# Mathematics and Statistics Courses

## Actuarial Mathematics Courses

**Prerequisite/Corequisite**:

The following course must be completed previously: MATH 264 previously or concurrently. Permission of the Department is required.

**Description**: Measurement of interest; annuities and perpetuities; amortization and sinking funds; rates of return; bonds and related securities; life insurance.

**Component(s)**: Lecture

**Notes:**

**Prerequisite/Corequisite**:

The following course must be completed previously: ACTU 256.

**Description**: Measurement of mortality; pure endowments; life insurance; net single premiums; life annuities; net annual premiums; special topics.

**Component(s)**: Lecture

**Notes:**

Students who have received credit for MATH 327 may not take this course for credit.

**Description**: This lab features problem‑solving sessions for the professional examination on financial mathematics of the Society of Actuaries and the Casualty Actuarial Society.

**Component(s)**: Laboratory; Reading

**Notes:**

Students who have received credit for MATH 229 may not take this course for credit.

**Prerequisite/Corequisite**:

The following course must be completed previously: ACTU 257.

**Description**: Net level premium reserves; multiple life functions; multiple decrements, the expense factor; special topics.

**Component(s)**: Lecture

**Notes:**

Students who have received credit for MATH 427 may not take this course for credit.

**Description**: This lab will feature the use of programming languages and software applications.

**Component(s)**: Laboratory

**Notes:**

Students who have received credit for MATH 232 may not take this course for credit.

**Prerequisite/Corequisite**:

The following course must be completed previously: ACTU 357.

**Description**:

Valuation methods; gains and losses; dynamic control; special topics.

**Component(s)**: Lecture

**Prerequisite/Corequisite**:

The following course must be completed previously: ACTU 257.

**Description**: Applications of contingency theory in health insurance, individual and collective risk theory, ruin theory.

**Component(s)**: Lecture

**Notes:**

Students who have received credit for MATH 428 may not take this course for credit.

**Prerequisite/Corequisite**:

The following course must be completed previously: ACTU 457. The following course must be completed previously or concurrently: STAT 349.

**Description**: Credibility approach to inference for heterogeneous data; classical, regression and Bayesian models; illustrations with insurance data.

**Component(s)**: Lecture

**Description**: This lab will be a workshop designed to prepare students for the Actuarial Models examination of the Society of Actuaries and the Casualty Actuarial Society.

**Component(s)**: Laboratory

**Notes:**

Students who have received credit for MATH 429 may not take this course for credit.

**Description**: Specific topics for this courses, and relevant prerequisites, are stated in the Undergraduate Class Schedule.

**Component(s)**: Lecture

**Notes:**

The content varies from term to term and from year to year. Students may re-register for this course, provided the course content has changed. Changes in content are indicated by the title of the course.

**Description**: Specific topics for this courses, and relevant prerequisites, are stated in the Undergraduate Class Schedule.

**Component(s)**: Lecture

**Notes:**

The content varies from term to term and from year to year. Students may re-register for this course, provided the course content has changed. Changes in content are indicated by the title of the course.

## Mathematical and Computational Finance Courses

**Prerequisite/Corequisite**: The following courses must be completed previously: MAST 218 or MATH 264; MAST 221 or STAT 249.

**Description**: This course is an introduction to topics related to quantitative finance. Topics may include: financial derivatives, binomial option pricing models, Black-Scholes option pricing model, derivatives risk management, mean-variance portfolio theory, asset pricing models, investment risks, and behavioral finance.

**Component(s)**: Lecture

**Notes:**

- Students who have received credit for FINA 385 may not take this course for credit.

**Prerequisite/Corequisite**:

The following courses must be completed previously: MATH 264 or MAST 218; STAT 349 or MAST 223; MACF 301 or FINA 385.

**Description**: This course is a rigorous introduction to the theory of mathematical and computational finance. Topics include multi-period binomial model; state prices; change of measure; stopping times; European and American derivative securities; interest-rate models; interest-rate derivatives; hedging; and convergence to the Black-Scholes model.

**Component(s)**: Lecture

**Prerequisite/Corequisite**:

The following courses must be completed previously: MACF 401.

**Description**: This course is a continuation of MACF 401 and focuses on modelling and computational techniques beyond the binomial model. Topics include simulation; Monte- Carlo methods in finance; option valuation; hedging; heat equation; finite difference techniques; stability and convergence; exotic derivatives; risk management; and calibration and parameter estimation.

**Component(s)**: Lecture

**Description**: Specific topics for this course, and relevant prerequisites, are stated in the Undergraduate Class Schedule.

**Component(s)**: Lecture

**Notes:**

The content varies from term to term and from year to year. Students may re-register for this course, provided the course content has changed. Changes in content are indicated by the title of the course.

**Description**: Specific topics for this course, and relevant prerequisites, are stated in the Undergraduate Class Schedule.

**Component(s)**: Reading

**Notes:**

## Mathematics Courses

**Description**: This course is designed to give students the background necessary for MATH 201. Some previous exposure to algebra is assumed. Sets, algebraic techniques, inequalities, graphs of equations.

**Component(s)**: Lecture

**Notes:**

Students in programs leading to the BSc degree or the BA programs in Mathematics and Statistics may not take this course for credit to be applied to their program of concentration.

Students who have received credit or exemption for a course at the level of MATH 201 or above may not take this course for credit.

**Description**: Sets, inequalities, graphs of functions, and relations. Trigonometric, exponential, and logarithmic functions.

**Component(s)**: Lecture; Tutorial

**Notes:**

Students in programs leading to the BSc degree or the BA programs in Mathematics and Statistics may not take this course for credit to be applied to their program of concentration.

Students who have received credit or exemption for MATH 203 or equivalent, or for a course having MATH 203 or equivalent in its sequence of prerequisites, may not take this course for credit.

**Prerequisite/Corequisite**:

The following course must be completed previously: MATH 201 or equivalent.

**Description**: Progressions, combinations, permutations, binomial theorem, mathematical induction, inequalities, polynomials, cartesian and polar forms of complex numbers, conics.

**Component(s)**: Lecture; Tutorial

**Notes:**

Students in programs leading to the BSc degree or the BA programs in Mathematics and Statistics may not take this course for credit to be applied to their program of concentration.

Students who have received credit or an exemption for a course at the level of ACTU 256 or above; MAST 218 or above; MATH 251 or above; STAT 249 or above; or for a course having any of these courses in its sequence of prerequisites, may not take this course for credit.

**Prerequisite/Corequisite**:

The following course must be completed previously: MATH 201 or equivalent.

**Description**: Functional notation. Differentiation of polynomials. The power, product, quotient, and chain rules. Differentiation of elementary functions. Implicit differentiation. Higher derivatives. Maxima and minima. Applications: tangents to plane curves, graphing, related rates. Approximations using the differential. Antiderivatives, definite integrals, area.

**Component(s)**: Lecture; Tutorial

**Notes:**

Students who have received credit or an exemption for a course at the level of ACTU 256 or above; MAST 218 or above; MATH 251 or above; STAT 249 or above; or for a course having any of these courses in its sequence of prerequisites, may not take this course for credit.

**Prerequisite/Corequisite**:

The following course must be completed previously: MATH 201 or equivalent.

**Description**: Algebra and geometry of vectors, dot and cross products, lines and planes. System of equations, operations on matrices, rank, inverse, quadratic form, and rotation of axes.

**Component(s)**: Lecture; Tutorial

**Notes:**

Students who have received credit or an exemption for a course at the level of ACTU 256 or above; MATH 218 or above; MATH 251 or above; STAT 249 or above; or for a course having any of these courses in its sequence of prerequisites, may not take this course for credit.

**Prerequisite/Corequisite**:

The following course must be completed previously: MATH 203 or equivalent.

**Description**: Techniques of integration: substitutions, integration by parts, partial fractions. Improper integrals. Physical applications of the definite integral. Infinite series: tests for convergence. Power series, Taylor’s theorem.

**Component(s)**: Lecture; Tutorial

**Notes:**

Students who have received credit or an exemption for a course at the level of ACTU 256 or above; MAST 218 or above; MATH 251 or above; STAT 249 or above; or for a course having any of these courses in its sequence of prerequisites, may not take this course for credit.

**Description**: Coordinate systems. Radicals and distance formula. Polynomials, factoring, and graphing. Relations and functions. Linear and quadratic functions, equations, and systems. Exponents, exponential and logarithmic functions and equations.

**Component(s)**: Lecture; Tutorial

**Notes:**

Students who have received credit or exemption for a course at the level of MATH 201 or above may not take this course for credit.

**Prerequisite/Corequisite**:

The following course must be completed previously: MATH 206 or equivalent.

**Description**: This course is a prerequisite course for John Molson School of Business students*. Matrices, Gaussian elimination, input‑output analysis, progressions, compound interest, annuities, permutations and combinations, probability, binomial theorem, exponential and logarithmic functions, inequalities, linear programming.

**Component(s)**: Lecture

**Notes:**

**Prerequisite/Corequisite**:

The following course must be completed previously: MATH 206 or equivalent.

**Description**: This course is a prerequisite course for John Molson School of Business students*. Limits; differentiation of rational, exponential, and logarithmic functions; theory of maxima and minima; integration.

**Component(s)**: Lecture

**Notes:**

Students who have received credit or exemption for MATH 203 or equivalent may not take this course for credit.

**Description**: This course deals with a blend of fascinating mathematical themes in various contexts: historical, cultural, and practical. It is intended for non‑mathematics students. One of the aims of the course is to demonstrate the presence of mathematics and mathematical ideas in many aspects of modern life. At a deeper level, it is also intended to explain what mathematics is all about and why some easily stated assertions, such as Fermat’s last theorem, are so difficult to prove. Students who complete the course successfully should have enough understanding and knowledge of fundamental ideas and techniques of mathematics to appreciate its power, its beauty, and its relevance in so many different fields such as architecture, art, commerce, engineering, music, and all of the sciences.

**Component(s)**: Lecture

**Notes:**

Students enrolled in a Mathematics and Statistics program and students who have taken mathematics beyond the pre-calculus level may not take this course for credit.

Students who have received credit for this topic under a MATH 298 number may not take this course for credit.

**Description**: Mathematics is used to unravel the secrets of nature. This course introduces students to the world of mathematical ideas and mathematical thinking. Without being overly technical, that is, without requiring any formal background from the student other than high school mathematics, the course delves into some of the great ideas of mathematics. The topics discussed range from the geometric results of the Ancient Greeks to the notion of infinity to more modern developments.

**Component(s)**: Lecture

**Notes:**

This course is designed as a suitable elective for students following an undergraduate program. It has no formal prerequisites and will not qualify students to enrol for any other Mathematics course, and cannot be used to satisfy a Mathematics requirement in any BSc or BA program.

Students who have received credit for INTE 215 may not take this course for credit.

**Description**: This course is designed as an elective course for students who are not registered in a Mathematics and Statistics program. The particular topic varies from one term to the next and the material is dealt with in a manner appropriate for students who have no background in university‑level mathematics.

**Component(s)**: Lecture

**Notes:**

Students registered in a Mathematics and Statistics program may not take this course for credit.

**Description**: This course is designed as an elective course for students who are not registered in a Mathematics and Statistics program. The particular topic varies from one term to the next and the material is dealt with in a manner appropriate for students who have no background in university‑level mathematics.

**Component(s)**: Reading

**Notes:**

Students registered in a Mathematics and Statistics program may not take this course for credit.

**Prerequisite/Corequisite**:

The following courses must be completed previously: Cegep Mathematics 203 or 201-NYB or MATH 205.

**Description**: First‑order differential equations (first‑ and second‑order chemical reactions). Hermite, Laguerre, and Legendre equations. Solutions by power series. Eigenfunctions and eigenvalues, Sturm‑Liouville theory.

**Component(s)**: Lecture

**Prerequisite/Corequisite**:

The following courses must be completed previously: MATH 204 and MATH 205 or equivalent.

**Description**: Matrices and linear equations; vector spaces; bases, dimension and rank; linear mappings and algebra of linear operators; matrix representation of linear operators; determinants; eigenvalues and eigenvectors; diagonalization.

**Component(s)**: Lecture

**Notes:**

**Prerequisite/Corequisite**:

The following course must be completed previously: MATH 251 or equivalent.

**Description**: Characteristic and minimum polynomials; invariant subspaces, invariant direct sums; nilpotent operators, Jordan canonical form; cyclic subspaces; rational canonical form; bilinear and quadratic forms; inner product; orthogonality; adjoint operators and orthogonal operators.

**Component(s)**: Lecture

**Notes:**

Students who have received credit for MAST 235 may not take this course for credit.

**Prerequisite/Corequisite**:

The following courses must be completed previously: MATH 204 and MATH 205 or equivalent.

**Description**: Introduction to limits and continuity in Rn. Multivariate calculus: the derivative as a linear approximation; matrix representation of derivatives; tangent spaces; gradients, extrema, including Lagrange multipliers, Taylor’s formula and the classification of critical points.

**Component(s)**: Lecture

**Notes:**

Students who have received credit for MAST 218 may not take this course for credit.

**Prerequisite/Corequisite**:

The following course must be completed previously: MATH 264 or equivalent.

**Description**: Implicit functions and the implicit function theorem. Multiple integrals and change of variables. Curves, surfaces and vector calculus.

**Component(s)**: Lecture

**Notes:**

Students who have received credit for MAST 219 may not take this course for credit.

**Prerequisite/Corequisite**:

18 credits in post-Cegep Mathematics.

**Description**: General principles of counting, permutations, combinations, identities, partitions, generating functions, Fibonacci numbers, Stirling numbers, Catalan numbers, principle of inclusion‑exclusion. Graphs, subgraphs, isomorphism, Euler graphs, Hamilton paths and cycles, planar graphs, Kuratowski’s Theorem, trees, colouring, 5‑colour theorem, matching, Hall’s theorem.

**Component(s)**: Lecture; Tutorial

**Notes:**

Students who have received credit for COMP 339 may not take this course for credit.

**Prerequisite/Corequisite**:

The following course must be completed previously: MATH 252.

**Description**: Matrices, linear transformations, determinants, metric concepts, inner‑product spaces, dual spaces, spectral theorem, bilinear and quadratic forms, canonical forms for linear transformation, matrix functions, selected topics.

**Component(s)**: Lecture

**Prerequisite/Corequisite**:

The following course must be completed previously: MATH 265 or equivalent; The following course must be completed previously or concurrently: MATH 252 or equivalent.

**Description**: Error analysis in numerical algorithms; solution of non‑linear equations; fixed point iterations, rate of convergence. Interpolations and approximations, Legendre polynomials. Numerical integration and quadrature.

**Component(s)**: Lecture

**Notes:**

Students who have received credit for MAST 334 may not take this course for credit.

**Prerequisite/Corequisite**:

The following course must be completed previously: MATH 251 or equivalent.

**Description**: Introduction to the theory of optimization; linear programming, simplex method; revised simplex method; transport and assignment problems; integer programming; introduction to graphs and networks.

**Component(s)**: Lecture

**Notes:**

Students who have received credit for MAST 224 or MATH 324 may not take this course for credit.

**Prerequisite/Corequisite**:

Students must complete 12 credits in post-Cegep Mathematics prior to enrolling. If prerequisites are not satisfied, permission of the Department is required.

**Description**:

Mathematical rigour: proofs and counter- examples; quantifiers; number systems; cardinality, decimal representation, density of the rationals, least upper bound. Sequences and series; review of functions, limits and continuity.

**Component(s)**: Lecture

**Prerequisite/Corequisite**: The following course must be completed previously: MATH 364 or equivalent.

**Description**: Connectedness and compactness in the reals. Intermediate value theorem; extreme values for continuous functions. Differential and integral calculus; fundamental theorem of calculus; power series.

**Prerequisite/Corequisite**:

The following course must be completed previously: MATH 265 or equivalent.

**Description**:

Algebra and geometry of complex numbers, linear transformations, analytic functions, Laurent’s series, calculus of residues, special functions.

**Component(s)**: Lecture

**Prerequisite/Corequisite**:

12 credits in post-Cegep Mathematics must be completed prior to enrolling. If prerequisites are not satisfied, permission of the Department is required.

**Description**: Introduction to the ring of integers and the integers modulo N. Groups: definitions and examples; sub‑groups, quotients and homomorphisms (including Lagrange’s theorem, Cayley’s theorem and the isomorphism theorems). Introduction to the Cauchy and Sylow theorems and applications.

**Component(s)**: Lecture

**Prerequisite/Corequisite**:

The following courses must be completed previously: MATH 265, MATH 251 or equivalent.

**Description**: Separable equations, exact equations, integrating factors, force fields, first order linear equations, input‑output concept, second order equations, Sturm‑Liouville problems, applications, series solutions, reduction of order, variation of parameters, nth‑order linear equations with constant coefficients, Laplace transforms, block diagrams, and signal‑flow graphs.

**Component(s)**: Lecture

**Notes:**

Students who have received credit for MAST 330 may not take this course for credit.

**Description**: This lab will demonstrate the use of MAPLE software for Calculus, Linear Algebra, and Statistics.

**Component(s)**: Laboratory

**Notes:**

Students who have received credit for MATH 232 may not take this course for credit.

**Prerequisite/Corequisite**:

18 credits in post-Cegep Mathematics.

**Description**: Number systems, division and factorization, number‑theoretic functions, congruences, algebraic congruences and primitive roots, quadratic residues, diophantine equations.

**Component(s)**: Lecture

**Prerequisite/Corequisite**:

The following courses must be completed previously: MATH 252; MATH 365. If prerequisites are not satisfied, permission of the Department is required.

**Description**: Early mathematics, Greek mathematics, European mathematics in the Middle Ages, the origin and development of analytic geometry and calculus, mathematics as free creation, the generality of mathematics in the 20th century.

**Component(s)**: Lecture

**Prerequisite/Corequisite**:

The following courses must be completed previously: MATH 265, MATH 365, MATH 370 or equivalent.

**Description**: Nature of problems, weak variations, the first variation, Euler’s equation. The second variation, Jacobi’s equation, Legendre’s test, conjugate points. Relative maxima and minima, iso‑perimetrical problems. Integrals with variable end points. Applications to problems in pure and applied mathematics; the principle of least action. Strong variations, the Weierstrass E‑function.

**Component(s)**: Lecture

**Prerequisite/Corequisite**:

The following courses must be completed previously: MATH 265, MATH 365. The following course must be completed previously or concurrently: MATH 464 or equivalent.

**Description**: Lebesque measure and integration on the real line, convergence theorems, absolute continuity, completeness of L2[0,1].

**Component(s)**: Lecture

**Prerequisite/Corequisite**:

The following course must be completed previously: MATH 369 or equivalent.

**Description**: Introduction to rings, ideals, euclidean domains, principal ideal domains and unique factorization domains; polynomial rings.

**Component(s)**: Lecture

**Prerequisite/Corequisite**:

The following course must be completed previously: MATH 470 or equivalent.

**Description**: Rings and modules; structure theorem of modules over principal ideal domains. Noetherian rings and modules (including Hilbert basis theorem for rings and modules). Hilbert’s Nullstellensatz.

**Component(s)**: Lecture

**Notes:**

Students who have received credit for MATH 491 may not take this course for credit.

**Prerequisite/Corequisite**:

The following course must be completed previously: MATH 470 or equivalent.

**Description**:

Elements of field and Galois theory, including straight-edge-and-compass construction and unsolvability of equations of fifth degree by radicals.

**Component(s)**: Lecture

**Notes:**

Students who have received credit for MATH 492 may not take this course for credit.

**Prerequisite/Corequisite**:

The following course must be completed previously: MATH 370 or equivalent.

**Description**: Canonical forms for second order linear equations with constant coefficients, classification of linear second order equations, method of separation of variables, first order PDE’s, method of characteristics. Non‑linear first order equations, complete integrals, Cauchy conditions, Cauchy‑Kowalewski theorem, Fourier and Laplace transforms, Green’s functions, integral representations, introduction to non‑linear PDE’s.

**Component(s)**: Lecture

**Notes:**

Students who have received credit for MATH 371 may not take this course for credit.

**Prerequisite/Corequisite**:

The following courses must be completed previously: MATH 265, MATH 365 or equivalent. If prerequisites are not satisfied, permission of the Department is required.

**Description**: Systems of linear differential equations; fundamental matrices; non‑homogeneous linear systems; non‑linear systems; solutions and trajectories; the phase plane; stability concepts; Liapounov’s second method; periodic solutions and limit cycles; introduction to boundary‑value problems and Sturm‑Liouville theory.

**Component(s)**: Lecture

**Notes:**

Students who have received credit for MATH 373 may not take this course for credit.

**Prerequisite/Corequisite**:

The following courses must be completed previously: MATH 265, MATH 365 or equivalent. If prerequisites are not satisfied, permission of the Department is required.

**Description**: Introduction to discrete dynamical modelling; periodic points; bifurcation; period three points; symbolic dynamics; chaos; transitivity; conjugacy; complex behaviour; introduction to fractals; computer simulations.

**Component(s)**: Lecture

**Notes:**

Students who have received credit for MATH 379 may not take this course for credit.

**Prerequisite/Corequisite**:

The following course must be completed previously: MATH 361. If prerequisites are not satisfied, permission of the Department is required.

**Description**: Classical methods of optimization, Lagrange multipliers, Kuhn‑Tucker conditions; line search methods, quadratic programming, gradient methods, introduction to dynamic programming.

**Component(s)**: Lecture

**Notes:**

Students who have received credit for MATH 436 may not take this course for credit.

**Prerequisite/Corequisite**:

The following course must be completed previously: MATH 365. If prerequisites are not satisfied, permission of the Department is required.

**Description**: Support and separation of convex sets, extreme point characterizations, convex and dual cones, Farkas’ theorem; minimax theorem of Game Theory, Legendre‑Fenchel conjugate, infimal convolution, subgradient calculus; Lagrangians, necessary and sufficient conditions for optimality in constrained minimization; the dual problem.

**Component(s)**: Lecture

**Prerequisite/Corequisite**:

The following courses must be completed previously: MATH 252, MATH 365, MATH 369.

**Description**: This is an introductory course in the geometric topology and differential geometry of surfaces. The topics covered will be selected from curvature, Theorema Egregium, Gauss‑Bonnet theorem, Euler characteristic, cohomology, homotopy groups, the applications of ideas and techniques from geometry and topology in knot or graph theory and map colourings. Notes: Students who have received credit for MATH 380 may not take this course for credit.

**Component(s)**: Lecture

**Notes:**

Students who have received credit for MATH 380 may not take this course for credit.

**Description**: Specific topics for this course, and prerequisites relevant in each case, are stated in the Undergraduate Class Schedule.

**Component(s)**: Lecture

**Notes:**

**Description**: Specific topics for this course, and prerequisites relevant in each case, are stated in the Undergraduate Class Schedule.

**Component(s)**: Reading

**Notes:**

## Mathematics and Statistics Courses

**Prerequisite/Corequisite**:

The following courses must be completed previously: Cegep Mathematics 105 or 201-NYC, 203 or 201- NYB.

**Description**: Functions; maxima and minima. Velocity and acceleration. Iterative solution of equations, parametric equation of curves. Integrals; change of variables, integration by parts, double integrals, numerical integration. Conic sections. Matrices, determinants, eigen‑values, eigenvectors, system of equations. Series and their convergence. Introduction to vector space and complex numbers. Word problems.

**Component(s)**: Lecture

**Notes:**

This course can be counted as an elective towards a 90-credit degree program, but must be taken before any other post-Cegep Mathematics course except for MAST 217, which may be taken concurrently. It must be taken, upon entry, by newly admitted students in the MATH/STAT Major who have less than 70% average in Cegep Mathematics courses.

**Prerequisite/Corequisite**:

The following courses must be completed previously: MATH 203 and MATH 204, or equivalent.

**Description**: This course aims to foster analytical thinking through a problem‑solving approach. Topics include construction of proofs, number systems, ordinality and cardinality, role of examples and counter examples, role of generalizations and specializations; role of symbols, notations and definitions; styles of mathematical discourse.

**Component(s)**: Lecture

**Notes:**

**Prerequisite/Corequisite**:

The following courses must be completed previously: MATH 204 and MATH 205, or equivalent.

**Description**: Vector geometry; lines and planes; curves in Rn; vector functions; vector differential calculus; extrema and Lagrange multipliers. Introduction to multiple integrals and coordinate transformations. Problem solving with a symbolic computation system, e.g. MAPLE.

**Component(s)**: Lecture

**Notes:**

Students who have received credit for MATH 264 may not take this course for credit.

**Prerequisite/Corequisite**:

The following course must be completed previously: MAST 218 or equivalent.

**Description**: Vector integral calculus; line and surface integrals; Green’s, Stokes’ and Gauss’ theorems; coordinate transformations and Jacobians. Power series, applications. Problem solving with a symbolic computation system, e.g. MAPLE.

**Component(s)**: Lecture

**Notes:**

Students who have received credit for MATH 265 may not take this course for credit.

**Prerequisite/Corequisite**:

The following courses must be completed previously: MATH 204 and MATH 205, or equivalent. The following courses must be completed previously or concurrently: MAST 218 or equivalent.

**Description**: Counting rules, discrete probability distributions; random sampling; conditional probability; means and variances, normal and other continuous sampling distributions. Applications. Use of statistical software, e.g. MINITAB.

**Component(s)**: Lecture

**Notes:**

Students enrolled in a Mathematics and Statistics program who take probability/statistics courses in other departments may not receive credit for this course. Please consult the Mathematics and Statistics undergraduate program advisor.

Students who have received credit for STAT 249, COMP 233 or ECON 221 may not take this course for credit.

**Prerequisite/Corequisite**:

The following course must be completed previously: MAST 221 or equivalent. The following course must be completed previously or concurrently: MAST 219 or equivalent.

**Description**: Markov chains; queuing theory; inventory theory; Markov decision processes; applications to reliability.

**Component(s)**: Lecture

**Notes:**

Students enrolled in a Mathematics and Statistics program who take probability/statistics courses in other departments may not receive credit for this course. Please consult the Mathematics and Statistics undergraduate program advisor.

Students who have received credit for STAT 349 may not take this course for credit.

**Prerequisite/Corequisite**:

The following courses must be completed previously: MATH 204 and MATH 205, or equivalent.

**Description**: An introduction to the use of a high‑level mathematical programming language (MAPLE or MATHEMATICA) as a practical aid in doing mathematics. Most classes are given in an interactive way in the computer laboratory. The emphasis is on applications, not on general programming techniques or abstract structures. The aim is to arrive at a sufficient working familiarity with the computer algebra language to permit its regular use in subsequent studies and applications. The commands and online resources are introduced through a review of arithmetic, complex numbers, algebra, Euclidean geometry, trigonometry, coordinate systems and graphing, elementary functions and transformations, series, derivatives, integrals, vectors and matrices. There may be additional topics from domains such as number theory, differential equations, integral transforms, probability and statistics.

**Component(s)**: Lecture

**Notes:**

**Prerequisite/Corequisite**:

The following course must be completed previously: MATH 204 or equivalent.

**Description**: System of linear equations, matrix operations, echelon forms and LU‑factorization; Rn: subspaces, linear dependence, basis, dimension, matrix transformations; eigenvalues and eigenvectors in Rn and applications (e.g. Markov chains, dynamical systems). A symbolic computation system, e.g. MAPLE, is extensively used.

**Component(s)**: Lecture

**Notes:**

**Prerequisite/Corequisite**:

The following course must be complete previously: MAST 234 or equivalent.

**Description**: Rn: Orthogonality, projections, Gram‑Schmidt method and QR‑factorization; applications to least square methods (data fitting, inconsistent systems). Symmetric matrices, principal axes theorem and applications. Special topics (e.g. coding theory, differential equations, error analysis). A symbolic computation system, e.g. MAPLE, is extensively used.

**Component(s)**: Lecture

**Notes:**

Students who have received credit for MATH 252 may not take this course for credit.

**Prerequisite/Corequisite**:

The following course must be completed previously: MATH 205 or equivalent.

**Description**: Introduction to the theory of optimization; linear programming; the simplex method; duality and transportation problem. Introduction to graphs and networks; applications. Use of computing softwares.

**Component(s)**: Lecture

**Notes:**

Students who have received credit for MAST 224 or MATH 361 may not take this course for credit.

**Prerequisite/Corequisite**:

The following courses must be completed previously: MAST 219, and MAST 234 or equivalent.

**Description**: First order differential equations; second order differential equations; Laplace transform methods; mathematical models and numerical methods.

**Component(s)**: Lecture

**Notes:**

Students who have received credit for MATH 370 may not take this course for credit.

**Prerequisite/Corequisite**:

The following courses must be completed previously: MAST 221, MAST 234 (or equivalent). The following course must be completed previously or concurrently: MAST 324.

**Description**: Introduction to mathematical modelling; predator‑prey models in biology, game theory, decision analysis, stability theory; modelling electric circuits.

**Component(s)**: Lecture

**Prerequisite/Corequisite**:

The following courses must be completed previously: MAST 217 or COMP 232 or equivalent; COMP 248 or equivalent; MAST 232. If prerequisites are not satisfied, permission of the Department is required.

**Description**: This course is an application‑oriented introduction to symbolic computation, as it applies to algebra, number theory and combinatorics covering the following topics: capabilities of symbolic systems (e.g. MAPLE), modular methods, arithmetic mod p, arithmetic mod m, matrices mod p, Chinese remainder theorem, polynomial factorization mod p. Applications to coding theory and cryptography. Combinatorial algorithms.

**Component(s)**: Lecture

**Notes:**

Students who have received credit for COMP 367 or COMP 467 may not take this course for credit.

**Prerequisite/Corequisite**:

The following course must be completed previously: MAST 221 or equivalent.

**Description**: Graphical and numerical descriptive methods; Estimation and hypothesis testing; linear regression and correlation; one way ANOVA; contingency and goodness of fit tests. Use of statistical software, e.g. MINITAB.

**Component(s)**: Lecture

**Notes:**

Students enrolled in a Mathematics and Statistics program who take probability/statistics courses in other departments may not receive credit for this course. Please consult the Mathematics and Statistics undergraduate program advisor.

Students who have received credit for STAT 360, BIOL 322, COMM 215 or GEOG 362 may not take this course for credit.

**Prerequisite/Corequisite**:

The following courses must be completed previously: MAST 219 or equivalent; MAST 232 or equivalent. The following course must be completed previously or concurrently: MAST 235.

**Description**: Introduction to computing softwares; numerical solution of non‑linear equations; interpolations and approximations; quadrature and numerical integration. Notes: Students who have received credit for MATH 354 may not take this course for credit.

**Component(s)**: Lecture

**Notes:**

Students who have received credit for MATH 354 may not take this course for credit.

**Prerequisite/Corequisite**:

The following course must be completed previously: MAST 218 or equivalent.

**Description**: Simple and compound interest; annuities; amortization and sinking funds; mortgage schemes; bonds and related securities; capital cost and depletion; spread‑sheet implementation.

**Component(s)**: Lecture

**Notes:**

**Prerequisite/Corequisite**: The following course must be completed previously: MAST 221 or equivalent; MAST 335 or equivalent.

**Description**: This class provides an overview of techniques used by life insurers, pension plans and Property and Casualty insurers to quantify and measure their liabilities. The course is subdivided into two main parts. The first aims at studying life-contingent liabilities such as life insurance and annuities. The second part provides an overview of methods utilized by Property and Casualty insurers to represent their liabilities.

**Component(s)**: Lecture

**Prerequisite/Corequisite**: The following courses must be completed previously: STAT 280; and MAST 333 or STAT 360.

**Description**: This lab course offers hands-on exposure to a broad array of problems and tasks frequently encountered in the data science practice. Examples of topics that are covered may include dataset and table construction, data curation and preparation, data exploration, non-traditional data types and large data sets (big data). Extensive programming duties and data analysis projects are assigned to students.

**Component(s)**: Laboratory

**Description**: Specific topics for this courses, and relevant prerequisites, are stated in the Undergraduate Class Schedule.

**Component(s)**: Lecture

**Notes:**

**Description**: Specific topics for this courses, and relevant prerequisites, are stated in the Undergraduate Class Schedule.

**Component(s)**: Reading

**Notes:**

## Statistics Courses

**Prerequisite/Corequisite**:

The following course must be completed previously or concurrently: MATH 264 or equivalent.

**Description**: Axiomatic approach to probability; combinatorial probability; discrete and continuous distributions; expectation; conditional expectation; random sampling and sampling distributions.

**Component(s)**: Lecture

**Notes:**

Students who have received credit for MAST 221 may take STAT 249 for credit only with prior permission of the Department. Students enrolled in a Mathematics and Statistics program who take probability/statistics courses in other departments may not receive credit for this course. Please consult a Mathematics and Statistics undergraduate program advisor.

Students who have received credit for COMP 233 or ECON 221 may not take this course for credit.

**Prerequisite/Corequisite**:

The following course must be completed previously: STAT 249 or equivalent. The following course must be completed previously or concurrently: MATH 265 or equivalent. If prerequisites are not satisfied, permission of the Department is required.

**Description**: Point and interval estimation; hypothesis testing; Neyman Pearson Lemma and likelihood ratio tests; introduction to correlation and regression.

**Component(s)**: Lecture

**Notes:**

Students enrolled in a Mathematics and Statistics program who take probability/statistics courses in other departments may not receive credit for this course. Please consult a Mathematics and Statistics undergraduate program advisor.

**Prerequisite/Corequisite**:

The following courses must be completed previously: MATH 203, MATH 204 or equivalent.

**Description**: This course is an introduction to statistical programming and computational statistics using the R programming language. Basic programming concepts such as data types, control structures, and algorithms are introduced. The course illustrates data manipulation methods, descriptive analyses, and data visualization tools. The use of linear algebra, statistical simulation, and optimization functions is also illustrated. Applications and examples use real data sets.

**Component(s)**: Lecture

**Notes:**

Students who have received credit for GEOG 264 may not take this course for credit.

**Description**: This lab is associated with STAT 249 and STAT 250 and features problem‑solving sessions for the probability examination of the Society of Actuaries and the Casualty Actuarial Society.

**Component(s)**: Laboratory

**Notes:**

Students who have received credit for MATH 329 may not take this course for credit.

**Prerequisite/Corequisite**:

The following course must be completed previously: STAT 250 or MAST 333.

**Description**: Concepts of statistical quality control; X‑bar, R, P, and C control charts, acceptance sampling, sampling inspection, continuous sampling plans.

**Component(s)**: Lecture

**Notes:**

Students who have received credit for MATH 342 may not take this course for credit.

**Prerequisite/Corequisite**:

The following course must be completed previously: STAT 250 or MAST 333.

**Description**: Basic sampling designs and estimators; simple random sampling, stratified, cluster and systematic sampling. Sampling with unequal probabilities; ratio and regression methods of estimation.

**Component(s)**: Lecture

**Notes:**

Students who have received credit for MATH 343 may not take this course for credit.

**Prerequisite/Corequisite**:

The following course must be completed previously: STAT 250 or MAST 333.

**Description**:

Theory of rank tests, sign test, Mann-Whitney and Wilcoxon one-sample and two-sample tests, Kruskal-Wallis test, goodness of fit tests, Kolmogorov-Smirnov test, Pearson chi-square test, rank correlation and Kendall’s tau.

**Component(s)**: Lecture

**Notes:**

Students who have received credit for MATH 347 may not take this course for credit.

**Prerequisite/Corequisite**:

The following course must be completed previously: STAT 249 or equivalent.

**Description**: Markov decision process and applications. Poisson process, queuing theory, inventory theory; applications.

**Component(s)**: Lecture

**Notes:**

Students who have received credit for MAST 223 may not take this course for credit.

**Prerequisite/Corequisite**:

The following course must be completed previously: STAT 250 or equivalent.

**Description**: Least‑squares estimators and their properties. General linear model with full rank. Analysis of residuals; adequacy of model, lack of fit test, weighted least squares; stepwise regression, Durbin‑Watson statistic; one way and two way analysis of variance.

**Component(s)**: Lecture

**Notes:**

**Prerequisite/Corequisite**:

The following course must be completed previously: MATH 251 or equivalent. The following course must be completed previously or concurrently: STAT 360 or equivalent.

**Description**: Supervised learning methods for regression and classification include linear models, variable selection methods, shrinkage, linear and quadratic discriminant, classification and regression trees, K‑nearest neighbours, support vector machines and neural networks. Unsupervised learning methods include clustering approaches and principal component analysis.

**Component(s)**: Lecture

**Notes:**

Students who have received credit for this topic under a STAT 497 number may not take this course for credit.

**Prerequisite/Corequisite**: The following courses must be completed previously: MAST 218 or MATH 264; MAST 234 or MATH 251; MAST 333 or STAT 360.

**Description**: This course offers an introduction to the theory of prediction with neural networks, demonstrating their construction, estimation, and use in predictive analysis. Various neural network architectures (feedforward, recurrent, convolutional) are presented. Advanced estimation techniques such as regularization and adaptive learning rates are also considered. Several applications of neural networks to common problems faced in practice are finally explored. Students also learn to apply methods seen in class; programming assignments using programming languages such as Python are included.

**Component(s)**: Lecture

**Description**: This lab will use various softwares such as SYSTAT, SAS, SPLUS, MINITAB for data analysis.

**Component(s)**: Laboratory

**Notes:**

Students who have received credit for MATH 232 may not take this course for credit.

**Prerequisite/Corequisite**:

The following courses must be completed previously: STAT 250, STAT 349.

**Description**: Central limit theorems and law of large numbers, convergence of random variables, characteristic function, moment generating function, probability generating functions, random walk and reflection principle.

**Component(s)**: Lecture

**Notes:**

Students who have received credit for MATH 451 may not take this course for credit.

**Prerequisite/Corequisite**: The following course must be completed previously: STAT 250. The following course must be completed previously or concurrently: STAT 349. If prerequisites are not satisfied permission of the Department is required.

**Description**: Derivation of standard sampling distributions; distribution of order-statistics; estimation, properties of estimators; Rao- Cramer inequality, Rao-Blackwell theorem, maximum likelihood and method of moments estimation, Neyman-Pearson theory, likelihood ratio tests and their properties.

**Component(s)**: Lecture

**Notes:**

- Students who have received credit for MATH 454 may not take this course for credit.

**Prerequisite/Corequisite**:

The following course must be completed previously: STAT 449.

**Description**: Poisson processes, continuous time Markov process, queuing models, birth and death processes, renewal theory.

**Component(s)**: Lecture

**Notes:**

Students who have received credit for MATH 353 may not take this course for credit.

**Prerequisite/Corequisite**:

The following course must be completed previously: STAT 360.

**Description**: Time series, forecasting by trend and irregular components (using multiple regression analysis and exponential smoothing); forecasting seasonal time series, additive and multiplicative decomposition methods, Box‑Jenkins methodology, moving average, autoregressive and mixed models.

**Component(s)**: Lecture

**Notes:**

Students who have received credit for MATH 443 may not take this course for credit.

**Prerequisite/Corequisite**:

The following course must be completed previously: STAT 349.

**Description**: Simulation and Monte‑Carlo techniques; selected topics in operations research.

**Component(s)**: Lecture

**Notes:**

Students who have received credit for MATH 437 may not take this course for credit.

**Prerequisite/Corequisite**:

The following courses must be completed previously: MATH 252; STAT 360 or equivalent.

**Description**: Multivariate normal distribution; estimation and testing of hypothesis about mean vector; multiple and partial correlation; MANOVA; principal components analysis.

**Component(s)**: Lecture

**Prerequisite/Corequisite**:

The following course must be completed previously: STAT 360.

**Description**: Construction and analysis of standard designs, including balanced designs; block designs; orthogonal designs; response surface designs.

**Component(s)**: Lecture

**Prerequisite/Corequisite**:

The following course must be completed previously: STAT 360. If prerequisites are not satisfied, permission of the Department is required.

**Description**: Statistical software packages in SAS or R are used for the analysis of real‑life data sets. Topics involve techniques from generalized linear models, model selection, log‑linear models for categorical data, logistic regression, survival models.

**Component(s)**: Lecture

**Description**: Specific topics for this course, and prerequisites relevant in each case, are stated in the Undergraduate Class Schedule.

**Component(s)**: Lecture

**Notes:**

**Description**: Specific topics for this course, and prerequisites relevant in each case, are stated in the Undergraduate Class Schedule.

**Component(s)**: Reading

**Notes:**