## Departmental Notes

*Subject Code for Biomathematics*: **BIOM**

*Subject Code for Mathematics*: **MATH**

*Subject Code for Statistics*: **STAT**

*World Wide Web Address*: www.queensu.ca/mathstat

*Head of Department*: Troy Day

*Associate Head of Department*: Andrew D. Lewis

*Department Manager*: Jeananne Vickery

*Departmental Office*: Jeffery Hall, Room 310

*Departmental Telephone*: 613-533-2390

*Departmental Fax*: 613-533-2964

*Chair of Undergraduate Studies*: Peter Taylor

*Undergraduate Office E-Mail Address*: mathstat@queensu.ca

*Coordinator of Graduate Studies*: Mike Roth

*Chair for Engineering Mathematics*: Serdar Yüskel

## Overview

The Department of Mathematics and Statistics offers degree Plans designed to appeal to a broad range of students, including those interested in pure mathematics, applied mathematics, the physical and the biological sciences, teaching, actuarial studies (science), probability, and statistics. Our instructors include leading researchers and many winners of national and university teaching awards. The Department offers various plans in Mathematics and in Statistics, leading to either a BA, BA (Hons.), BSc or BSc (Hons.) degree. A Plan in Mathematics and Engineering is also offered through the Faculty of Engineering and Applied Science. For full details of this program, see the Calendar of the Faculty of Engineering and Applied Science.

## Advice to Students

### Actuarial Science

Students interested in actuarial science should refer to the Actuarial Focus described in the Mathematics Major Plan. Examinations set by the Society of Actuaries are each intended to cover a range of topics in an integrated fashion. The first few of these examinations deal mainly with mathematics and statistics, plus some topics from economics and business. The Queen’s courses listed in the Actuarial Focus will give students background in specific areas needed to prepare students for the Society of Actuaries examinations. Information about the examinations can be obtained from the Society of Actuaries.

### Supporting Statistics Courses for Students in Other Disciplines

Students wishing to use statistics in their area of study should include in their degree plan at least 3.00 units beyond the introductory level.

## Special Study Opportunities

### Applied Mathematics Courses

Some applied mathematics (MTHE) courses designed for students in the Faculty of Engineering and Applied Science may also be open to students in the Faculty of Arts and Science. See the Department for details on registration in these courses.

### Courses of Instruction in the School of Graduate Studies and Research

With the permission of the instructor, the Department and the Registrar of the School of Graduate Studies and Research, undergraduate students may take for credit graduate courses in MATH or STAT for which they have the prerequisite background. This permission will require a minimum GPA of 3.50 in the mathematics and statistics courses of the first three years of their programs. Course descriptions are given in the Calendar of the School of Graduate Studies and Research.

## Faculty

- Selim G. Akl
- Fady Alajaji
- Thomas Barthelmé
- Gunnar Blohm
- Steven D. Blostein
- Oleg I. Bogoyavlenskij
- Francesco Cellarosi
- Bingshu E. Chen
- Troy Day
- Ivan Dimitrov
- Bahman Gharesifard
- Mark F. Green
- Martin Guay
- Wenyu Jiang
- Ernst Kani
- Boris Levit
- Andrew D. Lewis
- Ping Li
- Chunfang Devon Lin
- Tamás Linder
- Brian Ling
- Felicia Magpantay
- Abdol-Reza Mansouri
- Giusy Mazzone
- James McLellan
- James A. Mingo
- Charles Molson
- M. Ram Murty
- Dan Offin
- Charles Paquette
- Paul Y. Peng
- Catherine Pfaff
- Brad Rodgers
- Mike Roth
- Gregory G. Smith
- Yanglei Song
- Glen Takahara
- Peter Taylor
- Claude Tardif
- Dongsheng Tu
- David Wehlau
- Noriko Yui
- Serdar Yüksel
- Imed Zaguia

**Specializations**

**Majors**

### Joint Honours

### Generals/Minors

- Mathematics – General (Arts) – Bachelor of Arts
- Mathematics – General (Science) – Bachelor of Science
- Mathematics – Minor (Arts)
- Mathematics – Minor (Science)
- Statistics – General (Arts) – Bachelor of Arts
- Statistics – General (Science) – Bachelor of Science
- Statistics – Minor (Arts)
- Statistics – Minor (Science)

## Courses

### Biological Mathematics (BIOM)

**BIOM 300**

**Modeling Techniques in Biology**

**Units: 3.00**

Modeling will be presented in the context of biological examples drawn from ecology and evolution, including life history evolution, sexual selection, evolutionary epidemiology and medicine, and ecological interactions. Techniques will be drawn from dynamical systems, probability, optimization, and game theory with emphasis put on how to formulate and analyze models.

LEARNING HOURS 120 (36L;84P)

**Requirements:**Prerequisite (MATH 120 or MATH 121 or MATH 124) and (MATH 110 or MATH 111 or MATH 112).

**Offering Faculty:**Faculty of Arts and Science

### Mathematics (MATH)

**MATH 110**

**Linear Algebra**

**Units: 6.00**

For students intending a medial or major concentration in Mathematics or Statistics. Provides a thorough introduction to linear algebra up to and including eigenvalues and eigenvectors.

LEARNING HOURS 264 (72L;24T;168P).

**Requirements:**Prerequisite None. Exclusion MATH 111; MATH 112; MATH 212. Recommended At least one 4U Mathematics course.

**Offering Faculty:**Faculty of Arts and Science

**MATH 111**

**Linear Algebra**

**Units: 6.00**

An introduction to matrices and linear algebra. Emphasis on applications to biological and economic systems and to computer applications. Topics covered will include systems of equations, eigenvalues, recursions, orthogonality, regression analysis, and geometric transformations.

LEARNING HOURS 240 (72L;168P).

**Requirements:**Prerequisite None. Exclusion MATH 110; MATH 112. Recommended At least one 4U Mathematics course.

**Offering Faculty:**Faculty of Arts and Science

**MATH 112**

**Introduction to Linear Algebra**

**Units: 3.00**

A brief introduction to matrix algebra, linear algebra, and applications. Topics include systems of linear equations, matrix algebra, determinants, the vector spaces Rn and their subspaces, bases, co-ordinates, orthogonalization, linear transformations, eigenvectors, diagonalization of symmetric matrices, quadratic forms.

LEARNING HOURS 120 (36L;84P).

**Requirements:**Prerequisite None. Exclusion MATH 110; MATH 111. Recommended At least one 4U Mathematics course.

**Course Equivalencies:**MATH 110B/112 / APSC 174

**Offering Faculty:**Faculty of Arts and Science

**MATH 120**

**Differential and Integral Calculus**

**Units: 6.00**

A thorough discussion of calculus, including limits, continuity, differentiation, integration, multivariable differential calculus, and sequences and series.

LEARNING HOURS 288 (72L;24T;192P).

**Requirements:**Prerequisite None. Exclusion MATH 121; MATH 123; MATH 124; MATH 126. Recommended MHF4U and MCV4U or 4U AFIC or permission of the Department. Note This course is intended for students who plan to pursue a Major or Joint Honours Plan in Mathematics, Statistics, or Physics.

**Offering Faculty:**Faculty of Arts and Science

**MATH 121**

**Differential and Integral Calculus**

**Units: 6.00**

Differentiation and integration with applications to biology, physics, chemistry, economics, and social sciences; differential equations; multivariable differential calculus.

NOTE Also offered online. Consult Arts and Science Online. Learning Hours may vary.

NOTE Also offered at the Bader International Study Centre. Learning Hours may vary.

LEARNING HOURS 262 (48L;11G;72O).

**Requirements:**Prerequisite None. Exclusion MATH 120; MATH 123; MATH 124; MATH 126. Recommended MHF4U and MCV4U or equivalent, or 4U AFIC, or MATH P06, or permission of the Department. Note This course is intended for students who wish to pursue a Major or Joint Honours Plan in a subject other than Mathematics or Statistics.

**Course Equivalencies:**MATH121; MATH121B;MATH122B

**Offering Faculty:**Faculty of Arts and Science

**MATH 123**

**Differential and Integral Calculus I**

**Units: 3.00**

Differentiation and integration of elementary functions, with applications to physical and social sciences. Topics include limits, related rates, Taylor polynomials, and introductory techniques and applications of integration.

**Requirements:**Prerequisite Permission of the Department. Exclusion MATH 120; MATH 121; MATH 126. Note This course is not intended for students pursuing a MATH or STAT Plan.

**Offering Faculty:**Faculty of Arts and Science

**MATH 124**

**Differential and Integral Calculus II**

**Units: 3.00**

Topics include techniques of integration; differential equations, and multivariable differential calculus.

LEARNING HOURS 126 (36L;12T;78P).

**Requirements:**Prerequisite MATH 123 or permission of the Department. Exclusion MATH 120; MATH 121; MATH 126. Note For students who have credit for a one-term course in calculus. Topics covered are the same as those in the Winter term of MATH 121.

**Course Equivalencies:**APSC172, MATH124

**Offering Faculty:**Faculty of Arts and Science

**MATH 126**

**Differential and Integral Calculus**

**Units: 6.00**

Differentiation and integration of the elementary functions with applications to the social sciences and economics; Taylor polynomials; multivariable differential calculus.

LEARNING HOURS 240 (72L;24T;144P).

**Requirements:**Prerequisite None. Exclusion MATH 120; MATH 121; MATH 123; MATH 124; MATH 126. Note This course is primarily intended for students in the BAH program. Students in the BSCH, BCMPH or BCOM program should not enrol in this course.

**Offering Faculty:**Faculty of Arts and Science

**MATH 210**

**Rings and Fields**

**Units: 3.00**

Integers, polynomials, modular arithmetic, rings, ideals, homomorphisms, quotient rings, division algorithm, greatest common divisors, Euclidean domains, unique factorization, fields, finite fields.

LEARNING HOURS 132 (36L;12T;84P).

**Requirements:**Prerequisite MATH 110 or MATH 111 or (MATH 112 with permission of the Department). Exclusion MATH 211.

**Offering Faculty:**Faculty of Arts and Science

**MATH 211**

**Algebraic Methods**

**Units: 6.00**

Algebraic techniques used in applied mathematics, statistics, computer science and other areas. Polynomials, complex numbers; least squares approximations; discrete linear systems; eigenvalue estimation; non-negative matrices - Markov chains; permutation groups; linear Diophantine equations; introduction to algebraic structures.

LEARNING HOURS 240 (72L;168P).

**Requirements:**Prerequisite (MATH 120 or MATH 121 or MATH 124 or MATH 126) and (MATH 110 or MATH 111 or MATH 112). Exclusion MATH 210.

**Offering Faculty:**Faculty of Arts and Science

**MATH 212**

**Linear Algebra ll**

**Units: 3.00**

Vector spaces, direct sums, linear transformations, eigenvalues, eigenvectors, inner product spaces, self-adjoint operators, positive operators, singular-value decomposition, minimal polynomials, Jordan canonical form, the projection theorem, applications to approximation and optimization problems.

LEARNING HOURS 120 (36L;12T;72P).

**Requirements:**Prerequisite MATH 111 or MATH 112 or MTHE 217. Exclusion MATH 110. Equivalency MATH 312.

**Offering Faculty:**Faculty of Arts and Science

**MATH 221**

**Vector Calculus**

**Units: 3.00**

Double and triple integrals, including polar and spherical coordinates. Parameterized curves and line integrals. Gradient, divergence, and curl. Green's theorem. Parameterized surfaces and surface integrals. Stokes' and Gauss' Theorems.

LEARNING HOURS 120 (36L;84P).

**Requirements:**Prerequisite MATH 120 or MATH 121 or MATH 124 or MATH 126. Exclusion MATH 280. Recommended Some linear algebra.

**Offering Faculty:**Faculty of Arts and Science

**MATH 225**

**Ordinary Differential Equations**

**Units: 3.00**

An introduction to solving ordinary differential equations. Topics include first order differential equations, linear differential equations with constant coefficients, Laplace transforms, and systems of linear equations.

NOTE Some knowledge of linear algebra is assumed.

LEARNING HOURS 120 (36L;12T;72P).

**Requirements:**Prerequisite MATH 120 or MATH 121 or MATH 124 or MATH 126. Exclusion MATH 231. Equivalency MATH 232/3.0.

**Offering Faculty:**Faculty of Arts and Science

**MATH 228**

**Complex Analysis**

**Units: 3.00**

Complex arithmetic, complex plane. Differentiation, analytic functions. Elementary functions. Contour integration, Cauchy's Theorem, and Integral Formula. Taylor and Laurent series, residues with applications to evaluation of integrals.

LEARNING HOURS 120 (36L;12T;72P).

**Requirements:**Prerequisite (MATH 110 or MATH 111 or MATH 112) and (MATH 120 or MATH 121 or MATH 124). Exclusion MATH 326; PHYS 312; PHYS 317.

**Offering Faculty:**Faculty of Arts and Science

**MATH 231**

**Differential Equations**

**Units: 3.00**

An introduction to ordinary differential equations and their applications. Intended for students concentrating in Mathematics or Statistics.

LEARNING HOURS 132 (36L;12T;84P).

**Requirements:**Prerequisite (MATH 110 or MATH 111 or MATH 212) and (MATH 120 or MATH 121 or MATH 124). Exclusion MATH 225; MATH 226; MATH 232.

**Offering Faculty:**Faculty of Arts and Science

**MATH 272**

**Applications of Numerical Methods**

**Units: 3.00**

An introductory course on the use of computers in science. Topics include: solving linear and nonlinear equations, interpolation, integration, and numerical solutions of ordinary differential equations. Extensive use is made of MATLAB, a high level interactive numerical package.

LEARNING HOURS 120 (36L;12Lb;12T;60P).

**Requirements:**Prerequisite (MATH 110 or MATH 111 or MATH 212) and (CISC 101 or CISC 121) Corequisite (MATH 225 or MATH 231 or MATH 232). Exclusion CISC 271; PHYS 213; PHYS 313.

**Offering Faculty:**Faculty of Arts and Science

**MATH 280**

**Advanced Calculus**

**Units: 3.00**

Limits, continuity, C¹ and linear approximations of functions of several variables. Multiple integrals and Jacobians. Line and surface integrals. The theorems of Green, Stokes, and Gauss.

LEARNING HOURS 132 (36L;12T;84P).

**Requirements:**Prerequisite (MATH 110 or MATH 111 or MATH 112) and (MATH 120 or MATH 121 or MATH 124). Exclusion MATH 221.

**Offering Faculty:**Faculty of Arts and Science

**MATH 281**

**Introduction to Real Analysis**

**Units: 3.00**

Taylor's theorem, optimization, implicit and inverse function theorems. Elementary topology of Euclidean spaces. Sequences and series of numbers and functions. Pointwise and uniform convergence. Power series.

LEARNING HOURS 132 (36L;12T;84P).

**Offering Faculty:**Faculty of Arts and Science

**MATH 310**

**Group Theory**

**Units: 3.00**

Permutation groups, matrix groups, abstract groups, subgroups, homomorphisms, cosets, quotient groups, group actions, Sylow theorems.

LEARNING HOURS 132 (36L;96P).

**Requirements:**Prerequisite MATH 210.

**Course Equivalencies:**MATH310, MATH313

**Offering Faculty:**Faculty of Arts and Science

**MATH 311**

**Elementary Number Theory**

**Units: 3.00**

Congruences; Euler's theorem; continued fractions; prime numbers and their distribution; quadratic forms; Pell's equation; quadratic reciprocity; introduction to elliptic curves.

LEARNING HOURS 120 (36L;84P).

**Offering Faculty:**Faculty of Arts and Science

**MATH 314**

**Representations of the Symmetric Group**

**Units: 3.00**

The symmetric group consists of all permutations of a finite set or equivalently all the bijections from the set to itself. This course explores how to map the symmetric group into a collection of invertible matrices. To handle, count, and manipulate these objects, appropriate combinatorial tools are introduced.

LEARNING HOURS 132 (36L;96L).

**Offering Faculty:**Faculty of Arts and Science

**MATH 326**

**Functions of a Complex Variable**

**Units: 3.00**

Complex numbers, analytic functions, harmonic functions, Cauchy's Theorem, Taylor and Laurent series, calculus of residues, Rouche's Theorem.

LEARNING HOURS 120 (36L;12T;72P).

**Offering Faculty:**Faculty of Arts and Science

**MATH 328**

**Real Analysis**

**Units: 3.00**

Metric spaces, topological spaces, compactness, completeness, contraction mappings, sequences and series of functions, uniform convergence, normed linear spaces, Hibert space.

LEARNING HOURS 132 (36L;96P).

**Requirements:**Prerequisite MATH 281.

**Offering Faculty:**Faculty of Arts and Science

**MATH 334**

**Mathematical Methods for Engineering and Physics**

**Units: 3.00**

Banach and Hilbert spaces of continuous- and discrete-time signals; spaces of continuous and not necessarily continuous signals; continuous-discrete Fourier transform; continuous-continuous Fourier transform; discrete-continuous Fourier transform; discrete-discrete Fourier transform; transform inversion using Fourier series and Fourier integrals.

LEARNING HOURS 132 (36L;12T;84P).

**Requirements:**Prerequisite (MATH 110 or MATH 111 or MATH 212) and MATH 281. Exclusion PHYS 312; PHYS 316.

**Offering Faculty:**Faculty of Arts and Science

**MATH 335**

**Mathematics of Engineering Systems**

**Units: 3.00**

Linear input/output systems and their stability. Frequency-domain and time-domain analysis. Continuous and discrete time-modeling. Fourier, Laplace, and Z-transforms. Sampling and the discrete-time Fourier transform. Application to modulation of communications signals, filter design, and digital sampling.

LEARNING HOURS 132 (36L;12T;84P).

**Requirements:**Prerequisite MATH 334 and (MATH 228 or MATH 326). Exclusion PHYS 312. Equivalency MATH 236.

**Course Equivalencies:**MATH236, MATH335

**Offering Faculty:**Faculty of Arts and Science

**MATH 337**

**Stochastic Models in Operations Research**

**Units: 3.00**

Some probability distributions, simulation, Markov chains, queuing theory, dynamic programming, inventory theory.

LEARNING HOURS 120 (36L;84P).

**Offering Faculty:**Faculty of Arts and Science

**MATH 338**

**Fourier Methods for Boundary Value Problems**

**Units: 3.00**

Methods and theory for ordinary and partial differential equations; separation of variables in rectangular and cylindrical coordinate systems; sinusoidal and Bessel orthogonal functions; the wave, diffusion, and Laplace's equation; Sturm-Liouville theory; Fourier transform.

LEARNING HOURS 118 (36L;12T;70P).

**Requirements:**Prerequisite (MATH 221 or MATH 280) and (MATH 225 or MATH 231 or MATH 232) and (MATH 110 or MATH 111). Exclusion PHYS 312; PHYS 316.

**Offering Faculty:**Faculty of Arts and Science

**MATH 339**

**Evolutionary Game Theory**

**Units: 3.00**

This course highlights the usefulness of game theoretical approaches in solving problems in the natural sciences and economics. Basic ideas of game theory, including Nash equilibrium and mixed strategies; stability using approaches developed for the study of dynamical systems, including evolutionary stability and replicator dynamics; the emergence of co-operative behaviour; limitations of applying the theory to human behaviour.

LEARNING HOURS 120 (36L;84P).

**Requirements:**Prerequisite (MATH 120 or MATH 121 or MATH 124) and (MATH 110 or MATH 111 or MATH 112). Equivalency MATH 239. Recommended MATH 110 or MATH 111.

**Course Equivalencies:**MATH239, MATH339

**Offering Faculty:**Faculty of Arts and Science

**MATH 341**

**Differential Geometry**

**Units: 3.00**

Introductory geometry of curves/surfaces: directional/covariant derivative; differential forms; Frenet formulas; congruent curves; surfaces in R3: mappings, topology, intrinsic geometry; manifolds; Gaussian/mean curvature; geodesics, exponential map; Gauss-Bonnet Theorem; conjugate points; constant curvature surfaces.

LEARNING HOURS 132 (36L;96P).

**Offering Faculty:**Faculty of Arts and Science

**MATH 381**

**Mathematics with a Historical Perspective**

**Units: 3.00**

A historical perspective on mathematical ideas focusing on a selection of important and accessible theorems. A project is required.

LEARNING HOURS 120 (36L;12G;72P).

**Requirements:**Prerequisite (MATH 110 or MATH 111 or MATH 212) and (MATH 120 or MATH 121 or MATH 126).

**Offering Faculty:**Faculty of Arts and Science

**MATH 382**

**Mathematical Explorations**

**Units: 3.00**

Elementary mathematical material will be used to explore different ways of discovering results and mastering concepts. Topics will come from number theory, geometry, analysis, probability theory, and linear algebra. Much class time will be used for problem solving and presentations by students.

LEARNING HOURS 120 (36L;84P).

**Requirements:**Prerequisite (MATH 221 or MATH 225 or MATH 231 or MATH 280 or MATH 232/3.0) and (MATH 210 or MATH 211).

**Offering Faculty:**Faculty of Arts and Science

**MATH 384**

**Mathematical Theory of Interest**

**Units: 3.00**

Interest accumulation factors, annuities, amortization, sinking funds, bonds, yield rates, capital budgeting, contingent payments. Students will work mostly on their own; there will be a total of six survey lectures and six tests throughout the term, plus opportunity for individual help.

LEARNING HOURS 102 (12L;84P).

**Offering Faculty:**Faculty of Arts and Science

**MATH 385**

**Life Contingencies**

**Units: 3.00**

Measurement of mortality, life annuities, life insurance, premiums, reserves, cash values, population theory, multi-life functions, multiple-decrement functions. The classroom meetings will be primarily problem-solving sessions, based on assigned readings and problems.

LEARNING HOURS 108 (36L;72P).

**Requirements:**Prerequisite ([MATH 120 or MATH 121 or MATH 124 or MATH 126] and MATH 384 and [STAT 268 or STAT 351]) or permission of the Department.

**Offering Faculty:**Faculty of Arts and Science

**MATH 386**

**Our Number System - an Advanced Perspective**

**Units: 3.00**

Integers and rationals from the natural numbers; completing the rationals to the reals; consequences of completeness for sequences and calculus; extensions beyond rational numbers, real numbers, and complex numbers.

LEARNING HOURS 120 (36L;84P).

**Requirements:**Prerequisite MATH 281.

**Offering Faculty:**Faculty of Arts and Science

**MATH 387**

**Elementary Geometry - an Advanced Perspective**

**Units: 3.00**

In-depth follow-up to high school geometry: striking new results/connections; analysis/proof of new/familiar results from various perspectives; extensions (projective geometry, e.g.); relation of classical unsolvable constructions to modern algebra; models/technology for geometric exploration.

LEARNING HOURS 120 (36L;84P).

**Requirements:**Prerequisite (Level 3 or above and [MATH 221 or MATH 280 or MATH 281]) or permission of the Department.

**Offering Faculty:**Faculty of Arts and Science

**MATH 401**

**Graph Theory**

**Units: 3.00**

An introduction to graph theory, one of the central disciplines of discrete mathematics. Topics include graphs, subgraphs, trees, connectivity, Euler tours, Hamiltonian cycles, matchings, independent sets, cliques, colourings, and planarity. Given jointly with MATH 801.

LEARNING HOURS 120 (36L;84P).

**Requirements:**Prerequisite MATH 210 or MATH 211. Recommended Experience with abstract mathematics and mathematical proof, and a good foundation in linear algebra.

**Offering Faculty:**Faculty of Arts and Science

**MATH 402**

**Enumerative Combinatorics**

**Units: 3.00**

Enumerative combinatorics is concerned with counting the number of elements of a finite set. The techniques covered include inclusion-exclusion, bijective proofs, double-counting arguments, recurrence relations, and generating functions. Given jointly with MATH 802.

LEARNING HOURS 120 (36L;84P).

**Requirements:**Prerequisite MATH 210 or MATH 211. Recommended Experience with abstract mathematics and mathematical proof, and a good foundation in linear algebra.

**Offering Faculty:**Faculty of Arts and Science

**MATH 406**

**Introduction to Coding Theory**

**Units: 3.00**

Construction and properties of finite fields. Polynomials, vector spaces, block codes over finite fields. Hamming distance and other code parameters. Bounds relating code parameters. Cyclic codes and their structure as ideals. Weight distribution. Special codes and their relation to designs and projective planes. Decoding algorithms.

LEARNING HOURS 120 (36L;84P).

**Requirements:**Prerequisite MATH 210.

**Offering Faculty:**Faculty of Arts and Science

**MATH 413**

**Introduction to Algebraic Geometry**

**Units: 3.00**

An introduction to the study of systems of polynomial equations in one or many variables. Topics covered include the Hilbert basis theorem, the Nullstellenstaz, the dictionary between ideals and affine varieties, and projective geometry.

LEARNING HOURS 132 (36L;96P).

**Requirements:**Prerequisite MATH 210.

**Offering Faculty:**Faculty of Arts and Science

**MATH 414**

**Introduction to Galois Theory**

**Units: 3.00**

An introduction to Galois Theory and some of its applications.

LEARNING HOURS 132 (36L;96P).

**Requirements:**Prerequisite MATH 310.

**Offering Faculty:**Faculty of Arts and Science

**MATH 418**

**Number Theory and Cryptography**

**Units: 3.00**

Time estimates for arithmetic and elementary number theory algorithms (division algorithm, Euclidean algorithm, congruences), modular arithmetic, finite fields, quadratic residues. Simple cryptographic systems; public key, RSA. Primality and factoring: pseudoprimes, Pollard's rho-method, index calculus. Elliptic curve cryptography.

LEARNING HOURS 120 (36L;84P).

**Offering Faculty:**Faculty of Arts and Science

**MATH 421**

**Fourier Analysis**

**Units: 3.00**

An exploration of the modern theory of Fourier series: Abel and Cesàro summability; Dirichlet's and Fejér's kernels; term by term differentiation and integration; infinite products; Bernoulli numbers; the Fourier transform; the inversion theorem; convolution of functions; the Plancherel theorem; and the Poisson summation theorem.

LEARNING HOURS 132 (36L;96P).

**Requirements:**Prerequisite MATH 281 or permission of the Department.

**Offering Faculty:**Faculty of Arts and Science

**MATH 427**

**Introduction to Deterministic Dynamical Systems**

**Units: 3.00**

Topics include: global properties of flows and diffeomorphisms, Invariant sets and dynamics, Bifurcations of fixed and periodic points; stability and chaos. Examples will be selected by the instructor. Given jointly with MATH 827.

LEARNING HOURS 120 (36L;84P).

**Offering Faculty:**Faculty of Arts and Science

**MATH 429**

**Functional Analysis and Quantum Mechanics**

**Units: 3.00**

A generalization of linear algebra and calculus to infinite dimensional spaces. Now questions about continuity and completeness become crucial, and algebraic, topological, and analytical arguments need to be combined. We focus mainly on Hilbert spaces and the need for Functional Analysis will be motivated by its application to Quantum Mechanics.

LEARNING HOURS 132 (36L;12G;84P).

**Requirements:**Prerequisite ([MATH 110 or MATH 111 or MATH 112] and MATH 281) or permission of the Department.

**Offering Faculty:**Faculty of Arts and Science

**MATH 433**

**Continuum Mechanics with Applications**

**Units: 3.00**

Continuum mechanics lays the foundations for the study of the mechanical behavior of materials. After a review of vector and tensor analysis, the kinematics of continua are introduced. Conservation of mass, balance of momenta and energy are presented with the constitutive models. Applications are given in elasticity theory and fluid dynamics.

NOTE This is the MATH version of MTHE 433 in FEAS.

LEARNING HOURS 120 (36L;84P).

**Offering Faculty:**Faculty of Arts and Science

**MATH 434**

**Optimization Theory with Applications to Machine Learning**

**Units: 3.00**

Theory of convex sets and functions; separation theorems; primal-duel properties; geometric treatment of optimization problems; algorithmic procedures for solving constrained optimization programs; engineering and economic applications.

**Offering Faculty:**Faculty of Arts and Science

**MATH 436**

**Partial Differential Equations**

**Units: 3.00**

Quasilinear equations: Cauchy problems, method of characteristics; Cauchy-Kovalevski theorem; generalized solutions; wave equation, Huygens' principle, conservation of energy, domain of dependence; Laplace equation, boundary value problems, potential theory, Green's functions; heat equation, maximum principle.

LEARNING HOURS 132 (36L;96P).

**Requirements:**Prerequisite MATH 231 and MATH 280. Recommended MATH 328 or MATH 334 or MATH 338 or PHYS 312.

**Offering Faculty:**Faculty of Arts and Science

**MATH 437**

**Topics in Applied Mathematics**

**Units: 3.00**

Subject matter to vary from year to year. Given jointly with MATH 837.

LEARNING HOURS 132 (36L;96P).

**Requirements:**Prerequisite Permission of the Department.

**Offering Faculty:**Faculty of Arts and Science

**MATH 439**

**Lagrangian Mechanics, Dynamics, and Control**

**Units: 3.00**

Geometric modeling, including configuration space, tangent bundle, kinetic energy, inertia, and force. Euler-Lagrange equations using affine connections. The last part of the course develops one of the following three applications: mechanical systems with nonholonomic constraints; control theory for mechanical systems; equilibria and stability.

LEARNING HOURS 132 (36L;12T;84P).

**Offering Faculty:**Faculty of Arts and Science

**MATH 474**

**Information Theory**

**Units: 3.00**

Topics include: information measures, entropy, mutual information, modeling of information sources, lossless data compression, block encoding, variable-length encoding, Kraft inequality, fundamentals of channel coding, channel capacity, rate-distortion theory, lossy data compression, rate-distortion theorem. Given jointly with MATH 874.

LEARNING HOURS 140 (36L;104P).

**Offering Faculty:**Faculty of Arts and Science

**MATH 477**

**Data Compression and Source Coding**

**Units: 3.00**

Topics include: arithmetic coding, universal lossless coding, Lempel-Ziv and related dictionary based methods, rate distortion theory, scalar and vector quantization, predictive and transform coding, applications to speech and image coding.

LEARNING HOURS 120 (36L;12O;72P).

**Offering Faculty:**Faculty of Arts and Science

**MATH 497**

**Topics in Mathematics IV**

**Units: 3.00**

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

**Requirements:**Note The prerequisite can vary depending on specific course content, please consult the Instructor or visit the Department of Mathematics and Statistics webpage for more information.

**Offering Faculty:**Faculty of Arts and Science

**MATH 498**

**Topics in Mathematics V**

**Units: 3.00**

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

**Requirements:**Note The prerequisite can vary depending on specific course content, please consult the Instructor or visit the Department of Mathematics and Statistics webpage for more information.

**Offering Faculty:**Faculty of Arts and Science

**MATH 499**

**Topics In Mathematics**

**Units: 3.00**

Important topics in mathematics not covered in any other courses.

**Requirements:**Prerequisite Permission of the Department.

**Offering Faculty:**Faculty of Arts and Science

**MATH 594**

**Independent Study**

**Units: 3.00**

**Offering Faculty:**Faculty of Arts and Science

**MATH 595**

**Independent Study**

**Units: 6.00**

**Offering Faculty:**Faculty of Arts and Science

### Statistics (STAT)

**STAT 252**

**Introductory Applied Probability**

**Units: 3.00**

Basics of probability. Counting principle, binomial expansion. Conditional probability and Bayes' Theorem. Random variables, mean and variance. Bernoulli, binomial, geometric, hypergeometric and exponential distributions. Poisson approximation. Distribution, frequency and density functions. Normal distribution and central limit theorem.

NOTE STAT 252 is a new course for STAT Minors and Medials.

LEARNING HOURS 120 (36L;84P).

**Requirements:**Prerequisite MATH 120 or MATH 121 or MATH 126 or MATH 124. Exclusion STAT 268; STAT 351.

**Offering Faculty:**Faculty of Arts and Science

**STAT 263**

**Introduction to Statistics**

**Units: 3.00**

A basic course in statistical methods with the necessary probability included. Topics include probability models, random variables, distributions, estimation, hypothesis testing, elementary nonparametric methods.

NOTE Also offered online, consult Arts and Science Online (Learning Hours may vary).

LEARNING HOURS 120 (36L;84P).

**Requirements:**Prerequisite None. Exclusion BIOL 243; CHEE 209; COMM 162; ECON 250; GPHY 247; KNPE 251; NURS 323; POLS 285; PSYC 202; SOCY 211; STAM 200; STAT 267; STAT 367. One-Way Exclusion May not be taken with or after STAT 269. Recommended An Ontario 4U mathematics course or equivalent. Note This course is not open to Commerce students.

**Offering Faculty:**Faculty of Arts and Science

**STAT 268**

**Statistics and Probability I**

**Units: 3.00**

Basic ideas of probability theory such as random experiments, probabilities, random variables, expected values, independent events, joint distributions, conditional expectations, moment generating functions. Main results of probability theory including Chebyshev's inequality, law of large numbers, central limit theorem. Introduction to statistical computing.

LEARNING HOURS 120 (36L;84P).

**Requirements:**Prerequisite (MATH 120 or MATH 121 or MATH 122 or MATH 124). Corequisite (MATH 221 or MATH 280). Exclusion STAT 252; STAT 351.

**Offering Faculty:**Faculty of Arts and Science

**STAT 269**

**Statistics and Probability II**

**Units: 3.00**

Basic techniques of statistical estimation such as best unbiased estimates, moment estimates, maximum likelihood. Bayesian methods. Hypotheses testing. Classical distributions such as the t-distribution, F-distribution, beta distribution. These methods will be illustrated by simple linear regression. Statistical computing.

LEARNING HOURS 120 (36L;84P).

**Requirements:**Prerequisite (MATH 221 or MATH 280) and (STAT 252 or STAT 268 or STAT 351) or permission of the Department.

**Offering Faculty:**Faculty of Arts and Science

**STAT 351**

**Probability I**

**Units: 3.00**

Probability theory; probability models; random variables; jointly distributed random variables; transformations and generating functions. Inequalities and limit laws. Distributions: binomial, Poisson, exponential, gamma, normal. Applications: elementary stochastic processes, time-to-failure models, binary communication channels with Gaussian noise.

LEARNING HOURS 120 (36L;12T;72P).

**Offering Faculty:**Faculty of Arts and Science

**STAT 353**

**Probability II**

**Units: 3.00**

Intermediate probability theory as a basis for further study in mathematical statistics and stochastic processes; probability measures, expectations; modes of convergence of sequences of random variables; conditional expectations; independent systems of random variables; Gaussian systems; characteristic functions; Law of large numbers, Central limit theory; some notions of dependence.

LEARNING HOURS 120 (36L;84P).

**Requirements:**Prerequisite (STAT 252 or STAT 268 or STAT 351) and (MATH 110 or MATH 111 or MATH 112) and MATH 281.

**Offering Faculty:**Faculty of Arts and Science

**STAT 361**

**Applied Methods in Statistics I**

**Units: 3.00**

A detailed study of simple and multiple linear regression, residuals and model adequacy. The least squares solution for the general linear regression model. Analysis of variance for regression and simple designed experiments; analysis of categorical data.

LEARNING HOURS 120 (36L;84P).

**Requirements:**Prerequisite (MATH 110 or MATH 111 or MATH 112) and (STAT 252 or STAT 268 or STAT 351) and (STAT 263 or STAT 269) or permission of the Department. Exclusion ECON 351.

**Offering Faculty:**Faculty of Arts and Science

**STAT 362**

**R for Data Science**

**Units: 3.00**

Introduction to R, data creation and manipulation, data import and export, scripts and functions, control flow, debugging and profiling, data visualization, statistical inference, Monte Carlo methods, decision trees, support vector machines, neural network, numerical methods.

LEARNING HOURS 118 (36L;12G;70P).

**Requirements:**Prerequisite (STAT 252 or STAT 263 or STAT 268 or STAT 351) and (MATH 110 or MATH 111 or MATH 120 or MATH 121 or MATH 124 or MATH 126 or [MATH 112 and MATH 212]) or permission of the Department.

**Offering Faculty:**Faculty of Arts and Science

**STAT 455**

**Stochastic Processes and Applications**

**Units: 3.00**

Markov chains, birth and death processes, random walk problems, elementary renewal theory, Markov processes, Brownian motion and Poisson processes, queuing theory, branching processes. Given jointly with STAT 855.

LEARNING HOURS 120 (36L;12T;72P).

**Requirements:**Prerequisite STAT 353.

**Offering Faculty:**Faculty of Arts and Science

**STAT 456**

**Bayesian Analysis**

**Units: 3.00**

An introduction to Bayesian analysis and decision theory; elements of decision theory; Bayesian point estimation, set estimation, and hypothesis testing; special priors; computations for Bayesian analysis. Given Jointly with STAT 856.

LEARNING HOURS 120 (36L;84P).

**Requirements:**Prerequisite STAT 463 or permission of the Department.

**Offering Faculty:**Faculty of Arts and Science

**STAT 457**

**Statistical Learning II**

**Units: 3.00**

Introduction to the theory and application of statistical algorithms. Topics include classification, smoothing, model selection, optimization, sampling, supervised and unsupervised learning. Given jointly with STAT 857.

LEARNING HOURS 120 (36L;84P).

**Offering Faculty:**Faculty of Arts and Science

**STAT 462**

**Statistical Learning I**

**Units: 3.00**

A working knowledge of the statistical software R is assumed. Classification; spline and smoothing spline; regularization, ridge regression, and Lasso; model selection; treed-based methods; resampling methods; importance sampling; Markov chain Monte Carlo; Metropolis-Hasting algorithm; Gibbs sampling; optimization. Given jointly with STAT 862.

LEARNING HOURS 120 (36L;84P).

**Offering Faculty:**Faculty of Arts and Science

**STAT 463**

**Fundamentals of Statistical Inference**

**Units: 3.00**

Decision theory and Bayesian inference; principles of optimal statistical procedures; maximum likelihood principle; large sample theory for maximum likelihood estimates; principles of hypotheses testing and the Neyman-Pearson theory; generalized likelihood ratio tests; the chi-square, t, F and other distributions.

LEARNING HOURS 132 (36L;96P).

**Course Equivalencies:**STAT363; STAT463

**Offering Faculty:**Faculty of Arts and Science

**STAT 464**

**Discrete Time Series Analysis**

**Units: 3.00**

Autocorrelation and autocovariance, stationarity; ARIMA models; model identification and forecasting; spectral analysis. Applications to biological, physical and economic data.

LEARNING HOURS 120 (36L;84P).

**Offering Faculty:**Faculty of Arts and Science

**STAT 465**

**Quality Management**

**Units: 3.00**

An overview of the statistical and lean manufacturing tools and techniques used in the measurement and improvement of quality in business, government and industry today. Topics include management and planning tools, Six Sigma approach, statistical process charting, process capability analysis, measurement system analysis and factorial and fractional factorial design of experiments.

LEARNING HOURS 120 (36L;84P).

**Offering Faculty:**Faculty of Arts and Science

**STAT 466**

**Statistical Programming with SAS and Applications**

**Units: 3.00**

Introduction to the basic knowledge in programming, data management, and exploratory data analysis using SAS software: data manipulation and management; output delivery system; advanced text file generation, statistical procedures and data analysis, macro language, structure query language, and SAS applications in clinical trial, administrative financial data.

LEARNING HOURS 120 (36L;84P).

**Offering Faculty:**Faculty of Arts and Science

**STAT 471**

**Sampling and Experimental Design**

**Units: 3.00**

Simple random sampling; Unequal probability sampling; Stratified sampling; Cluster sampling; Multi-stage sampling; Analysis of variance and covariance; Block designs; Fractional factorial designs; Split-plot designs; Response surface methodology; Robust parameter designs for products and process improvement. Offered jointly with STAT 871.

LEARNING HOURS 120 (36L;84P).

**Requirements:**Prerequisite ([STAT 361 or ECON 351] and STAT 463) or permission of the Department. Equivalency STAT 362.

**Offering Faculty:**Faculty of Arts and Science

**STAT 473**

**Generalized Linear Models**

**Units: 3.00**

An introduction to advanced regression methods for binary, categorical, and count data. Major topics include maximum-likelihood method, binomial and Poisson regression, contingency tables, log linear models, and random effect models. The generalized linear models will be discussed both in theory and in applications to real data from a variety of sources. Given jointly with STAT 873.

LEARNING HOURS 120 (36L;84P).

**Offering Faculty:**Faculty of Arts and Science

**STAT 486**

**Survival Analysis**

**Units: 3.00**

Introduces the theory and application of survival analysis: survival distributions and their applications, parametric and nonparametric methods, proportional hazards models, counting process and proportional hazards regression, planning and designing clinical trials. Given jointly with STAT 886.

LEARNING HOURS 120 (36L;84P).

**Requirements:**Prerequisite ([STAT 361 or ECON 351] and STAT 463) or permission of the Department. Recommended STAT 462.

**Offering Faculty:**Faculty of Arts and Science

**STAT 499**

**Topics in Statistics**

**Units: 3.00**

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

**Requirements:**Prerequisite Permission of the Department. Exclusion STAT 505.

**Offering Faculty:**Faculty of Arts and Science

**STAT 506**

**Topics in Statistics II**

**Units: 3.00**

An important topic in probability or statistics not covered in any other course.

LEARNING HOURS 132 (24I;108P).

**Requirements:**Prerequisite Permission of the Department.

**Offering Faculty:**Faculty of Arts and Science