Course Descriptions
Not all courses described in the Course and Program Catalogue are offered each year. For a timetable of courses offered in 2013-2014, please consult the online registration information.
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
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-1P)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 Apprenticeship and Workplace 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 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 alternative prerequisite for MATH 110, 121, 123, or 125 (clears deficiencies in high school 30-level mathematics courses). MATH 102 may not be included in the courses comprising a major or honours in either 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 comprising a major or honours in either 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 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): Mathematics B30 and C30; or Pre-Calculus 30; or MATH 102 or MATH 104.
Note: Students wishing to complete a full year of calculus should register for either MATH 112 or 116 for Term 2. At the completion of MATH 110, students will be allowed the option of changing their choice of the Term 2 course. Students may have credit for only one of MATH 110, 121, 123 or 125.
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.
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.
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.
MATH 128.3 — 1/2(3L-1.5P)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.
Prerequisite(s): MATH 121 or MATH 125.
Note: Math 128 is designed to bring students who have credit for MATH 121 or MATH 125 to the same level as students who have completed MATH 110 and MATH 116. It is intended to complete the basic introduction to calculus for students in business, economics and the life sciences who may wish to take additional courses in mathematics and statistics. Students with credit for MATH 110, 112, 116, 123 or 124 may not take this course for credit.
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 MATH 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 or MATH 238 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 276 may not take this course for credit. Students obtaining a grade of 80% or better in this course may request permission from the Head of the Department of Mathematics and Statistics to register in courses for which MATH 276 is the stated prerequisite.
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 or 238 may not take this course for credit. Students obtaining a grade of 80% or better in this course may request permission from the Head of the Department of Mathematics and Statistics to register in courses for which MATH 238 is the stated prerequisite.
MATH 238.3 — 1(3L-1.5P)Introduction to Differential Equations and Series
Solutions of first order and linear differential equations, infinite sequences and series, power series, Taylor's series, power series solutions of differential equations, and elements of mathematical modelling.
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 are encouraged to take this course. Students with credit for MATH 224 or 226 may not take this course for credit.
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 comprising an honours program in either mathematics or statistics.
MATH 264.3 — 1/2(3L)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.
Prerequisite(s): 3 credit units of MATH or STAT.
Note: Students are not permitted to take more than one of MATH 264, 266 or 358 for credit. May not be included in the courses comprising a major or honours in either 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
Vector analysis, differentiation and integration of functions of several variables, line integrals and surface integrals.
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
An extension of MATH 276 to include a fuller discussion of parametrized surfaces and surface integrals, derivative as a linear mapping, inverse and implicit function theorems, change of variable formula for multiple integrals, Stokes' theorem and generalizations, max.-min. problems with constraints and analysis of critical points.
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 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 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, Sturm-Liouville problem, physical origin of heat, wave and Laplace equations, separation of variables, introduction to Fourier series.
Formerly: Half of MATH 338.6
Prerequisite(s): MATH 224.3 or MATH 226.3 or MATH 238.3 (or approval of instructor/department)
Note: Students with credit for MATH 338 may not take this course for credit.
MATH 339.3 — 1(3L-1.5P)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.
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 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 and MATH 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, MATH 361, or MATH 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, MATH 362, or MATH 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 comprising an honours program in either mathematics or statistics. Students with credit for MATH 360, MATH 361 or MATH 362 may not take this course 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 comprising an honours program in either 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 432.3 — 1/2(3L)Dynamical Systems and Chaos
One dimensional dynamics; the quadratic family, symbolic dynamics and chaos. Period doubling; conservative systems, action angle variables, KAM theory; complex analytic dynamics, the Mandelbrot and Julia sets.
Prerequisite(s): MATH 277, 266 and 379.
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 438.3 — 1/2(3L)Methods of Applied Mathematics
Calculus of variations, integral equations and applications.
Prerequisite(s): MATH 238, 276 and 277.
Note: Cannot receive credit for MATH 438.3 and MATH 838.3.
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 350.6 and MATH 452.3.
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; 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.
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 863.3 — 1/2(3L)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.
Note: MATH 862.3 is not a prerequisite for this course.
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 898.3Special Topics
Offered occasionally in special situations. Students interested in these courses should contact the department for more information.
MATH 899.6Special Topics
Offered occasionally in special situations. Students interested in these courses should contact the department for more information.
MATH 990Seminar
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 992.0Project
Students undertaking the project Master's degree (M.Math.) must register for this course.
MATH 994Research
Students writing a Master's thesis must register for this course.
MATH 996Research
Students writing a Ph.D. thesis must register for this course.
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