Department of Mathematics and Statistics

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)
RECOMMENDATION    At least one 4U mathematics course.
EXCLUSION    No more than 1 course from MATH 110/6.0; MATH 111/6.0; MATH 112/3.0.
EXCLUSION    No more than 1 course from MATH 110/6.0 and MATH 212/3.0.

Course Webpage: mast.queensu.ca/~dimitrov/MATH110/

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)
RECOMMENDATION    At least one 4U mathematics course.
EXCLUSION   No more than 1 course from MATH 110/6.0; MATH 111/6.0; MATH 112/3.0.

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)
RECOMMENDATION    At least one 4U mathematics course.
EXCLUSION   No more than 1 course from MATH 110/6.0; MATH 111/6.0; MATH 112/3.0.

A thorough discussion of calculus, including limits, continuity, differentiation, integration, multivariable differential calculus, and sequences and series.
NOTE    For students intending to pursue a medial or major plan in Mathematics or Statistics or Physics.
LEARNING HOURS    288 (72L;24T;192P)
RECOMMENDATION    MHF4U and MCV4U or 4U AFIC, or permission of the Department.
EXCLUSION    No more than 6.0 units from MATH 120/6.0; MATH 121/6.0; MATH 122/6.0; MATH 123/3.0; MATH 124/3.0; MATH 126/6.0.

Website: mast.queensu.ca/~math120/

Differentiation and integration with applications to biology, physics, chemistry, economics, and
social sciences; differential equations; multivariable differential calculus.
NOTE    For students intending to pursue a medial or major plan in a subject other than Mathematics or Statistics.
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)
RECOMMENDATION    MHF4U and MCV4U or equivalent, or 4U AFIC, or MATH P06/3.0, or permission of the Department.
EQUIVALENCY    MATH 122/6.0.
EXCLUSION    No more than 6.0 units from MATH 120/6.0; MATH 121/6.0; MATH 122/6.0; MATH 123/3.0; MATH 124/3.0; MATH 126/6.0.

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.
NOTE    Not intended for students pursuing a MATH or STAT plan.
PREREQUISITE    Permission of the Department.
EXCLUSION    No more than 6.0 units from MATH 120/6.0; MATH 121/6.0; MATH 122/6.0; MATH 123/3.0; MATH
124/3.0; MATH 126/6.0.

Topics include techniques of integration, differential equations, and multivariable differential
calculus.
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 121/6.0.
LEARNING HOURS    126 (36L;12T;78P)
PREREQUISITE    MATH 123/3.0 or permission of the Department.
EXCLUSION    No more than 6.0 units from MATH 120/6.0; MATH 121/6.0; MATH 122/6.0; MATH 123/3.0; MATH
124/3.0; MATH 126/6.0.

Differentiation and integration of the elementary functions, with applications to the social
sciences and economics; Taylor polynomials; multivariable differential calculus.
NOTE    Primarily intended for students in the BAH program. Students in the BSCH, BCMPH and BCOM
programs should not enrol in this course.
LEARNING HOURS    240 (72L;24T;144P)
EXCLUSION    No more than 6.0 units from MATH 120/6.0; MATH 121/6.0; MATH 122/6.0; MATH 123/3.0; MATH
124/3.0; MATH 126/6.0.

Integers, polynomials, modular arithmetic, rings, ideals, homomorphisms, quotient rings, division
algorithm, greatest common divisors, Euclidean domains, unique factorization, fields, finite
fields.
NOTE    Students with MATH 112/3.0 may ask for admission with the permissions of the Department.
LEARNING HOURS    132 (36L;12T;84P)
PREREQUISITE    MATH 110/6.0 or MATH 111/6.0 or (MATH 112/3.0 with permission of the Department).
EXCLUSION      No more than 1 course from MATH 210/3.0; MATH 211/6.0; MATH 213/3.0; MATH 217/3.0.

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)
PREREQUISITE    (MATH 120/6.0 or MATH 121/6.0 or MATH 124/3.0 or MATH 126/6.0 or MATH 122/6.0) and
(MATH 110/6.0 or MATH 111/6.0 or MATH 112/3.0).
EXCLUSION       No more than 1 course from MATH 210/3.0; MATH 211/6.0.

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)
PREREQUISITE    MATH 111/6.0 or MATH 112/3.0 or MTHE 217/3.0.
EXCLUSION    No more than 1 course from MATH 110/6.0 and MATH 212/3.0.
EQUIVALENCY    MATH 312/3.0.

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)
RECOMMENDATION    Some linear algebra.
PREREQUISITE      MATH 120/6.0 or MATH 121/6.0 or MATH 122/6.0 or MATH 124/3.0 or MATH 126/6.0.
EXCLUSION       No more than 3.0 units from MATH 221/3.0; MATH 227/3.0; MATH 280/3.0.

An introduction to solving ordinary differential equations. Topics include first order differential
equations, linear differential equations with constant coefficients, and applications, Laplace
transforms, systems of linear equations.
NOTE       Some knowledge of linear algebra is assumed.
NOTE    Also offered online. Consult Arts and Science Online.
LEARNING HOURS    may vary.
LEARNING HOURS    120 (36L;12T;72P)
EQUIVALENCY      MATH 232/3.0.
PREREQUISITE      MATH 120/6.0 or MATH 121/6.0 or MATH 124/3.0 or MATH 126/6.0 or MATH 122/6.0.
EXCLUSION      No more than 3 units from MATH 225/3.0; MATH 226/3.0; MATH 231/3.0; MATH 235/3.0; MATH 237/3.0; MATH 232/3.0.

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)
PREREQUISITE    (MATH 110/6.0 or MATH 111/6.0 or MATH 112/3.0) and (MATH 120/6.0 or MATH 121/6.0 or
MATH 122/6.0 or MATH 124/3.0).
EXCLUSION      No more than 1 course from MATH 228/3.0; MATH 326/3.0; PHYS 317/3.0; PHYS 312/6.0.

An introduction to ordinary differential equations and their applications. Intended for students
concentrating in Mathematics or Statistics.
LEARNING HOURS    132 (36L;12T;84P)
PREREQUISITE    (MATH 110/6.0 or MATH 111/6.0) and (MATH 120/6.0 or MATH 121/6.0 or MATH 122/6.0 or
MATH 124/3.0).
EXCLUSION      No more than 1 course from MATH 225/3.0; MATH 226/3.0; MATH 231/3.0; MATH 235/3.0; MATH
237/3.0;
MATH 232/3.0.

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)
PREREQUISITE    (MATH 110/6.0 or MATH 111/6.0 or MATH 212/3.0) and (CISC 101/3.0 or CISC 121/3.0).
COREQUISITE    MATH 225/3.0 or MATH 232/3.0.
EXCLUSION       No more than 3.0 units from CISC 271/3.0; MATH 272/3.0; PHYS 313/3.0.

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)
PREREQUISITE    (MATH 110/6.0 or MATH 111/6.0 or MATH 112/3.0) and (MATH 120/6.0 or MATH 121/6.0 or
MATH 122/6.0 or MATH 124/3.0).
EXCLUSION       No more than 3.0 units from MATH 221/3.0; MATH 227/3.0; MATH 280/3.0.

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)
PREREQUISITE    MATH 120/6.0 or MATH 121/6.0 or MATH 122/6.0 or MATH 124/3.0.

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)
RECOMMENDATION    MATH 110/6.0 or MATH 111/6.0.
PREREQUISITE    MATH 120/6.0 or MATH 121/6.0 or MATH 122/6.0 or MATH 124/3.0.

An exploration of the way in which the patterns that we observe in the world about us can be
described by language and understood with the tools of analysis and synthesis. A carefully selected
sequence of poems and mathematical problems will be examined in a discussion format, and students
will be expected to examine similar examples on their own.
NOTE      Administered by the Departments of English Language and Literature and Mathematics and
Statistics.
PREREQUISITE    Level 3 or above.

Permutation groups, matrix groups, abstract groups, subgroups, homomorphisms, cosets, quotient
groups, group actions, Sylow theorems.
LEARNING HOURS    132 (36L;96P)
PREREQUISITE    MATH 210/3.0 or MATH 217/3.0.

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)
PREREQUISITE    MATH 210/3.0 or MATH 211/6.0.

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;96P)
PREREQUISITE    MATH 210/3.0 or MATH 211/6.0.

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)
PREREQUISITE    MATH 281/3.0.
EXCLUSION      No more than 1 course from MATH 228/3.0; MATH 326/3.0; PHYS 317/3.0; PHYS 312/6.0.

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)
PREREQUISITE    MATH 281/3.0.

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)
PREREQUISITE      (MATH 110/6.0 or MATH 111/6.0 or MATH 212/3.0) and MATH 281/3.0.
EXCLUSION      No more than 1 course from MATH 334/3.0; PHYS 316/3.0; PHYS 312/6.0.

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)
PREREQUISITE    MATH 334/3.0 and (MATH 326/3.0 or MATH 228/3.0).
EXCLUSION    No more than 1 course from MATH 236/3.0; MATH 335/3.0; PHYS 312/6.0. EQUIVALENCY    MATH
236/3.0.

Some probability distributions, simulation, Markov chains, queuing theory, dynamic programming,
inventory theory.
LEARNING HOURS    120 (36L;84P)
PREREQUISITE    (STAT 268/3.0 or STAT 351/3.0) and (MATH 110/6.0 or MATH 111/6.0 or MATH 112/3.0) and
(MATH 120/6.0 or MATH 121/6.0 or MATH 122/6.0 or MATH 124/3.0).

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)
PREREQUISITE    (MATH 221/3.0 or MATH 280/3.0) and (MATH 231/3.0 or MATH 232/3.0) and (MATH 110/6.0 or
MATH 111/6.0).
EXCLUSION    No more than 1 course from MATH 338/3.0; PHYS 316/3.0; PHYS 312/6.0. EXCLUSION      No more
than 1 course from MATH 338/3.0; PHYS 317/3.0; PHYS 312/6.0.

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)
RECOMMENDATION    MATH 110/6.0 or MATH 111/6.0.
PREREQUISITE      MATH 120/6.0 or MATH 121/6.0 or MATH 122/6.0 or MATH 124/3.0.

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)
PREREQUISITE    MATH 110/6.0 and MATH 280/3.0.

A historical perspective on mathematical ideas focussing on a selection of important and accessible
theorems. A project is required.
LEARNING HOURS    120 (36L;12G;72P)
PREREQUISITE    (MATH 110/6.0 or MATH 111/6.0 or MATH 212/3.0) and (MATH 120/6.0 or MATH 121/6.0 or MATH 126/6.0 or MATH 122/6.0).

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)
PREREQUISITE    (MATH 221/3.0 or MATH 225/3.0 or MATH 231/3.0 or MATH 280/3.0 or MATH 232/3.0) and (MATH 210/3.0 or MATH 211/6.0).

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)
PREREQUISITE      Level 3 and (MATH 120/6.0 or MATH 121/6.0 or MATH 122/6.0 or MATH 124/3.0 or MATH 126/6.0).

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)
PREREQUISITE      (MATH 120/6.0 or MATH 121/6.0 or MATH 122/6.0 or MATH 124/3.0 or MATH 126/6.0) and MATH 384/3.0 and (STAT 268/3.0 or STAT 351/3.0), or permission of the Department.

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)
PREREQUISITE    MATH 281/3.0.

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)
PREREQUISITE      Level 3 and (MATH 221/3.0 or MATH 280/3.0 or MATH 281/3.0), or permission of the Department.

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 801/3.0.
LEARNING HOURS    120 (36L;84P)
RECOMMENDATION    Experience with abstract mathematics and mathematical proof, and a good foundation
in linear algebra.
PREREQUISITE     MATH 210/3.0 or MATH 211/6.0 or MATH 217/3.0.

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 802/3.0.
LEARNING HOURS    120 (36L;84P)
RECOMMENDATION    Experience with abstract mathematics and mathematical proof, and a good foundation in linear algebra.
PREREQUISITE     MATH 210/3.0 or MATH 211/6.0 or MATH 217/3.0.

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)
PREREQUISITE    MATH 210/3.0.

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)
PREREQUISITE    MATH 210/3.0.

An introduction to Galois Theory and some of its applications.
LEARNING HOURS    132 (36L;96P)
PREREQUISITE    MATH 310/3.0.

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)
PREREQUISITE      (MATH 210/3.0 or MATH 217/3.0) or (MATH 211/6.0 with permission of the Department).

An exploration of the modern theory of Fourier series: Abel and Cesaro summability; Dirichlet’s and
Fejér’s kernels; term by term differentiation and integration; infinite products; Bernoulli
numbers; Gibbs’s phenomenon.
LEARNING HOURS    132 (36L;96P)
PREREQUISITE    MATH 281/3.0 or permission of the Department.

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 827/3.0.
LEARNING HOURS    120 (36L;84P)
PREREQUISITE      MATH 328/3.0 and MATH 231/3.0, or permission of the Department.

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.

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.
PREREQUISITE    (MATH 110/6.0 or MATH 111/6.0 or MATH 212/3.0) and MATH 281/3.0.

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)
RECOMMENDATION    MATH 328/3.0 or MATH 334/3.0 or MATH 338/3.0 or PHYS 312/6.0.
PREREQUISITE    (MATH 231/3.0 or MATH 237/3.0) and MATH 280/3.0.

Subject matter to vary from year to year. Given jointly with MATH 837/3.0.
LEARNING HOURS    132 (36L;96P)
PREREQUISITE    Permission of the Department.

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)
PREREQUISITE    (MATH 231/3.0 or MATH 237/3.0) and (MATH 280/3.0 or MATH 281/3.0), or permission of the Department.

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 874/3.0.
LEARNING HOURS    140 (36L;104P)
RECOMMENDATION    STAT 353/3.0.
PREREQUISITE    STAT 268/3.0 or STAT 351/3.0.

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)
RECOMMENDATION    STAT 353/3.0.
PREREQUISITE    MATH 474/3.0.

Website: mast.queensu.ca/~math477/

An important topic in mathematics not covered in any other courses.
PREREQUISITE      Prerequisites vary depending on specific course content; consult instructor or
departmental webpage.

An important topic in mathematics not covered in any other courses.
PREREQUISITE      Prerequisites vary depending on specific course content; consult instructor or
departmental webpage.

Important topics in mathematics not covered in any other courses.
PREREQUISITE    Permission of the Department.