# Course offerings

Explore the courses offered to graduate and undergraduate students at the Department of Mathematics.

Note that the term information below is current as of the time when this document was produced. Course availability may vary by term or year. Always confirm your course planning in Aurora or by speaking to a science academic advisor.

Check with your instructor for up-to-date and term-specific information, such as whether the current offering has a website or additional materials. Official course details are available through the Academic Calendar; below is a general reference only and is subject to change.

## On this page

## Undergraduate courses

We provide a comprehensive list of undergraduate courses that students generally encounter throughout their academic studies. These courses range from foundational to specialized and advanced topics without specific year-by-year categorization.

### 2023 - 2024 courses

Below is the latest list of undergraduate courses for the academic years 2023-2024. This selection encompasses the newest curriculum adjustments and offerings. Here are the most recent course updates.

#### MATH 1010 - Applied Finite Mathematics

(Lab Required) For students needing to fill the requirement of a university level mathematics course. Introduces students to modern applications of discrete mathematics. Topics include: mathematics of finance, linear programming, graph theory, and game theory. This is a terminal course and may not be used as a prerequisite for other Mathematics courses. This course cannot be used as part of an Honours, Major, General or Minor program in the mathematical sciences.

Not available to any student already holding a grade of “C” or better in any Mathematics course with the exception of MATH 1020, FA 1020, the former MATH 1190 or MATH 1191.

Not to be taken concurrently with any other Mathematics course with the exception of MATH 1020, FA 1020 or MATH 1191.

No prerequisite.

#### MATH 1018 - Pre-Calculus in Practice

(Lab required) Essential topics in pre-calculus, with an emphasis on applications and elementary mathematical modeling in the sciences. This course is intended primarily for students who do not have credit for Pre-calculus Mathematics 40S (60%) and wish to continue in a subsequent course in Mathematics. May not be used for credit in a Mathematics Honours, Joint Honours, or Major program.

Not available to students who have previously obtained credit (grade of C or better) in

MATH 1200, MATH 1201, MATH 1210, MATH 1211, MATH 1220, MATH 1230, MATH 1240, MATH 1241, MATH 1300, MATH 1301, MATH 1310, MATH 1500, MATH 1501, MATH 1510, the former MATH 1520, or MATH 1524.

#### MATH 1020 - Mathematics in Art

Specific theory, structuring systems, and mathematical methods and principles used in works of art from various historical periods and contexts will be explored in relation to Euclidean and non-Euclidean geometries.

Topics include: linear perspective; shapes, patterns, balance and symmetry; ratio, proportion and harmony; and order, dynamics, and chaos. The course will be one half art and one half mathematics, team-taught by faculty from the School of Art and the Department of Mathematics.

This course is also given in the School of Art as FA 1020. This is a terminal course and may not be used as a prerequisite for other Mathematics courses. T

his course cannot be used as part of an Honours, Major, General or Minor program in the mathematical sciences. Not available to any student already holding a grade of “C” or better in any Mathematics course with the exception of MATH 1010, the former MATH 1190, or MATH 1191.

Not to be taken concurrently with any other Mathematics course with the exception of MATH 1010 or MATH 1191.

No prerequisite.

#### MATH 1080 - Fundamentals of Mathematical Reasoning

(Lab required) Logic, reasoning, problem solving, introduction to set theory, mathematical induction, introduction to number theory, bases of arithmetic and the standard algorithms, working with fractions and functions.

The course is recommended for students intending to become early or middle years school teachers.

This course cannot be used as part of an Honours, Major, General or Minor program in the mathematical sciences.

#### MATH 1090 - Mathematical Reasoning in Euclidean Geometry

(Lab required) Introduction to Euclidean geometry with emphasis on mathematical reasoning. Perimeter, area, volume, triangle congruence, parallel lines and quadrilaterals, similarity, circles, coordinate geometry or transformation geometry.

The course is recommended for students intending to become early or middle years school teachers.

This course cannot be used as part of an Honours, Major, General or Minor program in the mathematical sciences.

#### MATH 1210 - Techniques of Classical and Linear Algebra

(Lab required) To introduce a variety of practical algebraic concepts and skills necessary for the study of calculus and advanced engineering mathematics. The emphasis of this course is in the development of methodology and algebraic skill necessary for successful completion of subsequent engineering mathematics courses.

This course is intended for Engineering and Geophysics students.

May not be held with MATH 1200, MATH 1201, MATH 1211, MATH 1220, MATH 1300, MATH 1301, or MATH 1310.

#### MATH 1220 - Linear Algebra 1

(Lab required) This course is intended for students in mathematically rich disciplines including those planning to enter an Honours or Major program in Mathematics or Statistics.

An introduction to vectors, matrices, systems of linear equations and three-dimensional geometry.

May not be held with MATH 1210, MATH 1211, MATH 1300, MATH 1301, MATH 1310, or the former MATH 1680.

#### MATH 1230 - Differential Calculus

(Lab required) The course is intended for students in mathematically rich disciplines including those planning to enter an Honours or Major program in Mathematics or Statistics. Rigorous treatment of limits, continuity, and differentiation (with epsilon-delta proofs), applications in optimization problems, related rates, l'Hopital's rule, curve sketching, Taylor polynomials.

May not be held with MATH 1500, MATH 1501, MATH 1510, the former MATH 1520, MATH 1524, or the former MATH 1680.

#### MATH 1232 - Integral Calculus

(Lab required) This course is intended for students in mathematically rich disciplines including those planning to enter an Honours or Major program in Mathematics or Statistics.

Integral calculus: theory and techniques of integration, curve sketching (parametric and polar), volume, arc length, surface area and partial derivatives. Sequences and series.

#### MATH 1240 - Elementary Discrete Mathematics

(Lab required) The course is intended for students in mathematically rich disciplines including those planning to enter an Honours or Major program in Mathematics or Statistics.

An introduction to mathematical ideas, proof, techniques, and mathematical writing, explored through topics in discrete mathematics.

#### MATH 1300 - Vector Geometry and Linear Algebra

#### MATH 1500 - Introduction to Calculus

#### MATH 1510 - Applied Calculus 1

(Lab required) Functions and graphs; limits and continuity; differentiation of functions defined explicitly, implicitly and parametrically; applications of derivatives to velocity and acceleration, related rates, maxima and minima; differentials, indefinite and definite integrals, application of integration to area.

Physical applications in this course make it especially suitable for students intending to take programs in engineering.

May not be held with MATH 1230, MATH 1500, MATH 1501, the former MATH 1520, MATH 1524, or the former MATH 1680.

#### MATH 1524 - Mathematics for Management and Social Sciences

(Lab required) Differentiation and integration of functions of one variable. Solving systems of linear equations, introduction to matrices. Emphasizes applications in the areas of management and social sciences. May not be held with MATH 1230, MATH 1500, MATH 1501, MATH 1510, the former MATH 1520, the former MATH 1680, or MATH 1690.

#### MATH 1700 - Calculus 2

#### MATH 1710 - Applied Calculus 2

(Lab required) Applications of integration to volumes, centres of mass, moments of inertia, work and fluid pressure; differentiation of trigonometric, inverse trigonometric, exponential, and logarithmic functions; techniques of integration; polar coordinates.

Physical applications in this course make it especially suitable for students intending to take programs in engineering.

#### MATH 2020 - Algebra 1

(Lab required) The course is intended for students in mathematically rich disciplines. Groups, rings, fields: elementary concepts and examples. May not be held with MATH 2021 or the former MATH 3350.

#### MATH 2030 - Combinatorics 1

(Lab required) Introductory combinatorics, including basic counting, permutations and combinations, enumeration, inclusion-exclusion, pigeonhole principle, solving basic recursions, relations, and derangements.

May not be held MATH 2031 or the former MATH 3400.

#### MATH 2040 - Curves and Surfaces

(Lab required) Curves and surfaces in the plane and space. Intrinsic geometry of curves and surfaces: Serret Frenet frames, first and second fundamental forms, curvature and the Gauss map. Geodesics and parallel transport. Theorema Egregium and Gauss-Bonnet theorems.

#### MATH 2070 - Graph Theory 1

#### MATH 2080 - Introduction to Analysis

(Lab required) The course is intended for students in mathematically rich disciplines. Fundamental properties of the real number system as a complete ordered field, Archimedean property, existence of square roots, density of rational numbers, uncountability of real numbers. Sequences, subsequences, limit theorems, monotonicity, Bolzano-Weierstrass theorem, Cauchy sequences. Rigorous treatment of limits and continuity of functions of one and several variables. Uniform continuity. Applications.

May not be held with MATH 2081 or the former MATH 2202.

#### MATH 2090 - Linear Algebra 2

(Lab required) The course is intended for students in mathematically rich disciplines. Abstract vector spaces, linear transformations, bases and coordinatization, matrix representations, orthogonalization, diagonalization, principal axis theorem.

May not be held with MATH 2091, the former MATH 2300, the former MATH 2301, the former MATH 2350, or the former MATH 2352.

#### MATH 2130 - Engineering Mathematical Analysis

(Lab required) Multivariable differential and integral calculus up to and including multiple integrals in cylindrical and spherical coordinates. This course is intended for students in Engineering and Geophysics programs.

May not be held for credit with MATH 2150, MATH 2151, MATH 2720, MATH 2721, the former MATH 2110, or the former MATH 2750.

#### MATH 2132 - Engineering Mathematical Analysis 2

(Lab required) Infinite series, Taylor and Maclaurin Series; ordinary differential equations including Laplace transforms. This course is intended for students in Engineering and Geophysics programs.

May not be held for credit with the former MATH 2100, the former MATH 2730, the former MATH 2731, the former MATH 2800, or the former MATH 2801.

#### MATH 2150 - Multivariable Calculus

(Lab required) The course is intended for students in mathematically rich disciplines. Parametric curves, arc length and curvature. Functions of several variables. Level curves. Partial derivatives, gradient, divergence and curl. Max/min problems. Double and triple integrals, line and surface integrals of functions and vector fields, and applications. Green's, Stokes, and divergence theorems.

May not be held with MATH 2130, MATH 2151, MATH 2720, MATH 2721, or the former MATH 2750.

#### MATH 2160 - Numerical Analysis 1

(Lab required) Elementary techniques of numerical solution of mathematical problems: solution of equations, linear systems of equations, nonlinear equations; finite and divided differences, interpolation; numerical differentiation and integration.

May not be held with MATH 2120, MATH 2161, the former MATH 2600, or the former MATH 2601.

#### MATH 2170 - Number Theory 1

(Lab required) Prime numbers, unique factorization, linear congruences, Chinese remainder theorem, multiplicative functions, primitive roots and quadratic reciprocity.

May not be held with the former MATH 2500 or the former MATH 2501.

#### MATH 2180 - Real Analysis 1

(Lab required) Introduction to metric spaces including connectedness, compactness and continuity; topics in infinite series of numbers, and sequences and series of functions.

May not be held with the former MATH 3230.

#### MATH 2720 - Multivariable Calculus

(Lab required) Calculus of several variables. This course is intended for students in one of the following programs: Actuarial Mathematics, Data Science, Statistics (Honours or Majors), Physics (Honours or Majors), Geophysics (Honours or Majors), and Physical Geography.

May not be held with MATH 2130, MATH 2150, MATH 2151, MATH 2721, the former MATH 2110, or the former MATH 2750.

#### MATH 2740 - Mathematics of Data Science

(Lab required) This course introduces some of the mathematical tools used in Data Science. Topics include linear algebra: least squares, singular value decomposition, principal components analysis, and graph theory: centrality, social network theory, clustering.

This course can only be used as an elective in an Honours, Major, or Joint Honours program in Mathematics.

#### MATH 3120 - Applied Discrete Mathematics

(Lab Required) Sets, groups, graphs, and Boolean algebra. For Engineering students only. May not be held with COMP 2130.

#### MATH 3132 - Engineering Mathematical Analysis

(Lab required) Vector integral calculus; series of Ordinary differential equations; Fourier series and Partial differential equations. This course is intended for students in Engineering and Geophysics programs.

May not be held with former MATH 3100, the former MATH 3740, or the former MATH 3800.

#### MATH 3320 - Algebra 2

Basic structure theory of groups, integral domains and field extensions. Not to be held with the former MATH 3350.

#### MATH 3322 - Algebra 3

A continuation of topics in Algebra 1 and Algebra 2. More structure theory of groups, general ring theory, fields and field extensions, Galois theory.

#### MATH 3330 - Computational Algebra

An introduction to the use of computers for symbolic mathematical computation, involving solving nonlinear systems and differential equations. A suitable software package will be used to explore applications.

#### MATH 3340 - Complex Analysis 1

Analytic functions, Cauchy's theorem and integral formula, series representation of analytic functions, calculus of residues, Rouche's theorem and the principle of the argument. May not be held with the former MATH 3710.

#### MATH 3360 - Combinatorics 2

Advanced topics in combinatorics, including generating functions, elementary design theory, recurrences, chains and antichains, Polya counting. The course is challenging and is intended for students in mathematically rich disciplines.

May not be held with the former MATH 4400.

#### MATH 3370 - Graph Theory 2

Advanced topics in graph theory, including matchings and coverings, optimization, factors, flows, extremal graph theory, basic Ramsey theory, connectivity, and spectral graph theory. Selected applications in science and operations research are studied.

The course is challenging and is intended for students in mathematically rich disciplines.

May not be held with COMP 4340.

#### MATH 3380 - Introduction to Projective Planes

Affine planes and projective planes, cross ratio, complex projective plane (the great unifier), Desargues' theorem, projective planes over division rings, Pappus' theorem and commutativity, the fundamental theorem for projectivities on a line, introduction of coordinates in a projective plane.

May not be held with the former MATH 2552 or the former MATH 3430.

#### MATH 3390 - Introduction to Topology

Topological spaces, continuity, connectedness, compactness, separation properties. May not be held with the former MATH 3240.

#### MATH 3410 - Introduction to Mathematical Logic

Propositional and first-order logic. Recursion theory. May not be held with the former MATH 4250.

#### MATH 3420 - Numerical Analysis 2

Numerical methods for eigenvalue problems, nonlinear systems, initial-value problems, boundary-value problems; finite difference methods for ordinary and partial differential equations; error analysis. Not to be held with the former MATH 3600 or the former MATH 3601.

#### MATH 3440 - Ordinary Differential Equations

Theory and applications of ordinary differential equations; existence and uniqueness of solutions, linear systems, simple nonlinear systems. This course is theory-based and is intended for students in mathematically rich disciplines. Not to be held with the former MATH 3800.

#### MATH 3460 - Partial Differential Equations

Method of characteristics for first order PDEs, wave, beam, heat and Laplace equations, derivation of PDEs, existence and uniqueness, energy estimates, well-posedness, maximum principles, separation of variables. Not to be held with the former MATH 3810.

#### MATH 3470 - Real Analysis 2

Functions of bounded variation, Riemann-Stietjes integration and Lebesgue integration. Not to be held with the former MATH 3740 or the former MATH 3760.

#### MATH 3472 - Real Analysis 3

Fourier series and Fourier transforms; orthogonal systems and L2 theory, convergence and approximation. Multivariable calculus of maps from Rn to Rm, general chain rule and general notion of derivative, implicit function and inverse function theorems. Not to be held with the former MATH 3740 or the former MATH 3760.

#### MATH 3480 - Set Theory

Axiomatic set theory. Cardinality, well-ordered sets, ordinal numbers, cardinal numbers. Axiom of Choice. Ordinal and cardinal arithmetic. Transfinite induction and recursion. May not be held with the former MATH 3220.

#### MATH 3610 - Introduction to Mathematical Modelling

An introduction to the principles and techniques involved in the design, development, solution, testing and revision of mathematical models of real world phenomena illustrated through the discussion of case studies.

May not be held with the former MATH 3820 or the former MATH 3821.

#### MATH 4240 - Advanced Group Theory

Representation theory of finite groups, presentations of finite and infinite groups, or other topics.

#### MATH 4260 - Abstract Measure Theory

Lebesgue and abstract measures, measurable functions, convergence theorems, absolutely continuous functions, measure spaces, the Radon-Nikodym theorem, Fubini's and Tonnelli's theorems. Not to be held with the former MATH 4750.

#### MATH 4270 - Algebraic Topology

This course will serve as an introduction to elements of homotopy or homology theory. Not to be held with the former MATH 4230.

#### MATH 4280 - Basic Functional Analysis

Banach spaces, Hahn-Banach, open mapping and closed graph theorems, principle of uniform boundedness, linear operators and functionals, dual space, Lp and Lq spaces, weak and weak* topologies, Hilbert spaces and compact operators on a Hilbert space. Not to be held with the former MATH 4750.

#### MATH 4290 - Complex Analysis 2

Conformal mappings, normal families, harmonic and subharmonic functions, Perron's family, Dirichlet problem and Green's function. Not to be held with the former MATH 4710.

#### MATH 4300 - Combinatorial Geometry

Topics in combinatorial geometry, including arrangements of convex bodies, introduction to polytopes, problems in discrete geometry, repeated distances, and geometric graphs.

#### MATH 4320 - Dynamical Systems

Techniques for the qualitative analysis of nonlinear systems of ordinary differential equations and discrete-time systems. Not to be held with the former MATH 4800.

#### MATH 4330 - Fundamentals of Approximation Theory

Theoretical aspects of approximation theory: density, existence, uniqueness; direct and inverse theorems for polynomial approximation.

#### MATH 4340 - Introduction to Algebraic Geometry

This course will introduce students to the basics of affine and projective varieties through a combination of basic theoretical tools and elementary examples.

#### MATH 4360 - Introduction to Differential Geometry

Manifolds and submanifolds; vector and tensor fields, Lie brackets and derivatives. Also at least one of the following: exterior differential calculus and Stokes' theorem, introduction to Riemannian geometry, symplectic geometry and hamiltonian mechanics. Not to be held with the former MATH 4730.

#### MATH 4370 - Linear Algebra and Matrix Analysis

Vector and matrix norms, matrix factorizations, eigenvalues and eigenvectors, theory of non-negative matrices. Applications to differential equations, math biology, numerical analysis, digital image processing, data mining, GPS, Markov chains, graph theory, etc. will be given in this course. Not to be held with the former MATH 4310.

#### MATH 4380 - Mathematical Biology

Formulation, analysis and simulation of suitable models in mathematical biology. Applications will be chosen from fields such as population dynamics, epidemiology, ecology, immunology and cellular dynamics. Not to be held with the former MATH 3530.

#### MATH 4390 - Numerical Approximation Theory

Computational aspects of approximation by interpolatory polynomials, convolutions, artificial neural networks, splines and wavelets.

#### MATH 4440 - Numerical Analysis of Partial Differential Equations

Finite difference method, mathematical theory of Elliptic PDEs, finite element method, iterative solution of linear systems. Emphasis will be on the error analysis (stability, consistency and convergence) of the various methods.

#### MATH 4450 - Number Theory 2

Algebraic number theory, arithmetic geometry and analytic number theory, Diophantine equations, examples such as arithmetic of elliptic curves and Dirichlet L-functions. Not to be held with the former MATH 3450.

#### MATH 4460 - Partial Differential Equations 2

Green's function, Poisson, heat, Schrodinger and wave equations in two and three spatial dimensions, variational characterization of eigenvalues, Fourier and Laplace transforms, introduction to functional analytic techniques in PDEs. Not to be held with the former MATH 4810.

#### MATH 4470 - Rings and Modules

The general theory of (non-commutative) rings, modules and algebras.

#### MATH 4490 - Optimization

This course introduces the theory and practice of optimization. Both unconstrained and constrained problems are considered, as well as continuous and discrete optimization. Topics include linear programming, unconstrained optimization, constrained nonlinear optimization and integer programming. Applications to Statistics and Data Science will be explored. May not be held with the former MATH 3490.

#### MATH 4910 - Project Course in Mathematics 2

A research project by the student in consultation with the department head and an appropriate supervising Faculty member. A written report will be required to be submitted by the end of the term. An oral examination may be required. This course is restricted to students in the fourth year of the Honours or Major program in Mathematics and is not available to Graduate Students.

This course may not be held for credit with MATH 4900.

#### MATH 4920 - Topics in Mathematics 1

Topics of current interest in Mathematics or Applied Mathematics upon the interests and requirements of students and faculty, and will include specialized topics not available in regular course offerings.

## Graduate courses

We offer an extensive list of graduate courses that students typically encounter throughout their advanced academic pursuits. These courses span from foundational to specialized and high-level topics.

### 2023 - 2024 courses

Presented below is the most recent and updated list of graduate courses for the academic years 2023-2024. This compilation reflects the latest curricular changes and offerings for postgraduate students.

#### MATH 7240 – Advanced Group Theory

Representation theory of finite groups, presentations of finite and infinite groups, or other topics. May not be held with MATH 4240.

#### MATH 7260 – Abstract Measure Theory

Lebesgue and abstract measures, measurable functions, convergence theorems, absolutely continuous functions, measure spaces, the Radon-Nikodym theorem, Fubini's and Tonnelli's theorems. May not be held with MATH 4260 and the former MATH 4750.

#### MATH 7270 – Algebraic Topology

This course will serve as an introduction to elements of homotopy or homology theory. May not be held with MATH 4270 and the former MATH 4230.

#### MATH 7280 – Basic Functional Analysis

Banach spaces, Hahn-Banach, open mapping and closed graph theorems, linear operators and functionals, dual space, Hilbert spaces and compact operators. May not be held with MATH 4280 and the former MATH 4750.

#### MATH 7290 – Complex Analysis 2

Conformal mappings, normal families, harmonic and subharmonic functions, Perron's family, Dirichlet problem and Green's function. May not be held with MATH 4290 and the former MATH 4710.

#### MATH 7300 – Combinatorial Geometry

Topics in combinatorial geometry, including arrangements of convex bodies, introduction to polytopes, problems in discrete geometry, repeated distances, and geometric graphs. May not be held with MATH 4300.

#### MATH 7320 – Dynamical Systems

Techniques for the qualitative analysis of nonlinear systems of ordinary differential equations and discrete-time systems. May not be held with MATH 4320 and the former MATH 4800.

#### MATH 7330 – Fundamentals of Approximation Theory

Theoretical aspects of approximation theory: density, existence, uniqueness; direct and inverse theorems for polynomial approximation. May not be held with MATH 4330.

#### MATH 7340 – Introduction to Algebraic Geometry

This course will introduce students to the basics of affine and projective varieties through a combination of basic theoretical tools and elementary examples. May not be held with MATH 4340.

#### MATH 7360 – Introduction to Differential Geometry

Manifolds and submanifolds. One of: exterior calculus and Stokes' theorem, Riemannian or symplectic geometry, and Hamiltonian mechanics. May not be held with MATH 4360 and the former MATH 4730.

#### MATH 7370 – Linear Algebra and Matrix Analysis

Norms, matrix factorizations, eigenvalues/eigenvectors, theory of non-negative matrices. Applications to differential equations, math biology, numerical analysis, graph theory, etc. May not be held with MATH 4370 and the former MATH 4310.

#### MATH 7380 – Mathematical Biology

Formulation, analysis and simulation of models in math biology. Applications will be chosen from population dynamics, epidemiology, ecology, immunology and cellular dynamics. May not be held with MATH 4380 and the former MATH 3530.

#### MATH 7390 – Numerical Approximation Theory

Computational aspects of approximation by interpolatory polynomials, convolutions, artificial neural networks, splines and wavelets. May not be held with MATH 4390.

#### MATH 7440 – Numerical Analysis of Partial Differential Equations

Finite difference method, theory of Elliptic PDEs, finite element method, iterative solution of linear systems. Emphasis will be on the error analysis. May not be held with MATH 4440 and the former MATH 8150.

#### MATH 7450 – Number Theory 2

Algebraic number theory, arithmetic geometry and analytic number theory, Diophantine equations, examples such as arithmetic of elliptic curves and Dirichlet L- functions. May not be held with MATH 4450 and the former MATH 3450.

#### MATH 7460 – Partial Differential Equations 2

Green's function, Poisson, heat, Schrodinger and wave equations, Fourier and Laplace transforms, introduction to functional analytic techniques. May not be held with MATH 4460 and the former MATH 4810.

#### MATH 7470 – Rings and Modules

The general theory of (non-commutative) rings, modules and algebras. May not be held with MATH 4470.

#### MATH 8010 – Advanced Matrix Computations

Matrix computation, decomposition of matrices, iterative methods, sparse matrices, eigenvalue problems.

#### MATH 8110 – Applied Finite Element Analysis

Theory and practice of the finite element method of the solution of partial differential equations and its application to engineering and scientific problems. It includes the h, p and h-p versions, a priori and a posteriori error estimates, adaptability and the structure of finite element software.

#### MATH 8140 – Advanced Numerical Analysis of Differential & Integral Equations

Continuation of MATH 4440/7440. Topics include spectral methods, time dependent equations, multigrid, domain decomposition methods, problems on infinite domains, methods for boundary integral equations, Riemann-Hilbert problems and integrable systems.

#### MATH 8210 – Topics in Combinatorics 1

Topics will be chosen from the areas of algebraic combinatorics, coding theory, design theory, enumerative combinatorics, graph theory,

#### MATH 8310 – Partial Differential Equations 3

Continuation of MATH 4460/7460. Topics include functional analytic techniques for linear and nonlinear partial differential equations, conservation laws, KdV equation, singular perturbation, viscosity solutions.

#### MATH 8410 – Seminar in Applied and Computational Mathematics 1

Designed to accommodate special topics in applied or computational areas of mathematics not included in other course offerings. Students are advised to consult the department as to availability.

#### MATH 8420 – Seminar in Applied and Computational Mathematics 2

Designed to accommodate special topics in applied or computational areas of mathematics not included in other course offerings. Students are advised to consult the department as to availability.

#### MATH 8430 – Seminar in Mathematics 1

Designed to accommodate special topics not included in topics courses.

#### MATH 8440 – Seminar in Mathematics 2

Designed to accommodate special topics not included in topics courses.

#### MATH 8510 – Topics in Algebra 1

Designed to accommodate special topics not included in topics courses.

#### MATH 8520 – Topics in Algebra 2

Topics will be chosen from the areas of associative and non-associative algebras, Boolean algebra and lattice theory, category theory, group theory, ring theory and universal algebra.

#### MATH 8610 – Topics in Analysis 1

Topics will be chosen from the areas of asymptotics, functional analysis, operator theory, real and complex variables, summability theory, topological vector spaces.

#### MATH 8620 – Topics in Analysis 2

Topics will be chosen from the areas of asymptotics, functional analysis, operator theory, real and complex variables, summability theory, topological vector spaces.

#### MATH 8720 – Topics in Foundations 2

Topics will be chosen from the areas of logic, model theory, recursive functions, set theory.

#### MATH 8810 – Topics in Geometry 1

Topics will be chosen from the areas of algebraic curves, combinatorial geometry, Euclidean geometry, fractal geometry, groups and geometrics, projective geometry.

#### MATH 8910 – Topics in Topology 1

Topics will be chosen from the areas of compactifications and related extensions, covering properties, rings of continuous functions, set-theoretic topology, topological groups, uniformities and related structures.

#### MATH 8996 – MSc project 1

This is a project course exclusively for students enrolled in the Course-based MSc program. Students must submit a written report, on the order of 40 to 60 pages, which can be a survey of a topic in mathematics, for instance. This course is taken under the supervision of a faculty member. Course graded pass/fail.

#### MATH 8998 – MSc project 2

This is a project course exclusively for students enrolled in the teaching track of the Course-based MSc program. Students must submit a written report, on the order of 20-30 pages, which can be a survey of a topic in mathematics, for instance. In addition, students are required to teach one undergraduate course. This course is taken under the supervision of a faculty member. Course graded pass/fail.

## Contact us

**Department of Mathematics**

420 Machray Hall, 186 Dysart Road

University of Manitoba

Winnipeg, Manitoba, R3T 2N2 Canada