This Course and Program Catalogue is effective from May 2014 to April 2015.

Not all courses described in the Course and Program Catalogue are offered each year. For a list of course offerings in 2014-2015, please consult the class search website.

For general registration information, please visit students.usask.ca.

As of 2005-2006, certain course abbreviations have changed. Students with credit for a course under its former label may not take the relabeled course for credit.

The following conventions are used for course numbering:

- 010-099 represent non-degree level courses
- 100-699 represent undergraduate degree level courses
- 700-999 represent graduate degree level courses

Course Term and Instructional Code Designations are outlined here.

Please use the following form to look up courses and find detailed information on course prerequisites, corequisites, and other special notes. To view all 100-level courses in a subject, select a Subject Code and type 1% in the Course Number field. (200-level = 2%, etc.)

Mathematics for Education Students

An introductory course designed for students planning to teach at the elementary school level. Topics include basic algebra review, mathematics of finance, number theory, linear algebra, linear programming, counting techniques, probability and statistics.

Precalculus Mathematics

Discusses mathematical ideas essential for the study of calculus. Topics include: the fundamentals of algebra; functions, their properties and graphs; polynomial and rational functions; exponential and logarithmic functions; trigonometric and inverse trigonometric functions; trigonometric properties.

Elementary Calculus

An elementary introduction to calculus including functions, limits, derivatives, techniques of differentiation, curve sketching and maximum and minimum problems, antiderivatives and the integral.

Calculus I

Introduction to derivatives, limits, techniques of differentiation, maximum and minimum problems and other applications, implicit differentiation, anti-derivatives.

Calculus II

Techniques of integration; the definite integral and simple differential equations with applications and numerical techniques; the theoretical foundations of limits, including the epsilon-delta formulation; continuity and differentiability; advanced curve sketching; inverse functions; inverse trigonometric functions.

Mathematical Analysis for Business and Economics

An introduction to mathematics for business and economics students using examples from business to motivate mathematical techniques. Necessary mathematical terms and concepts are developed, but emphasis is on applications to business with sufficient theory to support applications. Topics: algebraic functions, mathematics of finance, analysis of functions, differential and integral calculus.

Calculus I for Engineers

A review of basic algebraic concepts, trigonometry and functions. An introduction to limits and differential and integral calculus, max-min problems, curve sketching, related rate problems. Specifically for students in the College of Engineering.

Calculus II for Engineers

Differentiation and integration of inverse trigonometric, exponential, hyperbolic and logarithmic functions with applications. Techniques of integration; applications to work, pressure, moments and centroids. Polar co-ordinates and parametric equations of plane curves; complex numbers.

Mathematics for the Life Sciences

An introduction to mathematical modeling with a focus on applications to the life sciences. Topics include: algebraic functions and their graphs, limits and rates of change, differentiation techniques and applications, exponential and logarithmic functions, integration and the area under a curve, introduction to differential equations. The main feature of this course is the use of structured examples from life sciences to establish a need for mathematical techniques. Necessary mathematical terms and concepts will be developed. The emphasis throughout this course is on applications of mathematics to life sciences with just enough theory to support applications. Extensive examples from Biology, Health, Chemistry and Physics will be used.

Calculus II for Applications

Trigonometric functions and their derivatives. Review of definite and indefinite integrals, the fundamental theorem of calculus, and the method of substitution. Areas between curves, and volumes of solids of revolution. Average value of a function over an interval. Work. Integration by parts. Trigonometric integrals and trigonometric substitution. Integration of rational functions. Approximate integration. Indeterminate forms and L'Hospital's Rule. Improper integrals. The formal definition of a limit (epsilon-delta). Arc lengths, and areas of surfaces of revolution. Introduction to differential equations.

Numerical Analysis I

An introductory course. Topics include errors, solutions of linear and non-linear equations, interpolation, numerical integration, solutions of ordinary differential equations.

Calculus III for Engineers

Vectors and coordinate geometry in 3- space; vector functions and curves; partial differentiation; applications to partial derivatives; multiple integration.

Calculus IV for Engineers

Vector fields; vector calculus; ordinary differential equations; sequences, series, and power series.

Intermediate Calculus I

Analytic geometry, vectors, vector functions, partial differentiation, multiple integration, line integrals and Green's theorem.

Intermediate Calculus II

Infinite sequences and series, complex numbers, first order and linear differential equations.

Introduction to Differential Equations

Solutions of first order and second order differential equations, elementary existence results, fundamentals of some operational and transform methods of solution, power series solutions, 2 x 2 systems, elementary numerical methods. An introduction to modelling will arise through the use of examples from the physical and biological sciences, economics and social sciences, engineering. Examples will include: population models, mechanical vibrations, Kepler's problem, predator-prey models.

Euclidean Geometry

A course in plane Euclidean geometry. Particularly recommended for teachers of mathematics.

Linear Algebra

Vector spaces, matrices and determinants, linear transformations, sets of linear equations, convex sets and n-dimensional geometry, characteristic value problems and quadratic forms.

Linear Algebra I

A study of linear equations, matrices and operations involving matrices, determinants, vector spaces and their linear transformations, characteristic values and vectors, reduction of matrices to canonical forms, and applications.

Vector Calculus I

A discussion of the real numbers including least upper bound; sequences and series and convergence criteria; vector analysis; limits and continuity in n-dimensions; differentiation in n-dimensions and the derivative as a linear mapping; curves in space.

Vector Calculus II

Maxima and minima of functions with and without constraints; Taylor polynomials; inverse and implicit function theorems; integration of functions of several variables and the change of variable formula for multiple integrals; line integrals and surface integrals; Green's, Gauss', Stokes' theorems; introduction to differential forms.

Special Topics

Offered occasionally by visiting faculty and in other special situations to cover, in depth, topics that are not thoroughly covered in regularly offered courses.

Special Topics

Offered occasionally by visiting faculty and in other special situations to cover, in depth, topics that are not thoroughly covered in regularly offered courses.

Honours Seminar I

Students taking an Honours program in Mathematics or Statistics, or a Double Honours program in Mathematics or Statistics and a second subject, are required to participate in this seminar, normally during the third year of their program.

Numerical Analysis II

Numerical methods in linear algebra. Topics covered include approximation theory, least squares, direct methods for linear equations, iterative methods in matrix algebra, eigenvalues, systems of non-linear equations.

Numerical Analysis III

Numerical differentiation and integration, initial-value, and boundary-value problems for ordinary differential equations, introduction to numerical solutions to partial-differential equations.

Graph Theory

Graph Theory and its contemporary applications including the nomenclature, special types of paths, matchings and coverings, and optimization problems soluble with graphs.

Combinatorics and Enumeration

The theory of Combinatorics and Enumeration and its contemporary applications, including generating functions and recurrence relations, and the Polya and Ramsey Theories. A wide variety of practical applications will be presented.

Applied Mathematics Differential Equations I

General theory for ordinary differential equations with constant coefficients, series solutions for ordinary differential equations, special functions, Sturm-Liouville problem, physical origin of heat, wave and Laplace equations, separation of variables, introduction to Fourier series.

Mathematical Modelling I

The course is designed to teach students how to apply Mathematics by formulating, analyzing and criticizing models arising in real-world situations. An important aspect in modelling a problem is to choose an appropriate set of mathematical methods - 'tools' - in which to formulate the problem mathematically. In most cases a problem can be categorized into one of three types, namely: continuous, discrete, and probabilistic. The course will consist of an introduction to mathematical modelling through examples of these three basic modelling types.

Applied Mathematics Differential Equations II

Laplace transform, function spaces, Fourier series, Fourier transform, introduction to distributions and generalized functions, Green's function, application to linear partial differential equations.

Introduction to Differential Geometry

Tensor calculus; curves and surfaces in 3-dimensional Euclidean space; mean and Gaussian curvature; geodesics; Euclidean motions; Gauss' Theorema Egregium.

Group Theory

Introduction to group theory, including: cyclic groups, symmetric groups, subgroups and normal subgroups, Lagrange's theorem, quotient groups and homomorphisms, isomorphism theorems, group actions, Sylow's theorem, simple groups, direct and semidirect products, fundamental theorem on finitely generated Abelian groups.

Rings and Fields

Introduction to ring and field theory, including: polynomial rings, matrix rings, ideals and homomorphisms, quotient rings, Chinese remainder theorem, Euclidean domains, principal ideal domains, unique factorization domains, introduction to module theory, basic theory of field extensions, splitting fields and algebraic closures, finite fields, introduction to Galois theory.

Abstract Algebra

Introduction to algebraic structures, notably groups and rings. Topics include binary operations, groups, subgroups, homomorphisms, cosets, Lagrange's theorem, permutation groups, the general linear group; rings, polynomial rings, Euclidean rings.

Number Theory

A course in elementary number theory with emphasis upon the interrelation of number theory and algebraic structures: review of unique factorization and congruences, the ring of integers modulo n and its units, Fermat's little theorem, Euler's function, Wilson's theorem, Chinese remainder theorem, finite fields, quadratic reciprocity, Gaussian integers, and the Fermat theorem on primes congruent to one modulo four.

Linear Algebra II

Follow-up to MATH 266. Further important properties of linear transformations, such as spectral theorems and Jordan normal form, will be dealt with.

Metric Spaces and Continuous Functions

A rigorous construction of the real numbers followed by an introduction to general metric spaces and their basic properties. Continuous functions are studied in detail.

Integration Theory

Review of the Newton, Riemann and Riemann-Stieltjes integrals and their shortcomings, the generalized integrals including the Lebesgue integral, the main convergence theorems, Lebesgue measure, Lp-spaces and an introduction to Fourier analysis.

Complex Analysis

Fundamental concepts, analytic functions, infinite series, integral theorems, calculus of residues, conformal mappings and applications.

Special Topics

Offered occasionally by visiting faculty and in other special situations to cover, in depth, topics that are not thoroughly covered in regularly offered courses.

Special Topics

Offered occasionally by visiting faculty and in other special situations to cover, in depth, topics that are not thoroughly covered in regularly offered courses.

Honours Seminar II

Students taking an Honours program in Mathematics or Statistics, or a Double Honours program in Mathematics or Statistics and a second subject, are required to participate in this seminar, normally during the fourth year of their program.

Applied Group Theory

Treats the following topics from group theory: permutation groups, crystallographic groups, kinematic groups, abstract groups, matrix Lie groups, group representations. Specific topics include the rotation group (spinors and quantum mechanical applications), the Lorentz group (representations and wave equations), SU (3) (its Lie algebra and physical relevance).

Mathematical Modelling II

This course is a continuation of MATH 336.3. The course is designed to further develop students' capacity to formulate, analyze and criticize mathematical models arising in real-world situations. The present course will put emphasis on student activities rather than on lectures. Students will be expected to work in small groups on problems chosen by the instructor and to develop their independent skills at the formulation, analysis and critique of specific problems, and ultimately come to a greater understanding of the modelling process.

Methods of Applied Mathematics

Calculus of variations, integral equations and applications.

Partial Differential Equations

Classification of second order partial differential equations, some properties of elliptic, parabolic, and hyperbolic equations, applications.

Introduction to Modern Differential Geometry

Submanifolds of Rn; Riemannian manifolds; tensors and differential forms; curvature and geodesics; selected applications.

Introduction to Cryptography

Presents a thorough introduction to the mathematical foundations of cryptography. Results from number theory and algebra and how they are used for the safe transmission of information are studied. Various security protocols, the mathematical principles needed for them, and the mathematical principles used in possible attacks are examined.

Elements of General Topology

Topological spaces, separation axioms, products, quotients, convergence, connectedness, extension theorems, and metric spaces.

Special Topics

Offered occasionally by visiting faculty and in other special situations to cover, in depth, topics that are not thoroughly covered in regularly offered courses.

Special Topics

Offered occasionally by visiting faculty and in other special situations to cover, in depth, topics that are not thoroughly covered in regularly offered courses.

Numerical Solution of Ordinary and Partial Differential Equations

One-Step methods for initial-value problems, multi-step methods, boundary-value problems; discussion of discretization error and propagation of errors, convergence, and stability. Partial Differential Equations: Some finite-difference schemes for hyperbolic, parabolic and elliptic partial differential equations, their stability and convergence; applications.

Special Topics in Applied Mathematics

The topics to be discussed will be related to recent developments in applied mathematics (numerical analysis, differential equations, mechanics, applied analysis, etc.) of interest to the instructor and students.

Methods of Applied Mathematics II

The course is devoted to classical topics in Applied Mathematics, including Integral equations, Theory of Distributions, Fourier Transforms, and Calculus of Variations. By the end of the course, students will be able to analyze modern mathematical models involving ordinary and partial differential equations and integral equations, and approach the solution from different points of view, building on knowledge of classical mathematical methods and hands-on practical experience gained in this course.

Methods of Applied Mathematics I

This course covers methods pertaining to the formulation and solution of problems involving linear and nonlinear Partial and Ordinary Differential Equations (PDE, ODE). Topics include: Linear equations of mathematical physics; Initial/boundary value problems; Bases of functions; Fourier series; Operators in function spaces; Separation of variables; Method of characteristics; Green’s functions; Traveling wave solutions. At the end of the term, students will be able to formulate complex mathematical models, and approach their solution from different points of view, building on knowledge of classical mathematical methods and hands-on practical experience gained in this course.

Noncommutative Algebra

An introduction to noncommutative algebra at the graduate level. Topics will be chosen based on the needs and interests of the student, and will typically include: structure theory of noncommutative rings (finite- and infinite-dimensional), representation theory of finite groups, module theory, introduction to Lie algebras.

Special Topics in Pure Mathematics

The topics to be discussed will be related to recent developments in an area of pure mathematics (analysis, topology, algebra, etc.) of interest to the students and instructor.

Functional Analysis

An introduction to functional analysis at the graduate level. Topics will include Normed and Banach spaces, Bounded linear operators, The Hahn-Banach Theorem, The Principle of Uniform Boundedness, The Open Mapping and Closed Graph Theorem, Weak and Weak topologies, Adjoint operators, Compact operators on Banach space, Hilbert spaces, Bounded linear operators on Hilbert spaces, Spectrum of operators on Hilbert spaces, Compact Normal operators.

Operator Theory

An introduction to operator theory at the graduate level. Topics will include Banach algebras, Specturm of an element in Banach algebras, Spectral radius, Analytic functional calculus, C-algebras of operators, Continuous and Borel functional calculus, Spectral measures.

Algebraic Topology I

Two-dimensional Manifolds, the Fundamental Group including the Seifert-Van Kampen Theorem, Applications to Knot Theory and Group Theory.

Special Topics

Offered occasionally in special situations. Students interested in these courses should contact the department for more information.

Special Topics

Offered occasionally in special situations. Students interested in these courses should contact the department for more information.

Seminar

All graduate students in the department enroll each year. Students attend the regular department colloquia. After the first year in their program, they are expected to join the regular seminar series in their area of specialization.

Project

Students undertaking the project Master's degree (M.Math.) must register for this course.

Research

Students writing a Master's thesis must register for this course.

Research

Students writing a Ph.D. thesis must register for this course.

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