Not all courses described in the Course and Program Catalogue are offered each year. For a list of course offerings in 2017-2018, 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

The following term designations are used:

- 1 - Term 1 only
- 2 - Term 2 only
- 3 - Term 3 only
- 1&2 - Term 1 and 2
- 1/2 - Either Term 1 or Term 2
- P - Phases (Medicine and Dentistry)
- Q - Quarters (Veterinary Medicine)

The following instructional code designations are used:

- L - Lecture
- P - Practicum/Lab
- S - Seminar/Discussion
- C - Clinical Service
- R - Reading
- T - Tutorial

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.)

### Results

**MATH 100.6 — 1&2(3L)**

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.

**Prerequisite(s):**Mathematics A30 or B30 or C30; or Foundations of Mathematics 30; or Pre-Calculus 30.

**Note:**Intended for students entering the Elementary Program in the College of Education. Does not fulfill requirements of a major or honours in either mathematics or statistics, or any other Arts & Science degree program. Students may have credit for MATH 100 and other junior mathematics and statistics courses subject to regulations of the Department of Mathematics and Statistics. See "Junior Mathematics Course Credits" in the Department's portion of the Arts and Science section of the Calendar.

**MATH 102.3 — 1/2(3L-1.5P)**

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.

**Prerequisite(s):**Mathematics A30 and B30; or Workplace and Apprenticeship Mathematics 30; or Foundations of Mathematics 30; or Pre-Calculus 30.

**Note:**This course may not be taken for credit concurrently with or after any other 100-level MATH course. Students are allowed to have credit for only one of MATH 102 or 104; students who take MATH 102 and then take MATH 104 will lose credit for MATH 102. This course may be used as an alternative prerequisite for MATH 110, 121, 123, or 125 (clears deficiencies in high school 30-level mathematics courses). Students who score below 60% on the Math Placement Test (http://math.usask.ca/placement) are advised to take MATH 102 to review their basis precalculus skills. MATH 102 may not be included in the courses required in C4 or C6 for Applied Mathematics, Mathematical Physics, Mathematics or Statistics. In Arts & Science programs, this course may be used only in the Electives Requirement.

**MATH 104.3 — 1/2(3L)**

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.

**Formerly:**MATH 101.

**Prerequisite(s):**Mathematics B30 or Foundations of Mathematics 30 or Pre-Calculus 30.

**Note:**Students with credit for MATH 101 may not take this course for credit. Students with credit for MATH 104 may subsequently receive credit for MATH 110, 121, 123 or 125. Students with credit for MATH 110, 121, 123, or 125 may not subsequently receive credit for MATH 104. Students may not register for MATH 104 concurrently with any of MATH 110, 121, 123, or 125. This course may not be included in the courses required in C4 or C6 for Applied Mathematics, Mathematical Physics, Mathematics or Statistics. Students are allowed to have credit for only one of MATH 102 and 104; students who take MATH 102 and then take MATH 104 will lose credit for MATH 102. This course may be used as an alternate prerequisite for MATH 110, 121, 123 or 125 (clears deficiencies in high school 30-level mathematics courses). Students who score below 60% on the Math Placement Test (http://math.usask.ca/placement) are advised to take MATH 102 to review their basis precalculus skills. Students with credit for one of MATH 101, 104, 110 or STAT 103 may subsequently take MATH 100 for half credit only. Students with credit for MATH 100 may subsequently take one of MATH 104, 110 or STAT 103 for credit.

**MATH 110.3 — 1/2(3L-1.5P)**

Calculus I

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

**Prerequisite(s):**Pre-Calculus 30 and a 60% score in the Math Placement Test; or Mathematics B30 and C30 and a 60% score in the Math Placement Test; or MATH 102 or MATH 104.

**Note:**Students who do not have credit for MATH 102 or MATH 104 must complete the Math Placement Test (http://math.usask.ca/placement) with a test score of 60% or higher in order to register in MATH 110. Students are encouraged to write the test at least 6 weeks prior to the start of the term to help ensure that space will be available in the class. Students who score below 60% on the Math Placement Test will not be allowed to register in MATH 110 in the upcoming term; such students are encouraged to register for MATH 102 to improve their basic precalculus skills. Students with credit for MATH 100 may subsequently take one of MATH 104, 110 or STAT 103 for credit.

**MATH 116.3 — 1/2(3L-1.5P)**

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.

**Prerequisite(s):**MATH 110.

**Note:**Intended to complete the basic introduction to calculus for students in the mathematical and physical sciences, and for others who require a solid introduction to calculus. The specified prerequisite for most second-year courses in mathematics and statistics, including all courses accepted in major and honours programs. Students may have credit for only one of MATH 112, 116, 124, or 128. Students with credit for MATH 123 may take this course for credit.

**MATH 121.3 — 1(3L-1.5P)**

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.

**Restriction:**Enrolment in the Edwards School of Business.

**Prerequisite(s):**Mathematics B30 and C30; or Foundations of Mathematics 30 or Pre-Calculus 30 (Pre-Calculus 30 preferred); or MATH 102 or MATH 104.

**Note:**Students may have credit for only one of MATH 110, 121, 123, or 125. Arts & Science students needing 6 credit units of 100-level calculus should take MATH 110 followed by MATH 116. Students who score below 60% on the Math Placement Test (http://math.usask.ca/placement) are advised to take MATH 102 to review their basis precalculus skills.

**MATH 123.3 — 1(3L-1.5P)**

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.

**Restriction(s):**Enrolment in the College of Engineering.

**Prerequisite(s):**Mathematics A30, B30 and C30; or Pre-Calculus 30; or MATH 102 or MATH 104.

**Note:**Students may have credit for only one of MATH 110, 121, 123, or 125. Students who score below 60% on the Math Placement Test (http://math.usask.ca/placement) are advised to take MATH 102 to review their basis precalculus skills.

**MATH 124.3 — 2(3L-1.5P)**

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.

**Restriction(s):**Enrolment in the College of Engineering.

**Prerequisite(s):**MATH 123 (taken).

**Note:**Students may have credit for only one of MATH 112, 116, 124, or 128.

**MATH 125.3 — 1(3L-1.5P)**

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.

**Prerequisite(s):**Mathematics A30, B30 and C30; or Pre-Calculus 30; or MATH 102 or MATH 104.

**Note(s):**Students may receive credit for only one of MATH 110, 121, 123, or 125. Students with credit for MATH 115 may not take this course for credit. Arts & Science students needing 6 credit units of 100-level calculus should take MATH 110 followed by MATH 116. This course is restricted to students Majoring in Biology; Biology & Biotechnology; Anatomy & Cell Biology; Biochemistry; Biochemistry & Biotechnology; Biotechnology, Microbiology & Immunology; Environment & Society; Environmental Biology; Microbiology & Immunology; Physiology & Pharmacology; Toxicology; or Pharmacy. Students who score below 60% on the Math Placement Test (http://math.usask.ca/placement) are advised to take MATH 102 to review their basis precalculus skills.

**MATH 164.3 — 1/2(3L-1.5P)**

Introduction to Linear Algebra

Systems of linear equations over the real numbers. Vector algebra on ordered n-tuples (Euclidean n-space). Representation of linear systems as rectangular matrices. Elementary row operations; the row canonical form of a matrix. Basic matrix algebra (addition, subtraction, scalar multiplication). Matrix-vector multiplication; linear maps between Euclidean spaces. Matrix multiplication, square matrices, algorithms for matrix inverses. Introduction to determinants, eigenvalues,eigenvectors, and applications. Numerical linear algebra with computer algebra systems. Applications of linear algebra to other disciplines.

**Prerequisite(s):**Precalculus 30; or Foundations of Mathematics 30; or Mathematics B30 and C30; or 3 credit units of MATH or STAT

**Note:**Formerly MATH 264. Students with credit for MATH 264 will not receive credit for this course. Students with credit for this course may subsequently take MATH 266.3 for credit. However, students with credit for MATH 266 or MATH 358 may not subsequently take this course for credit. This course may not be included in the courses required in Requirement C4 for degrees in Applied Mathematics, Mathematical Physics, Mathematics or Statistics, or in Requirement C6 for degrees in Mathematical Physics, Mathematics or Statistics.

**MATH 211.3 — 1/2(3L-1P)**

Numerical Analysis I

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

**Prerequisite(s):**MATH 110 and 116.

**MATH 223.3 — 1(3L-1P)**

Calculus III for Engineers

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

**Restriction(s):**Enrolment in the College of Engineering.

**Prerequisite(s):**MATH 123 and 124.

**Note:**Engineering students may take this course with prerequisite of MATH 110 and 116 if they seek permission of the Engineering Students' Centre. Arts & Science students majoring in Physics may receive permission to take this course by contacting the Department of Mathematics and Statistics. Students with credit for MATH 225 or 276 may not take this course for credit.

**MATH 224.3 — 2(3L-1P)**

Calculus IV for Engineers

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

**Restriction(s):**Enrolment in the College of Engineering.

**Prerequisite(s):**MATH 123, 124 and 223 (all taken).

**Note:**Arts & Science students majoring in Physics may receive permission to take this course by contacting the Department of Mathematics and Statistics. Students with credit for MATH 226 may not take this course for credit.

**MATH 225.3 — 1(3L-1P)**

Intermediate Calculus I

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

**Prerequisite(s):**(MATH 110 and 116) or (MATH 121 or MATH 125; and MATH 128).

**Note:**Students with credit for MATH 223 or MATH 276 may not take this course for credit.

**MATH 226.3 — 2(3L-1P)**

Intermediate Calculus II

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

**Prerequisite(s):**(MATH 110 and 116) or (MATH 121 or MATH 125; and MATH 128).

**Note:**Students with credit for MATH 224 may not take this course for credit.

**MATH 238.3 — 1(3L-1.5P)**

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.

**Prerequisite(s):**(MATH 110 and 116) or (MATH 121 or MATH 125; and MATH 128) or (MATH 123 and MATH 124).

**Note:**Students intending to enter an honours or double honours program are encouraged to take this course.

**MATH 258.3 — 1/2(3L-1P)**

Euclidean Geometry

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

**Prerequisite(s):**One of MATH 100, 104 (formerly 101), 110, 121, 123, 125, or STAT 103.

**Note:**Basic introduction to high school geometry recommended. May not be included in the courses required in C4 or C6 for Honours programs in Applied Mathematics, Mathematical Physics, Mathematics or Statistics.

**MATH 266.3 — 1/2(3L)**

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.

**Prerequisite(s):**(MATH 110 and 116) or (MATH 121 or MATH 125; and MATH 128).

**Note:**Designed to meet the needs of students majoring or honouring in mathematics, statistics, computer science or one of the natural sciences. Students are not permitted to take more than one of MATH 264, 266 or 358 for credit.

**MATH 276.3 — 1(3L-1.5P)**

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.

**Prerequisite(s):**(MATH 110 and 116) or (MATH 121 or MATH 125; and MATH 128).

**Note:**Students intending to enter an Honours or Double Honours program in Mathematics or Statistics are encouraged to take this course. Students with credit for MATH 223 or 225 may not take this course for credit.

**MATH 277.3 — 1/2(3L-1.5P)**

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.

**Prerequisite(s):**MATH 276 (or MATH 225 with a grade of 80% or better).

**MATH 298.3 — 1/2(3L)**

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.

**MATH 299.6 — 1&2(3L)**

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.

**MATH 301.0 — (1S)**

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.

**MATH 313.3 — 1/2(3L)**

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.

**Prerequisite(s):**MATH 211, and 266 or equivalent in linear algebra.

**Note:**Students may receive credit for a maximum of two of MATH 313, 314 and 315.

**MATH 314.3 — 1/2(3L)**

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.

**Prerequisite(s):**MATH 211 and 238.

**Note:**Students may receive credit for a maximum of two of MATH 313, 314 and 315.

**MATH 327.3 — 1/2(3L)**

Graph Theory

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

**Prerequisite(s):**MATH 164 (formerly MATH 264) or 266, and either CMPT 260 or 6 credit units 200-level MATH.

**MATH 328.3 — 1/2(3L)**

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.

**Prerequisite(s):**MATH 164 (fomerly MATH 264) or 266, and either CMPT 260 or 6 credit units 200-level MATH.

**MATH 331.3 — 1(3L-1.5P)**

Applied Mathematics Differential Equations I

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

**Formerly:**Half of MATH 338

**Prerequisite(s):**MATH 224 or MATH 226 or MATH 238 (or approval of instructor/department)

**Note:**Students with credit for MATH 338 may not take this course for credit.

**MATH 336.3 — 1/2(3L)**

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.

**Prerequisite(s):**MATH 211.3, MATH 164.3 (formerly MATH 264) or 266.3, STAT 241.3, 6 credit units in 200-level calculus: (MATH 223.3 and 224.3) or (MATH 225.3 and 226.3) or (MATH 276.3 and 277.3).

**MATH 339.3 — 1(3L-1.5P)**

Applied Mathematics Differential Equations II

Sturm-Liouville theory, function spaces, introduction to distributions and generalized functions, Fourier transform, Laplace transform, Green's function, applications to linear differential equations.

**Formerly:**Half of MATH 338.6

**Prerequisite(s):**MATH 331.3 or approval of the instructor

**Note:**Students with credit for MATH 338 may not take this course for credit.

**MATH 352.3 — 1/2(3L)**

Introduction to Differential Geometry

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

**Formerly:**Half of MATH 350.6.

**Prerequisite(s):**Algebra prerequisite: MATH 164 (formerly MATH 264) or MATH 266; Calculus and Differential Equations prerequisite: (MATH 238 and MATH 276 and MATH 277) or (MATH 223 and MATH 224) or (MATH 225 and MATH 226 - with grades of at least 80% and permission of the Head of the Department of Mathematics and Statistics).

**Note:**Students may receive credit for only one of MATH 350 or 352.

**MATH 361.3 — 1(3L-1P)**

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.

**Prerequisite(s):**MATH 266

**Note:**Students may receive credit for only one of MATH 360 or 361 or 363.

**MATH 362.3 — 1(3L-1P)**

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.

**Prerequisite(s):**MATH 266

**Note:**Students may receive credit for only one of MATH 360 or 362 or 363.

**MATH 363.3 — 2(3L)**

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.

**Prerequisite(s):**One of MATH 100, 104 (formerly 101), 110, 121, 123, 125, or STAT 103.

**Note:**Recommended for teachers of mathematics. May not be included in the courses required in C4 or C6 for Honours Programs in Applied Mathematics, Mathematical Physics, Mathematics or Statistics. Students with credit for MATH 360 or 361 or 362 may not take MATH 363 for credit.

**MATH 364.3 — 1(3L)**

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.

**Prerequisite(s):**One of MATH 100, 104 (formerly 101), 110, 121, 123, 125, or STAT 103.

**Note:**Recommended for teachers of mathematics. May not be included in the courses required in C4 or C6 for Honours Programs in Applied Mathematics, Mathematical Physics, Mathematics or Statistics.

**MATH 366.3 — 1/2(3L)**

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.

**Prerequisite(s):**MATH 266.

**Note:**Designed to meet the needs of major and honours students in mathematics, as well as students majoring in computer science or one of the natural sciences.

**MATH 371.3 — 1(3L)**

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.

**Prerequisite(s):**MATH 238 and 276.

**MATH 373.3 — 1/2(3L)**

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.

**Prerequisite(s):**MATH 371.

**Note:**Students with credit for MATH 470 may not take this course for credit.

**MATH 379.3 — 2(3L)**

Complex Analysis

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

**Prerequisite(s):**MATH 225 or 276; and MATH 226 or 238.

**MATH 398.3 — 1/2(3S)**

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.

**MATH 399.6 — 1&2(3S)**

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.

**MATH 401.0 — 1&2(1.5S)**

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.

**Prerequisite(s):**MATH 301.0.

**MATH 433.3 — 1/2(3L)**

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).

**Prerequisite(s):**MATH 276 and MATH 366; or MATH 276 and MATH 266 and permission of the instructor.

**Note:**MATH 277 is recommended.

**MATH 436.3 — 1/2(3P)**

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.

**Prerequisite(s):**MATH 336 or permission of the instructor.

**MATH 438.3 — 1/2(3L)**

Methods of Applied Mathematics

Calculus of variations, integral equations and applications.

**Prerequisite(s):**MATH 238, 276 and 277.

**Note:**Students cannot receive credit for MATH 438 and MATH 838.

**MATH 439.3 — 1/2(3L)**

Partial Differential Equations

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

**Prerequisite(s):**MATH 238, 276 and 277.

**MATH 452.3 — 1/2(3L)**

Introduction to Modern Differential Geometry

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

**Formerly:**Half of MATH 350.6.

**Prerequisite(s):**Algebra prerequisite: MATH 366; Differential Geometry and Analysis prerequisite: MATH 352 or MATH 371

**Note:**Students may receive credit for only one of MATH 350 or 452.

**MATH 465.3 — 1/2(3L-1.5T)**

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.

**Prerequisite(s):**MATH 364 or permission of the Head of Mathematics and Statistics.

**MATH 485.3 — 1/2(3L)**

Elements of General Topology

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

**Prerequisite(s):**MATH 371.

**MATH 498.3 — 1/2(3S)**

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.

**MATH 499.6 — 1&2(3S)**

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.

**MATH 811.3 — 1&2(3L)**

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.

**Formerly:**MATH 814

**Prerequisite(s):**MATH 314 and MATH 338 or equivalents, or by permission of the instructor.

**Note:**Students with credit for MATH 814 cannot receive credit for this course.

**MATH 818.3 — 1/2/1&2(3L)**

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.

**Prerequisite(s):**A graduate course in applied mathematics, or permission of the department.

**Note:**Students may take this course more than once for credit, provided the topic covered in each offering differs substantially. Students must consult the Department to ensure that the topics covered are different.

**MATH 838.3 — 1/2(3L)**

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.

**Prerequisite(s):**(MATH 331.3, MATH 339.3, MATH 371.3, and MATH 373.3), or equivalents as determined by the colllege, or permission of the instructor.

**Note:**Cannot receive credit for MATH 438.3 and MATH 838.3. Cannot receive credit for MATH 838.6 and MATH 838.3.

**MATH 839.3 — 1/2(3L)**

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; Greenâ€™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.

**Prerequisite(s):**(MATH 331.3, MATH 339.3, MATH 371.3, MATH 373.3, and MATH 379.3), or equivalents as determined by the colllege, or permission of the instructor.

**Note:**Cannot receive credit for MATH 439.3 and MATH 839.3.

**MATH 872.3 — 1/2/1&2(3L)**

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.

**Note:**Students may take this course more than once for credit, provided the topic covered in each offering differs substantially. Students must consult the Department to ensure that the topics covered are different.

**MATH 875.3 — 1/2(3L)**

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.

**Prerequisite(s):**MATH 371, MATH 373, and MATH 379 or equivalent.

**MATH 876.3 — 1/2(3L)**

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.

**Prerequisite(s):**MATH 371, MATH 373, and MATH 379 or equivalent.

**MATH 882.3 — 1/2(3L)**

Algebraic Topology I

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

**Prerequisite(s):**MATH 485.

**MATH 898.3**

Special Topics

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

**MATH 899.6**

Special Topics

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

**MATH 990**

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.

**MATH 992.0**

Project

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

**MATH 994**

Research

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

**MATH 996**

Research

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