## Mathematics (MATH) Courses Listing

Topics covered in this course include: numeracy and number sense, measurement, geometry and spacial reasoning, patterning, algebra, probability, and data management. Special attention is given to the development of a conceptual understanding of mathematics, as well as the appropriate use of manipulatives and concrete materials.

Credit Weight:
1.0
Offering:
3-0; 3-0
Notes:
This course is open only to students in either a Primary-Junior or Junior-Intermediate Concurrent Education program. The course may not be used to fulfill Math or Science elective requirements in any other programs.
Course Classifications:
Type C: Engineering, Mathematical and Natural Sciences
An introduction to probability; random variables; discrete distributions. Analysis of data: measures of dispersion and location; normal, t, chi-square and f tests, contingency tables, analysis of variance; linear regression and correlation.

Credit Weight:
0.5
Offering:
3-1; 0-0
Notes:
This course is not acceptable for credit in Mathematics or Computer Science programs. Students in other programs can receive credit for only one of Mathematics 0210, 0212 and 2321.
Course Classifications:
Type C: Engineering, Mathematical and Natural Sciences
An introduction to probability; the binomial, poisson and normal distributions; analysis of data; statistical inference; ANOVA; linear regression and correlation; nonparametric methods.

Credit Weight:
0.5
Offering:
3-1; 0-0
Notes:
This course is not acceptable for credit in Mathematics or Computer Science programs. Students in other programs can receive credit for only one of Mathematics 0210, 0212 and 2321.
For students without grade 12 U Advanced Functions or equivalent. Cartesian coordinate systems; linear equations and straight lines; quadratic equations and parabolas; functions, including domain, range, graph, and composition of functions; angles and radian measure; the trigonometric functions, their graphs, and identities; the sine and cosine rules; polar coordinates; conic sections; and inequalities.

Credit Weight:
0.5
Offering:
3-2; 0-0
Course Classifications:
Type C: Engineering, Mathematical and Natural Sciences
For students without grade 12 U Calculus and Vectors or equivalent. Cartesian coordinates; vectors in two and three dimensions; the dot product and components of vectors; the cross product; equations of lines and planes; complex numbers; vector spaces over the real and complex number systems; linear independence, bases and spanning sets; subspaces; matrices; addition and scalar multiplication of matrices; matrix multiplication; the transpose of a matrix; invertible matrices; systems of linear equations and row reduction; and determinants, including Cramer's rule.

Credit Weight:
0.5
Offering:
3-2; 0-0
Course Classifications:
Type C: Engineering, Mathematical and Natural Sciences
Exponents and logarithms and their algebra; geometric progressions; binomial coefficients and the binomial theorem; mathematical induction; sequences and their limits; the exponential and natural logarithm functions; infinite series; and tests for convergence of infinite series.

Credit Weight:
0.5
Prerequisite(s):
Mathematics 1051
Offering:
0-0; 3-2
Notes:
Students who have previous credit in Mathematics 1052 - Introductory Calculus I and Mathematics 1072 - Introductory Calculus II, can be given credit for Mathematics 1077 - Sequences and Series and Mathematics 1078 - Elementary Calculus. Students who have previous credit in Mathematics 1052 but not Mathematics 1072 cannot be given credit for either Mathematics 1077 or Mathematics 1078.
Course Classifications:
Type C: Engineering, Mathematical and Natural Sciences
For students without Grade 12 U Calculus and Vectors or equivalent. Limits of functions and their properties; limits of exponential, logarithmic, and trigonometric functions; indeterminate and infinite limits; continuity of functions; the definition of derivatives; equations of tangent lines; differentiation of the elementary functions; differentiation rules; applications of differential calculus including optimization, related rates, and curve sketching; anti-derivatives, the fundamental theorem of calculus, and area problems.

Credit Weight:
0.5
Corequisite(s):
Mathematics 1077
Offering:
0-0; 3-2
Notes:
Students who have previous credit in Mathematics 1052 - Introductory Calculus I and Mathematics 1072 - Introductory Calculus II, can be given credit for Mathematics 1077 - Sequences and Series and Mathematics 1078 - Elementary Calculus. Students who have previous credit in Mathematics 1052 but not Mathematics 1072 cannot be given credit for either Mathematics 1077 or Mathematics 1078.
Course Classifications:
Type C: Engineering, Mathematical and Natural Sciences
Students are taught the principles of mathematics, both mechanics and applications, in relation to whole numbers, common fractions, ratio and proportion, decimal fractions, per cent, signed numbers, exponents, scientific notation, and simple algebraic expressions. Students will also learn calculator usage. Examples drawn from native art and culture will be incorporated as appropriate, and the students will write and present papers on topics relating mathematics and Aboriginal culture.

Credit Weight:
0.0
Offering:
3-1; 0-0
Notes:
A non-credit course open only to Native Access students
Continues on from Math 1130. Topics include: Solving equations; formula manipulation; measurement, including the English and metric systems; and descriptive statistics, including graphs and measures of central tendency. Examples drawn from native art and culture will be incorporated as appropriate. The students will write and present papers on topics relating mathematics and Aboriginal culture.

Credit Weight:
0.0
Offering:
0-0; 3-1
Notes:
A non-credit course open only to Native Access students
Students are taught the principles of mathematics, both mechanics and applications, in relation to whole numbers, common fractions, ratio and proportion, decimal fractions, and per cent. Students will also be taught about weights and measures, including the metric and English systems; computing dosages; and temperature.

Credit Weight:
0.0
Offering:
3-1; 0-0
Notes:
A non-credit course open only to students in the Native Nursing Entry program.
Course Classifications:
Type C: Engineering, Mathematical and Natural Sciences
Continues on from Mathematics 1135. Topics include: exponents; scientific notation; calculator usage; solving equations; formula manipulation; and descriptive statistics, including graphs and measures of central tendency.

Credit Weight:
0.00
Prerequisite(s):
Mathematics 1135 or permission of the Chair of the Department
Offering:
0-0; 3-1
Notes:
A non-credit course open only to students in the Native Nursing Entry program.
Course Classifications:
Type C: Engineering, Mathematical and Natural Sciences
Functions, the derivative, logarithmic and exponential functions, the graphs of functions, applications of the derivative.

Credit Weight:
0.5
Prerequisite(s):
MHF4U or permission of the Chair of the Department
Offering:
3-1; 0-0
Notes:
Students who have previous credit in Mathematics 1160 may not take Mathematics 1151 for credit.
Course Classifications:
Type C: Engineering, Mathematical and Natural Sciences
Fundamental Theorem of Calculus, integration, applications of integration, and infinite series.

Credit Weight:
0.5
Prerequisite(s):
Mathematics 1151 or permission of the Chair of the Department
Offering:
0-0; 3-1
Notes:
Students who have previous credit in Mathematics 1160 may not take Mathematics 1152 for credit.
Course Classifications:
Type C: Engineering, Mathematical and Natural Sciences
Basic properties of the real number system; limits and continuity of functions; derivatives and differentiation formulas; applications of derivatives; anti-derivatives, definite integrals, indefinite integrals; Fundamental Theorem of Calculus; u-substitution.

Credit Weight:
0.5
Prerequisite(s):
MHF4U or permission of the Chair of the Department
Offering:
3-1; 0-0
Notes:
Students who have previous credit in Mathematics 1180 may not take Mathematics 1171 for credit.
Course Classifications:
Type C: Engineering, Mathematical and Natural Sciences
Applications of integrals; one-to-one functions and inverses; logarithmic, exponential, power and inverse trigonometric functions; techniques of integration; limits of sequences; indeterminate forms; improper integrals; infinite series; tests for convergence; Taylor series; power series.

Credit Weight:
0.5
Prerequisite(s):
Mathematics 1171 or permission of the Chair of the Department
Offering:
0-0; 3-1
Notes:
Students who have previous credit in Mathematics 1180 may not take Mathematics 1172 for credit.
Course Classifications:
Type C: Engineering, Mathematical and Natural Sciences
Application of differentiation; definite and indefinite integrals; transcendental functions; complex numbers; techniques of integration.

Credit Weight:
0.5
Prerequisite(s):
Mathematics 1077 or MHF4U
Offering:
3-1; 0-0
Notes:
Engineering students may substitute Mathematics 1171 for Mathematics 1210, with permission of the Dean of the Faculty of Engineering.
Course Classifications:
Type C: Engineering, Mathematical and Natural Sciences
Applications of integration, introduction to multiple integrals sequences and series; power series.

Credit Weight:
0.5
Prerequisite(s):
Mathematics 1210
Offering:
0-0; 3-1
Notes:
Engineering students may substitute Mathematics 1172 for Mathematics 1230, with permission of the Dean of the Faculty of Engineering.
Course Classifications:
Type C: Engineering, Mathematical and Natural Sciences
Sets, logic, and functions; Boolean Algebras, Algorithms; Basic counting principles; permutations and combinations; discrete probability, recurrence relations; principle of inclusion and exclusion; pigeonhole principle; graph theory.

Credit Weight:
0.5
Prerequisite(s):
MHF4U or permission of the Chair of the Department
Offering:
3-1; 0-0
Notes:
Students who have previous credit in Mathematics 1281 may not take Mathematics 1271/1272 for credit.
Course Classifications:
Type C: Engineering, Mathematical and Natural Sciences
An introduction to proofs and to writing mathematics. Logic; propositional calculus; quantifiers, rules of inference, sets; set operations; cardinality and countability; relations, including partial orders and equivalence relations; functions; proof techniques such as direct proof; indirect proof; contradiction, and mathematical induction; basic properties of the integers.

Credit Weight:
0.5
Prerequisite(s):
MHF4U or permission of the Chair of the Department
Offering:
0-0; 3-1
Notes:
Students who have previous credit in Mathematics 1281 may not take Mathematics 1271/1272 for credit.
Course Classifications:
Type C: Engineering, Mathematical and Natural Sciences
An introductory course in ordinary differential equations. First order differential equations; exact equations; separation of variables, integrating factors, linear and non-linear equations, higher order differential equations, linear, constant co-efficients, homogeneous, non-homogeneous. Systems of differential equations, Laplace transforms, series solution. The emphasis is on applications to engineering problems.

Credit Weight:
0.5
Prerequisite(s):
Mathematics 1230
Offering:
3-1; 0-0
Notes:
Students who have previous credit in Mathematics 3010 may not take Mathematics 2050 for credit.
Course Classifications:
Type C: Engineering, Mathematical and Natural Sciences
The first part of the course is an introduction to matrix algebra. Solutions of simultaneous equations. Gaussian elimination. Vector and matrix notation. Determinants. Linear independence. Eigenvectors and diagonalization.

The second part of the course is an introduction to probability and statistics. Simple ways of analyzing data. Concept of probability. Discrete and continuous probability. Point and interval estimation. Significance tests. Regression and correlation analysis.

Credit Weight:
0.5
Offering:
0-0; 3-1
Course Classifications:
Type C: Engineering, Mathematical and Natural Sciences
The second part of the course is an introduction to probability and statistics. Simple ways of analyzing data. Concept of probability. Discrete and continuous probability. Point and interval estimation. Significance tests. Regression and correlation analysis.

Matrix algebra, determinants, and systems of linear equations; eigenvalues, eigenvectors, and diagonalization; separable and linear ordinary differential equations (ODEs) with constant coefficients; Laplace transforms; systems of linear ODEs; Fourier transforms and Fourier series.

Credit Weight:
0.5
Prerequisite(s):
Mathematics 1230
Offering:
4 hours of lectures per week plus 1 hour of tutorials every second week, in the fall term
Notes:
Restricted to students in the BEng (Electrical Engineering) Lakehead Georgian Partnership program.
Solutions of first order differential equations; applications. Solutions of second order linear differential equations with constant coefficients. Methods of finding particular solutions. Solutions of second order linear differential equations with variable coefficients. Applications.

Credit Weight:
0.5
Prerequisite(s):
Mathematics 1152 or 1172
Offering:
3-0; or 3-0
Course Classifications:
Type C: Engineering, Mathematical and Natural Sciences
Coordinate systems and vectors; parametric curves and surfaces; partial differentiation; multiple integration; vector fields; and vector calculus including Green's theorem, Stokes' theorem, and the divergence theorem.

Credit Weight:
0.5
Prerequisite(s):
Mathematics 1172 or permission of the Chair of the Department
Offering:
3-0; or 3-0
Course Classifications:
Type C: Engineering, Mathematical and Natural Sciences
An introduction to groups, rings, and fields. Topics include properties of integers, subgroups, group homomorphisms, normal subgroups, factor groups, permutation groups, subrings, ring homomorphisms, ideals, and quotient rings.

Credit Weight:
0.5
Prerequisite(s):
Mathematics 1272
Offering:
3-0; 0-0
Notes:
Students who have previous credit in both Mathematics 2231 and 2233 may not take Mathematics 2232/2234 for credit.
Course Classifications:
Type C: Engineering, Mathematical and Natural Sciences
The properties of groups, rings, and fields are developed. Topics include polynomial rings, factorization, unique factorization domains, Euclidean domains, simple groups, Fundamental Theorem of Finite Abelian Groups. Additional topics may include field extensions, finite fields, geometric constructions, and the classificationÂ of groups of small order.

Credit Weight:
0.5
Prerequisite(s):
Mathematics 2232
Offering:
0-0; 3-0
Notes:
Students who have previous credit in both Mathematics 2231 and 2233 may not take Mathematics 2232/2234 for credit.
Course Classifications:
Type C: Engineering, Mathematical and Natural Sciences
Matrices and systems of linear equations; linear transformations and matrices; elementary matrix algebra; determinants; vector spaces; change of bases; real eigenvalues and eigenvectors; applications.

Credit Weight:
0.5
Offering:
3-0; 0-0
Course Classifications:
Type C: Engineering, Mathematical and Natural Sciences
Eigenvalues and eigenvectors; diagonalization; inner product spaces; orthogonal bases; least-squares problems; symmetric matrices; quadratic forms; singular value decomposition; applications.

Credit Weight:
0.5
Prerequisite(s):
Mathematics 2255
Offering:
0-0; 3-0
Course Classifications:
Type C: Engineering, Mathematical and Natural Sciences
Sample space and events, elementary probability. Descriptive statistics using tables and charts. Measures of central tendency, variability and association. Basic discrete and continuous distributions. Hypothesis testing and confidence intervals. Simple linear regression and correlation.

Credit Weight:
0.5
Prerequisite(s):
MHF4U or one FCE in Mathematics
Offering:
3-1; 0-0
Notes:
Not recognized as a mathematics credit for Mathematics or Computer Science majors.
Course Classifications:
Type C: Engineering, Mathematical and Natural Sciences
An introduction to statistical methods. Techniques include estimation, tests of hypothesis, analysis of variance and topics in experimental design. Students will also work with statistical software for data analysis.

Credit Weight:
0.5
Prerequisite(s):
Mathematics 2310
Offering:
3-1; or 3-1
Notes:
Not recognized as a mathematics credit for Mathematics or Computer Science majors.
Course Classifications:
Type C: Engineering, Mathematical and Natural Sciences
Vectors, vector functions, and vector fields. Divergence, curl, and gradient in rectangular, cylindrical, and spherical co-ordinate systems. Line, surface, and multiple integrals. Theorems of Green, Gauss, and Stokes.

Credit Weight:
0.5
Prerequisite(s):
Mathematics 1230
Corequisite(s):
Mathematics 2050
Offering:
3-1; 0-0
Notes:
Students who have previous credit in Mathematics 4012 may not take Mathematics 3012 for credit.
Course Classifications:
Type C: Engineering, Mathematical and Natural Sciences
Power series and series solutions of differential equations. Power series solutions of Bessel's equation. Sturm-Liouville theorem and eigenfunctions. Linear partial differential equations (PDEs). Fourier Series in one and two variables. Fourier-Bessel solutions of boundary value problems. Complex functions and integrals. Cauchy's integral formula.

Credit Weight:
0.5
Prerequisite(s):
Mathematics 3012 and either Mathematics 2050 or 2090
Offering:
0-0; 3-1
Notes:
Students who have previous credit in Mathematics 4032 may not take Mathematics 3032 for credit.
Course Classifications:
Type C: Engineering, Mathematical and Natural Sciences
Error analysis, root finding; numerical integration; solution of linear equations; solution of ordinary and partial differential equations.

Credit Weight:
0.5
Prerequisite(s):
Mathematics 2050 and 2070 or permission of the Chair of the Department
Offering:
0-0; 3-1
Notes:
Students who have previous credit in Mathematics 4050 may not take Mathematics 3050 for credit.
Course Classifications:
Type C: Engineering, Mathematical and Natural Sciences
Basic set theory. Introduction to logic and proofs. Functions and relations. Mathematical induction and recursion. Algorithms; time estimates and orders of magnitude. Basic combinations. Graphs. Boolean algebras.

Credit Weight:
0.5
Offering:
3-1; 0-0
Notes:
Open to students in other programs with permission of the Department. Students who have previous credit in Mathematics 4071 may not take Mathematics 3071 for credit.
Course Classifications:
Type C: Engineering, Mathematical and Natural Sciences
A study of partial differential equations (e.g. diffusion, wave, potential); boundary value problems; Sturm-Liouville problems; Fourier series; special functions.

Credit Weight:
0.5
Prerequisite(s):
Mathematics 2111, 2131
Offering:
3-0; 0-0
Notes:
Students who have previous credit in Mathematics 3131 may not take Mathematics 3111 for credit.
Course Classifications:
Type C: Engineering, Mathematical and Natural Sciences
A study of partial differential equations in polar, cylindrical and spherical co-ordinates; special functions; non-homogeneous problems; Fourier and other transform techniques.

Credit Weight:
0.5
Prerequisite(s):
Mathematics 3111
Offering:
0-0; 3-0
Notes:
Students who have previous credit in Mathematics 3133 may not take Mathematics 3113 for credit.
Course Classifications:
Type C: Engineering, Mathematical and Natural Sciences
A study of partial differential equations (e.g. diffusion, wave, potential); boundary value problems; Sturm-Liouville problems; Fourier series; special functions.

Credit Weight:
0.5
Prerequisite(s):
Mathematics 2111, 2131
Offering:
3-0; 0-0
Notes:
Students who have previous credit in Mathematics 3111 may not take Mathematics 3131 for credit.
Course Classifications:
Type C: Engineering, Mathematical and Natural Sciences
A study of partial differential equations in polar, cylindrical and spherical co-ordinates; special functions; non-homogeneous problems; Fourier and other transform techniques.

Credit Weight:
0.5
Prerequisite(s):
Mathematics 3131
Offering:
0-0; 3-0
Notes:
Students who have previous credit in Mathematics 3113 may not take Mathematics 3133 for credit.
Course Classifications:
Type C: Engineering, Mathematical and Natural Sciences
The geometry of the complex plane, analytic functions, Moebius transformations, the Cauchy-Goursat theorem, power series, the residue theorem, conformal mapping.

Credit Weight:
0.5
Prerequisite(s):
Mathematics 3231 and 3233 or 2131
Offering:
3-0; 0-0
Course Classifications:
Type C: Engineering, Mathematical and Natural Sciences
Directed studies and research under the guidance of a faculty member in an area of mathematics. The student's transcript shall contain a title descriptive of the work accomplished under the course.

Credit Weight:
0.5
Prerequisite(s):
Permission of the Chair of the Department
Special Topic:
Yes
Offering:
3-0; 0-0
Course Classifications:
Type C: Engineering, Mathematical and Natural Sciences
Directed studies and research under the guidance of a faculty member in an area of mathematics. The student's transcript shall contain a title descriptive of the work accomplished under the course.

Credit Weight:
0.5
Prerequisite(s):
Permission of the Chair of the Department
Special Topic:
Yes
Offering:
0-0; 3-0
Course Classifications:
Type C: Engineering, Mathematical and Natural Sciences
Review of logic and set theory; properties of the real numbers; order completeness of the reals; metric space topology including completeness, compactness, and connectedness; numerical sequences and series.

Credit Weight:
0.5
Prerequisite(s):
Mathematics 1172 and either Mathematics 1272 or permission of the Chair of the Department
Offering:
3-0; 0-0
Course Classifications:
Type C: Engineering, Mathematical and Natural Sciences
Limits of functions, continuity, the derivative of a real function, the mean value theorems, l'Hospital's rule, Taylor's theorem, the Riemann integral, sequences and series of functions, uniform and pointwise convergence, and power series.

Credit Weight:
0.5
Prerequisite(s):
Mathematics 3231
Offering:
0-0; 3-0
Course Classifications:
Type C: Engineering, Mathematical and Natural Sciences
Linear programming including simplex methods, sensitivity analysis, the duality theorem, complementary slackness, and the dual simplex method. Integer programming. Selected topics from: interior point method, quadratic programming, network flows, transportation algorithms, and two-person zero-sum games.

Credit Weight:
0.5
Prerequisite(s):
One of Mathematics 1071, 2255 or 2070; or permission of the Chair of the Department
Offering:
3-0; 0-0
Course Classifications:
Type C: Engineering, Mathematical and Natural Sciences
A mathematical introduction to the theory and application of probability. Topics may include distributions and their properties, limit theorems, expectation and simulations.

Credit Weight:
0.5
Prerequisite(s):
Mathematics 1172
Offering:
3-1; 0-0
Notes:
Students who have previous credit in Mathematics 2331 may not take Mathematics 3332 for credit.
Course Classifications:
Type C: Engineering, Mathematical and Natural Sciences
Topics selected from network algorithms, game theory, inventory models, sequencing and scheduling, dynamic programming, decision-making methods, queuing theory, and simulation.

Credit Weight:
0.5
Prerequisite(s):
Mathematics 3332 or permission of the Chair of the Department
Offering:
3-0; or 3-0
Course Classifications:
Type C: Engineering, Mathematical and Natural Sciences
A mathematical introduction to statistics, using the probability theory developed in Mathematics 3332. Topics include point and interval estimation, test of hypothesis, non-parametric methods, goodness of fit, experimental design, analysis of variance and covariance, regression and correlation.

Credit Weight:
0.5
Prerequisite(s):
Mathematics 3332
Offering:
0-0; 3-1
Notes:
Students who have previous credit in Mathematics 2333 may not take Mathematics 3334 for credit.
Course Classifications:
Type C: Engineering, Mathematical and Natural Sciences
An introduction to various numerical techniques for such tasks as approximating integrals, solving systems of equations, solving ordinary and partial differential equations, finding roots of equations in one variable and approximating functions.

Credit Weight:
0.5
Prerequisite(s):
Mathematics 2111, or equivalent
Offering:
3-1; or 3-1
Course Classifications:
Type C: Engineering, Mathematical and Natural Sciences
Planar curves, including the Jordan curve theorem and the isoperimetric inequality; space curves, including the Frenet frame, indicatrices and total curvature, knots and links; regular surfaces; first and second fundamental forms; tensor notation; Gauss' equations and Christoffel symbols; geodesics; the Gauss-Bonnet theorem and applications.

Credit Weight:
0.5
Prerequisite(s):
Mathematics 2131 or 3012
Offering:
3-0; or 3-0
Course Classifications:
Type C: Engineering, Mathematical and Natural Sciences
The course content is intended to help students develop techniques to solve problems from various mathematical fields. Problems will be drawn from probability, algebra, geometry, combinatorics, and other branches of mathematics. Proofs will tend to involve combining techniques such as induction, proof by contradiction, and counting arguments.

Credit Weight:
0.5
Prerequisite(s):
Mathematics 2232
Offering:
3-0; or 3-0
Course Classifications:
Type C: Engineering, Mathematical and Natural Sciences
An introduction to numerical methods for interpolation, least squares problems, real symmetric algebraic eigenproblems, matrix factorization and the solution of linear equations, including norms and error analysis.

Credit Weight:
0.5
Prerequisite(s):
Mathematics 2255 and 2275
Offering:
3-0; 0-0
Course Classifications:
Type C: Engineering, Mathematical and Natural Sciences
Review of primes and basic number theory, binomial coefficients and other special number sequences, generating functions, graphs, trees, paths and connectivity, matchings, colourings, flows, and algorithms in combinatorics and graph theory.

Credit Weight:
0.5
Prerequisite(s):
Mathematics 1271 or permission of the Chair of the Department
Offering:
3-0; or 3-0
Course Classifications:
Type C: Engineering, Mathematical and Natural Sciences
A mathematical introduction to the theory of cryptography and cryptoanalysis.

Credit Weight:
0.5
Prerequisite(s):
Mathematics 1271 or 3071
Offering:
3-0; or 3-0
Course Classifications:
Type C: Engineering, Mathematical and Natural Sciences
Probability and relative frequency; joint probabilities of related and independent events; Bayes' Theorem; statistical independence; random variables; cumulative distribution functions; probability density functions; parameters describing the central tendency and dispersion of distribution; probability distribution functions in engineering; law of large numbers; central limit theorem; testing hypotheses and goodness of fit; sampling theory; linear correlation and regression.

Credit Weight:
0.5
Prerequisite(s):
Mathematics 2070
Offering:
3-0; 0-0
Course Classifications:
Type C: Engineering, Mathematical and Natural Sciences
Measure spaces, measurable functions, measures, the integral, integrable functions, the Lebesgue dominated convergence theorem, modes of convergence, Egoroff's theorem, the Hahn and Jordan decomposition theorems, the Radon-Nikodym theorem, Lebesgue spaces, and the Reisz representation theorem for Lebesgue spaces.

Credit Weight:
0.5
Prerequisite(s):
Mathematics 3233
Offering:
3-0; or 3-0
Course Classifications:
Type C: Engineering, Mathematical and Natural Sciences
The course material covers normed vector spaces, bounded operators, Baire category, the Banach-Steinhaus theorem,the open mapping theorem, the closed graph theorem, the Hahn-Banach theorems, Hilbert spaces, the Riesz representation theorem, and compact operators.

Credit Weight:
0.5
Prerequisite(s):
Mathematics 3233
Offering:
3-0; or 3-0
Course Classifications:
Type C: Engineering, Mathematical and Natural Sciences
Topology of Rn. Continuity and differentiability of functions from Rn to Rm. Taylor's Theorem for functions of n variables. Maxima and minima; positive definite and negative definite quadratic forms. The Inverse Function Theorem and the Implicit Function Theorem. Fubini's Theorem. Change of variables in multiple integrals.

Credit Weight:
0.5
Prerequisite(s):
Mathematics 3231
Offering:
0-0; 3-0
Course Classifications:
Type C: Engineering, Mathematical and Natural Sciences
Directed studies and research under the guidance of a faculty member in an area of mathematics. The student's transcript shall contain a title descriptive of the work accomplished under the reading course, if possible.

Credit Weight:
0.5
Prerequisite(s):
Honours year standing in Mathematics
Special Topic:
Yes
Course Classifications:
Type C: Engineering, Mathematical and Natural Sciences
Directed studies and research under the guidance of a faculty member in an area of mathematics. The student's transcript shall contain a title descriptive of the work accomplished under the reading course, if possible.

Credit Weight:
0.5
Prerequisite(s):
Honours year standing in Mathematics
Special Topic:
Yes
Course Classifications:
Type C: Engineering, Mathematical and Natural Sciences
Topological spaces; neighbourhoods, bases, and sub-bases; product spaces and weak topologies; nets and filters; convergence; separation axioms, including Urysohn's lemma and Tietze's extension theorem; compact and locally compact spaces, including Tychonoff's theorem and compactifications; metrizability; and connectedness.

Credit Weight:
0.5
Prerequisite(s):
Mathematics 3233 or permission of the Chair of the Department
Offering:
3-0; or 3-0
Course Classifications:
Type C: Engineering, Mathematical and Natural Sciences
Fourier analysis on the circle, Dirichlet kernel, Fejer's theorem, convergence of Fourier series.

Credit Weight:
0.5
Prerequisite(s):
Mathematics 3233
Offering:
3-0; or 3-0
Course Classifications:
Type C: Engineering, Mathematical and Natural Sciences
Required of honours mathematics majors in their fourth year. Normally consists of seminars presented by the staff and students, who are asked to prepare and present a number of papers.

Credit Weight:
1.0
Prerequisite(s):
Honours year standing in Mathematics
Offering:
3-0; 3-0
Course Classifications:
Type C: Engineering, Mathematical and Natural Sciences
An introduction to Galois Theory; field extensions; splitting fields; the Galois group; Fundamental Theorem of Galois Theory; insolvability of the quintic.

Credit Weight:
0.5
Prerequisite(s):
Mathematics 2234
Offering:
3-0; or 3-0
Course Classifications:
Type C: Engineering, Mathematical and Natural Sciences