## Advice for Undergraduate Students

2nd Year Students in **2018/19** *(PDF, 120 KB)*

3rd & 4th Year Students in **2018/19** *(PDF, 105 KB)*

## Undergraduate MATH Courses

**100 Level Courses**

**MATH 110**- Linear Algebra

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/

**MATH 111**- Linear Algebra

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.

**MATH 112**- Introduction to Linear Algebra

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.

**MATH 120**- Differential and Integral Calculus

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/

**MATH 121**- Differential and Integral Calculus

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.

**MATH 123**- Differential & Integral Calculus I

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.

**MATH 124**- Differential & Integral Calculus II

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.

**MATH 126**- Differential & Integral Calculus

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.

**200 Level Courses**

**MATH 210**- Rings and Fields

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.

**MATH 211**- Algebraic Methods

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.

**MATH 212**- Linear Algebra II

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.

**MATH 221**- Vector Calculus

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.

**MATH 225**- Ordinary Differential Equations

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.

**MATH 228**- Complex Analysis

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.

**MATH 231**- Differential Equations

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.

**MATH 272**- Applications of Numerical Methods

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.

**MATH 280**- Advanced Calculus

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.

**MATH 281**- Introduction to Real Analysis

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.

**300 Level Courses**

**BIOM 300**- Modeling Techniques in Biology

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.

**IDIS 303**- Mathematics and Poetry

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.

**MATH 310**- Group Theory

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.

**MATH 311**- Elementary Number Theory

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.

**MATH 326**- Functions of a Complex Variable

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.

**MATH 328**- Real Analysis

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.

**MATH 334**- Mathematical Methods for Engineering and Physics

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.

**MATH 335**- Mathematics of Engineering Systems

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.

**MATH 337**- Introduction to Operations Research Models

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).

**MATH 338**- Fourier Methods for Boundary Value Problems

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.

**MATH 339**- Evolutionary Game Theory

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.

**MATH 341**- Differential Geometry

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.

**MATH 381**- Mathematics with a Historical Perspective

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).

**MATH 382**- Mathematical Explorations

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).

**MATH 384**- Mathematical Theory of Interest

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).

**MATH 385**- Life Contingencies

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.

**MATH 386**- Our Number System – an Advanced Perspective

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.

**MATH 387**- Elementary Geometry – an Advanced Perspective

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.

**400 Level Courses**

**MATH 401**- Graph Theory

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.

**MATH 402**- Enumerative Combinatorics

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.

**MATH 406**- Introduction to Coding Theory

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.

**MATH 413**- Introduction to Algebraic Geometry

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.

**MATH 414**- Introduction to Galois Theory

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

**MATH 418**- Number Theory and Cryptography

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).

**MATH 421**- Fourier Series

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.

**MATH 427**- Introduction to Deterministic Dynamical Systems

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.

**MATH 434**- Optimization Theory and Applications

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.

**MATH 436**- Partial Differential Equations

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.

**MATH 437**- Topics in Applied Mathematics

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.

**MATH 439**- Lagrangian Mechanics, Dynamics, and Control

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.

**MATH 474**- Information Theory

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.

**MATH 477**- Data Compression & Source Coding

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/

**MATH 497**- Topics in Mathematics IV

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

departmental webpage.

**MATH 498**- Topics in Mathematics V

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

departmental webpage.

**MATH 499**- Topics in Mathematics

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