Results 1 - 72 of 72 Courses

Mathematics
Department of Mathematics & Statistics, College of Arts and Science

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Some courses are restricted to students enrolled in a particular college. Restrictions are noted in prerequisites.

UNDERGRADUATE DEGREE COURSES
MATH 100.6
Registration Info — 2004-2005 Regular Session» Mathematics for Education Students
1&2(3L)
Prerequisite(s): Mathematics A30 or B30 or C30 (or, under the old mathematics curriculum, Algebra 30). For students intending to enter the Elementary Program in the College of Education.

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.

Note: This course may not be included in the courses comprising a major or honours in Mathematics or Statistics and does not meet the requirement of any Arts & Science degree program. Students who have credit for a university course in mathematics (at least 3 credit units) are not permitted to take MATH 100 for credit. Students who have taken MATH 100, and subsequently take other junior mathematics courses, will be governed by the regulations of the Department of Mathematics and Statistics.

MATH 101.3
Registration Info — 2004-2005 Regular Session» Elementary Calculus
1/2(3L)
Prerequisite(s): Mathematics B30 (or Algebra 30).

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

Note: This course may not be included in the courses comprising a major or Honours in Mathematics or Statistics.

This course may not be used as a prerequisite for MATH 112 or 116. Students who have credit for MATH 102.6 may not take this course for credit.

This course may not be used in Requirement 1 for Program Type C.

MATH 110.3
Registration Info — 2004-2005 Regular Session» Calculus I
1/2(3L-1.5P)
Prerequisite(s): Mathematics B30 and Mathematics C30 (or, under the old mathematics curriculum, Algebra 30 and Geometry-Trigonometry 30).

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

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 who have credit for MATH 112, 116, or 123 may not take this course for credit. Students who have credit for the former MATH 102 and subsequently take MATH 110 will lose credit for half of MATH 102. Students who have credit for MATH 101 and subsequently take MATH 110 will lose credit for MATH 101.

MATH 112.3
Registration Info — 2004-2005 Regular Session» Rudiments of Integral Calculus
1/2(3L-1.5P)
Prerequisite(s): MATH 110.

Techniques of integration; the definite integral and simple differential equations - with applications and numerical techniques.

Note: MATH 112 is intended to be a terminal course in calculus and should be taken only by those students who are content to limit their mathematical options. Students who may require a more thorough grounding in calculus are advised to take MATH 116. MATH 112 may not be included in the courses comprising a major or Honours in Mathematics or Statistics. Students who have credit for MATH 116 or 124 may not take this course for credit. Students with credit for MATH 123 may take this course for credit. Students who take MATH 112 and who subsequently require MATH 116 in their programs, must take MATH 116 but will not receive credit for it toward degree requirements in the College of Arts and Science. Students who have credit for the former MATH 102 and subsequently take MATH 112 will lose credit for half of MATH 102.

MATH 115.3
Registration Info — 2004-2005 Regular Session» Calculus for Pharmacy
1/2(3L-1.5P)
Prerequisite(s): MATH B30, MATH C30. Restricted to students enrolled in the College of Pharmacy & Nutrition.

Introduction to differential and integral calculus. Techniques of differentiation, curve sketching, and rate problems. Emphasis will be on topics that are most relevant to pharmaceutical applications of calculus.

MATH 116.3
Registration Info — 2004-2005 Regular Session» Calculus II
1/2(3L-1.5P)
Prerequisite(s): MATH 110.

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

Note: MATH 116 is 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. MATH 116 is the specified prerequisite for most second-year courses in mathematics and statistics, including all courses accepted in major and Honours programs.

Students who have credit for MATH 112 or 124 may not take this course for credit. Students with credit for MATH 123 may take this course for credit. Students who have credit for the former MATH 102 and subsequently take MATH 116 will lose credit for half of MATH 102.

MATH 124.3
Registration Info — 2004-2005 Regular Session» Calculus II for Engineers
2(3L-1.5P)
Prerequisite(s): MATH 110. Restricted to students enrolled in the College of Engineering.

Differentiation and integration of inverse trigonometric functions, 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.

MATH 211.3
Registration Info — 2004-2005 Regular Session» Numerical Analysis I
1/2(3L-1P)
Prerequisite(s): MATH 110 and 116.

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

MATH 213.3
Registration Info — 2004-2005 Regular Session» Linear Programming and Game Theory
2(3L)
Prerequisite(s): One of MATH 100, 101, (or 102), 110 or STATS 103.

Inequalities, Solutions of Linear Equations, Simplex Method, Transportation Problem, Duality, Game Theory and its transformation into a linear programming problem. Applications will be emphasized.

Note: May not be included in the courses comprising a major or Honours in Mathematics or Statistics. Students with credit for COMM 393 or CMPT 393 may not take this course for credit.

MATH 223.3
Registration Info — 2004-2005 Regular Session» Intermediate Calculus
1(3L-1P)
Prerequisite(s): MATH 110 and 124. Restricted to students enrolled in the College of Engineering.

Vectors in two and three dimensions, vector calculus, space geometry, multiple integration and partial differentiation, line integrals and Green's Theorem.

MATH 224.3
Registration Info — 2004-2005 Regular Session» Differential Equations
2(3L-1P)
Prerequisite(s): MATH 110 and 124. Restricted to students enrolled in the College of Engineering.

Differential equations of first and second order, sequences and series, convergence, Taylor's Series and elementary series.

MATH 225.3
Registration Info — 2004-2005 Regular Session» Intermediate Calculus I
1(3L-1P)
Prerequisite(s): MATH 110 and 116.

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

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
Registration Info — 2004-2005 Regular Session» Intermediate Calculus II
2(3L-1P)
Prerequisite(s): MATH 110 and 116.

The topics to be discussed include infinite sequences and series, complex numbers, and first order and linear differential equations.

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
Registration Info — 2004-2005 Regular Session» Introduction to Differential Equations and Series
1(3L-1.5P)
Prerequisite(s): MATH 110 and 116.

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.

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
Registration Info — 2004-2005 Regular Session» Euclidean Geometry
1/2(3L-1P)
Prerequisite(s): One of MATH 100, 101, (or 102), 110 or STATS 103.

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

Note: It is recommended that students have had a basic introduction to high school geometry. This course may not be included in the courses comprising an Honours program in either Mathematics or Statistics.

MATH 264.3
Registration Info — 2004-2005 Regular Session» Linear Algebra
1/2(3L)
Prerequisite(s): One of MATH 100, 101, (or 102), 110 or STATS 103.

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

Note: Students are not permitted to take more than one of MATH 264, 266 or 358 for credit. This course may not be included in the courses comprising a major or Honours in Mathematics and Statistics

MATH 266.3
Registration Info — 2004-2005 Regular Session» Linear Algebra I
1/2(3L)
Prerequisite(s): MATH 110 and 116.

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.

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
Registration Info — 2004-2005 Regular Session» Vector Calculus I
1(3L-1.5P)
Prerequisite(s): MATH 110 and 116.

Vector analysis, differentiation and integration of functions of several variables, line integrals and surface integrals.

Note: Students intending to enter an Honours or Double Honours program are encouraged to take this course.

Students are not permitted to take MATH 276 and either 223 or 225 for credit.

MATH 277.3
Registration Info — 2004-2005 Regular Session» Vector Calculus II
1/2(3L-1.5P)
Prerequisite(s): MATH 276 (or MATH 225 with a grade of 80% or better).

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.

MATH 313.3
Registration Info — 2004-2005 Regular Session» Numerical Analysis II
1(3L)
Prerequisite(s): MATH 211, and either 266 or an equivalent course in linear algebra.

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.

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

MATH 314.3
Registration Info — 2004-2005 Regular Session» Numerical Analysis III
2(3L)
Prerequisite(s): MATH 211 and 238.

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

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

MATH 315.3
Registration Info — 2004-2005 Regular Session» Applications of Numerical Methods
1/2(3L)
Prerequisite(s): MATH 238 or 224 or 226; MATH 264 or 266; MATH 211.

Surveys numerical methods used in solving engineering problems in the areas of: linear equations, non-linear equations, eigenvalue problems, curve fitting and interpolation, numerical differentiation and integration, ordinary differential equations (initial-value and boundary-value problems), partial differential equations and optimization.

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

MATH 327.3
Registration Info — 2004-2005 Regular Session» Graph Theory
1(3L)
Prerequisite(s): MATH 264 or 266, and either CMPT 260 or 6 credit units of 200-level mathematics.

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

MATH 328.3
Registration Info — 2004-2005 Regular Session» Combinatorics and Enumeration
2(3L)
Prerequisite(s): MATH 264 or 266, and either CMPT 260 or 6 credit units of second year mathematics.

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.

MATH 338.6
Registration Info — 2004-2005 Regular Session» Differential Equations II
1&2(3L)
Prerequisite(s): MATH 238 or 226.

Use of Laplace transforms, theory of infinite series, solution of ordinary linear equations in series, Sturm-Liouville problems, Fourier series, Bessel and Legendre functions, the Fourier integral, the Laplace, diffusion, and wave equations, calculus of variations, matrices, quadratic forms, oscillations of conservative systems.

MATH 350.6
Registration Info — 2004-2005 Regular Session» Differential Geometry
1&2(3L)
Prerequisite(s): MATH 276 or 225, and 277.

Curves in 3-space, Euclidean motions, surface theory, introduction to differentiable manifolds, Gaussian and mean curvature, imbedding conditions, geodesics, parallel transport, Gauss-Bonnet theorem.

MATH 358.6
Registration Info — 2004-2005 Regular Session» Projective Geometry and Linear Algebra
1&2(3L)
Prerequisite(s): MATH 110 and 112 or 116.

Provides an introduction to the projective line and plane, determinants, vector spaces, linear equations, linear transformations, and eigenvalues.

Note: Particularly recommended for teachers of mathematics. May not be included in the courses comprising an Honours program in mathematics or statistics.

Students are not permitted to take more than one of MATH 264, 266 or 358. Students who have credit for a course or half-course in linear algebra are not permitted to take this course for credit.

MATH 360.6
Registration Info — 2004-2005 Regular Session» Algebra I
1&2(3L)
Prerequisite(s): MATH 264, 266 or 358.

Groups, rings, unique factorization domains, modules over principal ideal domains, vector spaces, linear transformations and canonical forms.

Note: Students may not obtain credit for both MATH 363 and 360.

MATH 363.3
Registration Info — 2004-2005 Regular Session» Abstract Algebra
2(3L)
Prerequisite(s): One of MATH 100, 101, (or 102), 110 or STATS 103.

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.

Note: Recommended for teachers of mathematics. May not be included in the courses comprising an Honours program in either Mathematics or Statistics.

Students having credit for MATH 360 may not take this course for credit.

MATH 364.3
Registration Info — 2004-2005 Regular Session» Number Theory
1(3L)
Prerequisite(s): One of MATH 100, 101, (or 102), 110 or STATS 103.

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.

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
Registration Info — 2004-2005 Regular Session» Linear Algebra II
1(3L)
Prerequisite(s): MATH 266.

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

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

MATH 371.3
Registration Info — 2004-2005 Regular Session» Metric Spaces and Continuous Functions
1(3L)
Prerequisite(s): MATH 238 and 276.

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.

MATH 373.3
Registration Info — 2004-2005 Regular Session» Integration Theory
1/2(3L)
Prerequisite(s): MATH 371.

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.

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

MATH 379.3
Registration Info — 2004-2005 Regular Session» Complex Analysis
2(3L)
Prerequisite(s): MATH 225 or 276, and 226 or 238.

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

MATH 401.0
Registration Info — 2004-2005 Regular Session» Seminar
1&2(1.5S)

Students in Honours Mathematics or in Double Honours Programs in Mathematics and a second subject are required to participate in this seminar during their third and fourth years.

MATH 431.3
Registration Info — 2004-2005 Regular Session» Ordinary Differential Equations
1/2(3L)
Prerequisite(s): MATH 277, 366 and 371.

Existence and uniqueness of solutions; time dependent and time independent linear systems; submanifolds of euclidean space, phase space, vector fields, flows; equilibria; linearization; stable, unstable and center manifolds; local bifurcations; planar flows; numerical methods.

MATH 432.3
Registration Info — 2004-2005 Regular Session» Dynamical Systems and Chaos
1/2(3L)
Prerequisite(s): MATH 277, 266 and 379.

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.

MATH 433.3
Registration Info — 2004-2005 Regular Session» Applied Group Theory
1/2(3L)
Prerequisite(s): MATH 276 and 366 (or MATH 276 and 266 and permission of the instructor). MATH 277 is desirable.

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).

MATH 434.3
Registration Info — 2004-2005 Regular Session» Applied Topology in Physics and Chemistry
1/2(3L)
Prerequisite(s): MATH 276, or 225 with permission of the instructor. It is advisable to complete MATH 371 and 379 either previously or concurrently.

Basic notions of topology, knot theory and graph theory are introduced and applied to the study of physical and chemical problems such as the classification of defects in an ordered medium as well as knotting and linking in models of DNA.

MATH 438.3
Registration Info — 2004-2005 Regular Session» Methods of Applied Mathematics
1(3L)
Prerequisite(s): MATH 238, 276 and 277.

Calculus of variations, integral equations and applications.

MATH 439.3
Registration Info — 2004-2005 Regular Session» Partial Differential Equations
2(3L)
Prerequisite(s): MATH 238, 276 and 277.

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

MATH 485.3
Registration Info — 2004-2005 Regular Session» Elements of General Topology
1/2(3L)
Prerequisite(s): MATH 371.

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




Special Topics

These courses are offered occasionally by visiting faculty and in other special situations. Students interested in these courses should contact the department for more information.
MATH 398.3

1/2(3S)

MATH 399.6

1&2(3S)

MATH 498.3

1/2(3S)

MATH 499.6

1&2(3S)

GRADUATE COURSES
Department of Mathematics & Statistics, College of Graduate Studies & Research

The following courses are for students who have completed the Honours program in mathematics, or equivalent; other students must obtain the permission of the department.

MATH 814.6
Registration Info — 2004-2005 Regular Session» Numerical Solution of Ordinary and Partial Differential Equations
1&2(3L)
Prerequisite(s): MATH 314 and 338; knowledge of a programming language.

Ordinary 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.

MATH 818.3
Registration Info — 2004-2005 Regular Session» Special Topics in Applied Mathematics
1/2(3L), 1&2(3L)
Prerequisite(s): A graduate course in applied mathematics; or permission of the department.

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.

MATH 830.6
Registration Info — 2004-2005 Regular Session» Applied Functional Analysis
1/2(3L)
Prerequisite(s): A course in linear algebra and an intermediate level calculus course.

Cauchy sequences, uniform convergence (e - d); Hilbert spaces; distributions and Sobolev spaces; boundary - value problems in (partial) differential equations; variational methods; weak solutions; Lax - Milgram lemma; finite element method.

MATH 832.3
Registration Info — 2004-2005 Regular Session» Mathematical Foundations of Classical Mechanics
1/2(3S)
Prerequisite(s): MATH 350; or permission of the department.

Symplectic geometry, canonical transformations, Poisson structures, Lagrangian systems, Legendre transformations, Hamiltonian systems, non-relativistic and relativistic mechanical systems.

MATH 833.3
Registration Info — 2004-2005 Regular Session» Mathematical Foundations of Quantum Theory
1/2(3L)
Prerequisite(s): MATH 373; or permission of the department.

Linear operators in Hilbert space, spectral theorem for self-adjoint operators, axioms of non-relativistic quantum mechanics, measurements, Schrödinger and Heisenberg pictures, commutation relations.

MATH 834.3
Registration Info — 2004-2005 Regular Session» Mathematical Foundations of Relativity
1/2(3L)
Prerequisite(s) or Corequisite(s): MATH 350 or Corequisite(s): MATH 852; or permission of the instructor.

Space-time as a differentiable manifold, Minkowski space equations of general relativity, cauchy problem, cosmological models.

MATH 835.3
Registration Info — 2004-2005 Regular Session» Non-linear Analysis
1/2(3L)
Prerequisite(s): MATH 852; and a course in Functional Analysis or permission of the department.

Non-linear P.D.E. including: Einstein's equations, Yang-Mills equations, non-linear wave and Schrödinger equations, Korteweg-de Vries equation. Infinite dimensional Hamiltonian systems, classical field theories, conservation laws, symmetry groups. Inverse scattering method. Bäcklund transformations.

MATH 837.6
Registration Info — 2004-2005 Regular Session» Differential and Integral Equations
1&2(3L)
Prerequisite(s): MATH 366 and 371.

Existence and uniqueness theory, self-adjoint and non-self-adjoint boundary-value problems, Poincaré-Bendixson theory, integral equations of the Fredholm Type, singular integral equations, solutions of differential equations in a Banach space.

MATH 838.6
Registration Info — 2004-2005 Regular Session» Theory of Partial Differential Equations
1&2(3L)
Prerequisite(s): MATH 439.

The Cauchy problem, Dirichlet and Neumann problems, existence and uniqueness.

MATH 851.6
Registration Info — 2004-2005 Regular Session» Differential Geometry
1/2(3L)
Prerequisite(s): MATH 350; or permission of the department.

Differentiable manifolds (over R & C), tensor fields, differential forms, and Lie groups. Stoke's theorem, Poincaré and Dolbeault lemmas. Sheaf cohomology theory and the De Rham theorem. Vector bundles, connections and Chern classes, and Grassmannians. Dolbeault cohomology, Elliptic operator theory and the Hodge theorem. Poincaré and Serre duality.

MATH 852.3
Registration Info — 2004-2005 Regular Session» Differential and Riemannian Geometry I
1/2(3L)
Prerequisite(s): MATH 350.

Manifolds, tensor fields, integral curves and flows, Lie derivative, exterior calculus, Frobenius Theorem, vector and principal bundles, connections, curvature, Cartan equations, holonomy, Riemannian and pseudo-Riemannian geometry, equivalence problem.

MATH 860.6
Registration Info — 2004-2005 Regular Session» Algebraic Number Theory
1&2(3L)

Valuations, p-adic numbers, quadratic forms, the Hasse-Minkowski theorem, modules, orders, Dirichlet's unit theorem, divisor theory for algebraic number fields.

MATH 862.3
Registration Info — 2004-2005 Regular Session» Algebra I
1/2(3L)
Prerequisite(s): MATH 360.

Rings, modules, ideals, factorization, field theory, Galois theory.

MATH 863.3
Registration Info — 2004-2005 Regular Session» Algebra II
1/2(3L)
Prerequisite(s): MATH 862.

Commutative algebra, multilinear algebra, non-commutative algebra.

MATH 871.3
Registration Info — 2004-2005 Regular Session» Abstract Analysis
1/2(3L)
Prerequisite(s): MATH 373.

Basic Measure and Integration Theory. Regular Borel Measure. The Radon-Nikodym Theorem, Product Measure and Fubini's Theorem. Fourier Analysis on Rn.

MATH 872.0
Registration Info — 2004-2005 Regular Session» Special Topics in Pure Mathematics
1/2(3L), 1&2(3L)

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.

MATH 875.3
Registration Info — 2004-2005 Regular Session» Functional Analysis
1/2(3L)

Introduces functional analysis with an emphasis on Banach and Hilbert spaces. The main results of Hahn-Banach, Krein-Milman and Banach-Steinhaus are developed and used to study concrete spaces, operators, the projection lattice and the ideal of compact operators on Hilbert space.

MATH 876.3
Registration Info — 2004-2005 Regular Session» Banach Algebras and Spectral Theory
1/2(3L)
Prerequisite(s): MATH 875; or equivalent.

The necessary theory of Banach Algebras and the functional calculus are developed for the spectral theorem for bounded self-adjoint operators on Hilbert space. Various applications and extensions presented.

MATH 879.3
Registration Info — 2004-2005 Regular Session» Complex Analysis
1/2(3L)
Prerequisite(s): MATH 379.

After a review of basic properties of analytic functions the course will cover such topics as: Analytic Continuation, Riemann Mapping Theorem, Mittag-Leffler's Theorem, Runge's Theorem, Picard's Theorem, etc.

MATH 881.6
Registration Info — 2004-2005 Regular Session» General Topology
1&2(3L)

MATH 882.3
Registration Info — 2004-2005 Regular Session» Algebraic Topology I
1/2(3L)
Prerequisite(s): MATH 485.

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

MATH 883.3
Registration Info — 2004-2005 Regular Session» Algebraic Topology II
1/2(3L)
Prerequisite(s): MATH 882.

Simplicial and Singular Homology, The Lefschetz Fixed-Point Theorem, Cohomology, Duality in Manifolds.

MATH 990
Registration Info — 2004-2005 Regular Session» 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 992.6
Registration Info — 2004-2005 Regular Session» Project

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

MATH 994
Registration Info — 2004-2005 Regular Session» Research

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

MATH 996
Registration Info — 2004-2005 Regular Session» Research

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

  Results 1 - 72 of 72 Courses