94
Symmetry Groups, Matrix Representations and Applications
Symmetry groups, their invariants and matrix representations. Permutation groups, rotation groups. Representations of discrete and continuous groups by linear transformations (matrices). General properties and constructions of group representations. Representations of specific groups. Lie groups and Lie algebras. Applications in various areas of Mathematics and Theoretical Physics.
Prerequisite(s): MATH 2P12 or permission of the instructor.
*MATH 3P95
Introduction to Mathematical Physics
(also offered as PHYS 3P95)
Topics may include Calculus of variations, Lagrangian and Hamiltonian mechanics, field theory, differential forms, vector and polyvector fields, tensor fields, Lie derivative, connection, Riemannian metric, Lie groups and algebras, manifolds, and mathematical ideas of quantum mechanics. Applications to theoretical physics.
Lectures, 3 hours per week; lab/tutorial, 1 hour per week.
Prerequisite(s): MATH 2P03 and 2P08.
Note: MATH 2P12 is recommended.
Completion of this course will replace previous assigned grade and credit obtained in MATH (PHYS) 4P64.
MATH 3P96
Computational Ergodic Theory and Dynamical Systems
Orbits of maps, counting and invariant measures, shift transformation, ergodicity and Birkhoff ergodic theorem, central limit theorem for dynamical systems, Poincare recurrence theorem, entropy and data compression, Lyapunov exponent, invariant subspaces, construction of stable and unstable manifolds for maps, symbolic dynamics and topological entropy.
Lectures, 3 hours per week; lab/tutorial, 1 hour per week.
Prerequisite(s): MATH 2P03, 2P12 and 2P81.
MATH 3P97
Introductory Topology
Introduction to metric and topological spaces; connectedness, completeness, countability axioms, separation properties, covering properties, metrization of topological spaces.
Lectures, 4 hours per week.
Prerequisite(s): MATH 2P04; MATH 2P12 and 2P13 or MATH 3P12 and 3P13.
MATH 3P98
Functional Analysis
Introduction to the theory of normed linear spaces, fixedpoint theorems, StoneWeierstrass approximation on metric spaces and preliminary applications on sequence spaces.
Lectures, 4 hours per week.
Prerequisite(s): MATH 3P97.
MATH 4F90
Honours Project
Independent project in an area of pure or applied mathematics, or mathematics education.
Restriction: open to MATH (single or combined) majors with either a minimum of 14.0 credits, a minimum 70 percent major average and a minimum 60 percent nonmajor average or approval to year 4 (honours) and permission of the instructor.
Note: carried out under the supervision of a faculty member. The supervisor must approve the topic in advance. Presentation of the project is required.
MATH 4P03
Advanced Real Analysis
Lebesgue integration on R^{n}; differentiation and absolute continuity; Fubini's theorem; L^{p} spaces, elementary theory of Banach and Hilbert spaces.
Lectures, 3 hours per week.
Prerequisite(s): MATH 3P03.
MATH 4P06
Special Topics
Advanced topics selected from ring theory, homological algebra, algebraic geometry, number theory, pointset topology, differential geometry, algebraic topology, ordinary or partial differential equations, dynamical systems or any other field of mathematics.
Lectures, 3 hours per week; lab/tutorial, 1 hour per week.
Restriction: permission of the instructor.
*MATH 4P09
Solitons and Nonlinear Wave Equations
(also offered as PHYS 4P09)
Linear and nonlinear travelling waves. Nonlinear evolution equations (Korteweg de Vries, nonlinear Schrodinger, sineGordon). Soliton solutions and their interaction properties. Lax pairs, inverse scattering, zerocurvature equations and Backlund transformations, Hamiltonian structures, and conservation laws.
Lectures, 3 hours per week; lab/tutorial, 1 hour per week.
Prerequisite(s): one of MATH 3P08, 3P09, 3P51, 3P52.
MATH 4P11
Topics in Groups
Advanced topics from group theory. Topics may include isomorphism theorems, Sylow theorems, finite abelian groups, free groups, nilpotent and solvable groups and some simple Lie groups.
Lectures, 3 hours per week; lab/tutorial, 1 hour per week.
Prerequisite(s): MATH 3P12.
MATH 4P13
Topics in Rings and Modules
Advanced topics from ring theory. Topics may include radicals, WedderburnArtin theorems, modules over rings and some special rings.
Lectures, 3 hours per week; lab/tutorial, 1 hour per week.
Prerequisite(s): MATH 3P13.
MATH 4P23
Great Moments in Mathematics II
Development of modern mathematics from medieval times to the present. Fibonacci's calculation revolution, the disputes over cubic equations, Pascal and probability, Fermat's last theorem, Newton and Calculus, Euler and infinite series, set theory and the possibilities of inconsistencies in mathematics.
Lectures, 4 hours per week.
Prerequisite(s): MATH 1P02 or 1P06; MATH 1P11 or 1P12; MATH 3P23 (2P93).
Completion of this course will replace previous assigned grade and credit obtained in MATH 3P93.
#MATH 4P61
Theory of Computation
(also offered as COSC 4P61)
Regular languages and finite state machines: deterministic and nondeterministic machines, Kleene's theorem, the pumping lemma, MyhillNerode Theorem and decidable questions. Contextfree languages: generation by contextfree grammars and acceptance by pushdown automata, pumping lemma, closure properties, decidability. Turing machines: recursively enumerable languages, universal Turing machines, halting problem and other undecidable questions.
Lectures, 3 hours per week.
Restriction: open to COSC (single or combined), BCB, CAST, CNET, GAMP and NEUR Neurocomputing stream majors.
Prerequisite(s): MATH 1P67.
Note: MATH students may take this course with permission of Department.
MATH 4P71
Combinatorics
Review of basic enumeration including distribution problems, inclusionexclusion and generating functions. Polya theory. Finite fields. Orthogonal Latin squares, affine and projective planes. Coding theory and cryptography.
Lectures, 3 hours per week; tutorial, 1 hour per week.
Prerequisite(s): MATH 2P92 (2P71) or permission of the instructor.
MATH 4P81
Sampling Theory
Theory of finite population sampling; simple random sampling; sampling proportion; estimation of sample size; stratified random sampling; optimal allocation of sample sizes; ratio estimators; regression estimators; systematic and cluster sampling; multistage sampling; errors in surveys; computational techniques and use of SAS, Maple or other statistical packages and related topics.
Lectures, 3 hours per week; lab, 1 hour per week.
Prerequisite(s): MATH 3P85 or permission of the instructor.
MATH 4P82
Nonparametric Statistics
Order statistics, rank statistics, methods based on binomial distribution, contingency tables, Kolmogorov Smirnov statistics, nonparametric analysis of variance, nonparametric regression, comparisons with parametric methods. Computational techniques and use of SAS, Maple or other statistical packages.
Lectures, 3 hours per week; lab/tutorial, 1 hour per week.
Prerequisite(s): MATH 3P85 or permission of the instructor.
MATH 4P84
Topics in Stochastic Processes and Models
Topics may include general stochastic processes, Markov chains and processes, renewal process, branching theory, stationary processes, stochastic models, Monte Carlo simulations and related topics. Use of SAS, Maple or other statistical packages.
Lectures, 3 hours per week; lab/tutorial, 1 hour per week.
Prerequisite(s): MATH 3P85 or permission of the instructor.
MATH 4P85
Topics in Advanced Statistics
Topics may include advanced topics in stochastic processes and models, queueing theory, time series analysis, multivariate analysis, Bayesian statistics, advanced methods and theory in statistical inference, and related topics. Use of SAS, Maple or other statistical packages.
Lectures, 3 hours per week; lab/tutorial, 1 hour per week.
Prerequisite(s): MATH 3P85 or permission of the instructor.
MATH 4P90
Euclidean and Non Euclidean Geometry II
Topics in Euclidean and nonEuclidean geometry chosen from the classification of isometries in selected geometries, projective geometry, spherical geometry, finite geometries and axiomatic systems for plane Euclidean geometry.
Lectures, 3 hours per week; lab/tutorial, 1 hour per week.
Prerequisite(s): MATH 1P11 or 1P12; MATH 2P90.
Completion of this course will replace previous assigned grade and credit obtained in MATH 3P90.
MATH 4P92
Topics in Number Theory and Cryptography
Topics may include algebraic number theory, analytic number theory and cryptography.
Lectures, 3 hours per week; lab/tutorial, 1 hour per week.
Restriction: permission of the Department.
Prerequisite(s): MATH 1P11 or 1P12; one of MATH 2P12, 2P81, 2P92 (2P71), 3P12.
*MATH 4P94
Relativity Theory and Black Holes
(also offered as PHYS 4P94)
Review of Special Relativity and Minkowski spacetime. Introduction to General Relativity theory; the spacetime metric, geodesics, light cones, horizons, asymptotic flatness; energymomentum of particles and light rays. Curvature and field equations. Static black holes (Schwarzschild metric), properties of light rays and particle orbits. Rotating black holes (Kerr metric).
Lectures, 3 hours per week; lab/tutorial, 1 hour per week.
Prerequisite(s): MATH 2P03, 2P08, 3P06, PHYS 2P20 and 2P50 or permission of the instructor.
MATH 4P96
Technology and Mathematics Education
Topics may include contemporary research concerning digital technologies, such as computer algebra systems and Web 2.0, in learning and teaching mathematics, design of educational tools using VB.NET, HTML, Geometer's Sketchpad, Maple, Flash, critical appraisal of interactive learning objects in mathematics education.
Lectures, 2 hours per week; lab/tutorial, 2 hours per week.
Prerequisite(s): MATH 1P40 and two and onehalf MATH credits or permission of the instructor.
COOP COURSES
MATH 0N01
Coop Work Placement I
First coop work placement (4 months) with an approved employer.
Restriction: open to MATH and MICA Coop students.
MATH 0N02
Coop Work Placement II
Second coop work placement (4 months) with an approved employer.
Restriction: open to MATH and MICA Coop students.
MATH 0N03
Coop Work Placement III
Third coop work placement (4 months) with an approved employer.
Restriction: open to MATH and MICA Coop students.
MATH 0N04
Coop Work Placement IV
Optional coop work placement (4 months) with an approved employer.
Restriction: open to MATH and MICA Coop students.
MATH 0N05
Coop Work Placement V
Optional coop work placement (4 months) with an approved employer.
Restriction: open to MATH and MICA Coop students.
MATH 2C01
Coop Reflective Learning and Integration I
Provides students with the opportunity to apply what they've learned in their academic studies through careeroriented work experiences at employer sites.
Restriction: open to MATH and MICA Coop students.
Prerequisite(s): SCIE 0N90.
Corequisite(s): MATH 0N01.
Note: students will be required to prepare learning objectives, participate in a site visit, write a work term report and receive a successful work term performance evaluation.
MATH 2C02
Coop Reflective Learning and Integration II
Provides students with the opportunity to apply what they've learned in their academic studies through careeroriented work experiences at employer sites.
Restriction: open to MATH and MICA Coop students.
Prerequisite(s): SCIE 0N90.
Corequisite(s): MATH 0N02.
Note: students will be required to prepare learning objectives, participate in a site visit, write a work term report and receive a successful work term performance evaluation.
MATH 2C03
Coop Reflective Learning and Integration III
Provides students with the opportunity to apply what they've learned in their academic studies through careeroriented work experiences at employer sites.
Restriction: open to MATH and MICA Coop students.
Prerequisite(s): SCIE 0N90.
Corequisite(s): MATH 0N03.
Note: students will be required to prepare learning objectives, participate in a site visit, write a work term report and receive a successful work term performance evaluation.
MATH 2C04
Coop Reflective Learning and Integration IV
Provides students with the opportunity to apply what they've learned in their academic studies through careeroriented work experiences at employer sites.
Restriction: open to MATH and MICA Coop students.
Prerequisite(s): SCIE 0N90.
Corequisite(s): MATH 0N04.
Note: students will be required to prepare learning objectives, participate in a site visit, write a work term report and receive a successful work term performance evaluation.
MATH 2C05
Coop Reflective Learning and Integration V
Provides students with the opportunity to apply what they've learned in their academic studies through careeroriented work experiences at employer sites.
Restriction: open to MATH and MICA Coop students.
Prerequisite(s): SCIE 0N90.
Corequisite(s): MATH 0N05.
Note: students will be required to prepare learning objectives, participate in a site visit, write a work term report and receive a successful work term performance evaluation.

