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LAKEHEAD CALENDAR 2009-2010

Lakehead 2009-2010 Academic Courses Undergraduate Courses Mathematics Courses
Mathematics Courses

Courses not offered this academic year (fall/winter terms) are indicated by the words "NOT OFFERED THIS YEAR" below the course description. Nevertheless, students should refer to the Timetable as a final check.

All course selections are subject to the consent of the department. Prerequisites may be waived if the department so decides.

The lecture and laboratory hours for each course, given beneath the course description for each of the two terms (for example 3-3; 3-0 would indicate 3 lecture hours in each term, 3 lab hours in the first term only), indicate the relative amount of work required. The actual duration of lectures and laboratories is at the discretion of the department.

Notes:
1. Students cannot obtain credit for two courses covering essentially the same material. Some examples are: Mathematics 0210, 0212, 4030; Mathematics 1160 and 1180; Mathematics 2321 and 2331/2333.
2. Courses marked with a * are not acceptable for mathematics credit in any of the programs offered by the Department of Mathematical Sciences or the Department of Computer Science.

Mathematics 0140      Concepts of Basic Mathematics for Teachers
Credit Weight: 1.0
Description: 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.
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.
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*Mathematics 0210      Quantitative Methods for the Social Scientist
Credit Weight: 0.5
Description: 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.
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.
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*Mathematics 0212      Quantitative Methods for the Health Scientist
Credit Weight: 0.5
Description: An introduction to probability; the binomial, poisson and normal distributions; analysis of data; statistical inference; ANOVA; linear regression and correlation; nonparametric methods.
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.
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Mathematics 1051      Functions and Trigonometry
Credit Weight: 0.5
Description: 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.
Offering: 3-2; 0-0
Notes: Students who have taken Mathematics 1050 - Trigonometry and Analytical Geometry, can be given credit for Mathematics 1051 - Functions and Trigonometry.
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Mathematics 1071      Vectors and Matrices
Credit Weight: 0.5
Description: 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.
Offering: 3-2; 0-0
Notes: Students who have taken Mathematics 1070 - Matrix Algebra can be given credit for Mathematics 1071 - Vectors and Matrices.
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Mathematics 1077      Sequences and Series
Credit Weight: 0.5
Prerequisite(s): Math 1051
Description: 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.
Offering: 0-0; 3-2
Notes: Students who have taken 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 taken Mathematics 1052 but not Mathematics 1072 cannot be given credit for either Mathematics 1077 or Mathematics 1078.
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Mathematics 1078      Elementary Calculus
Credit Weight: 0.5
Corequisite(s): Math 1077
Description: 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.
Offering: 0-0; 3-2
Notes: Students who have taken 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 taken Mathematics 1052 but not Mathematics 1072 cannot be given credit for either Mathematics 1077 or Mathematics 1078.
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Mathematics 1120      Mathematics for Nursing
Credit Weight: 1
Description: This course offers the basic mathematics necessary to further the study of quantitative methods. Topics include: algebra-multiplication; division; squaring; powers and exponents; simple formulas; factoring; equations; graphs; word problems. Mathematics for nursing students - weights and measures (metric); computing dosages; calculation of IV flow rate; preparing solutions.
Offering: 3-1; 3-1
Notes: This course is open only to students in the Native Nurses Entry program.
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Mathematics 1130      Math Skills for Native Access Students I
Credit Weight: 0.0
Description:

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.


Offering: 3-1; 0-0
Notes: A non-credit course open only to Native Access students
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Mathematics 1131      Math Skills for Native Access Students II
Credit Weight: 0.0
Description:

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.


Offering: 0-0; 3-1
Notes: A non-credit course open only to Native Access students
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Mathematics 1160      Calculus for Social and Life Sciences
Credit Weight: 1
Prerequisite(s): MHF4U or permission of the Department
Description: Functions, the derivative, logarithmic and exponential functions, the graphs of functions, applications of the derivative, integration, applications of integration, and infinite series.
Offering: 3-1; 3-1
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Mathematics 1180      Calculus
Credit Weight: 1
Prerequisite(s): MHF4U or permission of the Department
Description: Basic properties of the real number system, definitions and basic properties of algebraic and transcendental functions together with their differential and integral calculus, basic results of analysis and applications of differential and integral calculus, and sequences and series.
Offering: 3-1; 3-1
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Mathematics 1210      Calculus I
Credit Weight: 0.5
Prerequisite(s): Mathematics 1077 or MHF4U
Description: Application of differentiation; definite and indefinite integrals; transcendental functions; complex numbers; techniques of integration.
Offering: 3-1; 0-0
Notes: Students who have taken Mathematics 2010 previously may not take Mathematics 1210 for credit.
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Mathematics 1230      Calculus II
Credit Weight: 0.5
Prerequisite(s): Mathematics 1210
Description: Applications of integration, introduction to multiple integrals sequences and series; power series. Note:
Offering: 0-0; 3-1
Notes: Engineering students may substitute Math 1180 for Math 1210/1230, with permission of the Dean of the Faculty of Engineering. Students who have taken Mathematics 2030 previously may not take Mathematics 1230 for credit.
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Mathematics 1281      Discrete Mathematics
Credit Weight: 1
Prerequisite(s): MHF4U or permission of the Department
Description: Basic set theory; introduction to logic and proofs including propositional calculus, quantifiers, and mathematical induction; basic combinatorics; discrete probability; relations, including recurrence relations, equivalence relations, and partial orderings; graphs and trees; Boolean algebra; and algorithms.
Offering: 3-1; 3-1
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Mathematics 1990      Co-op Work Term I
Credit Weight: 0.5
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Mathematics 2050      Applied Analysis I
Credit Weight: 0.5
Prerequisite(s): Mathematics 1230
Description: 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.
Offering: 3-1; 0-0
Notes: Students who have taken Mathematics 3010 previously may not take Mathematics 2050 for credit.
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Mathematics 2070      Applied Analysis II
Credit Weight: 0.5
Description: 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.
Offering: 0-0; 3-1
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Mathematics 2111      Differential Equations
Credit Weight: 0.5
Prerequisite(s): Mathematics 1160 or 1180
Description: 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.
Offering: 3-0; 0-0
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Mathematics 2131      Vector Calculus
Credit Weight: 0.5
Prerequisite(s): Mathematics 1180 or permission of the Department
Description: 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.
Offering: 0-0; 3-0
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Mathematics 2231      Ring Theory with Applications
Credit Weight: 0.5
Prerequisite(s): Mathematics 1281
Description: The division algorithm for integers, primes and unique factorization, modular arithmetic, rings, isomorphisms and homomorphisms of rings, polynomial rings, congruence of polynomials, ideals and quotient rings. Additional special topics may include: cryptography, lattices and Boolean algebras, and the Chinese remainder theorem.
Offering: 3-0; 0-0
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Mathematics 2233      Group Theory
Credit Weight: 0.5
Prerequisite(s): Mathematics 2231 and 2255
Description: Group theory, fields and field extensions, and Galois theory.
Offering: 0-0; 3-0
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Mathematics 2255      Linear Algebra I
Credit Weight: 0.5
Description: Matrices and systems of linear equations; linear transformations and matrices; elementary matrix algebra; determinants; vector spaces; change of bases; real eigenvalues and eigenvectors; applications.
Offering: 3-0; 0-0
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Mathematics 2275      Linear Algebra II
Credit Weight: 0.5
Prerequisite(s): Mathematics 2255
Description: Eigenvalues and eigenvectors; diagonalization; inner product spaces; orthogonal bases; least-squares problems; symmetric matrices; quadratic forms; singular value decomposition; applications.
Offering: 0-0; 3-0
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Mathematics 2321      Statistics
Credit Weight: 1
Prerequisite(s): Mathematics 1160
Description: Probability; discrete and continuous probability distributions; sampling distributions; chi-square, t and f tests of hypotheses; regression and correlation; analysis of variance.
Offering: 3-1; 3-1
Notes: Not recognized as a mathematics credit for Mathematics or Computer Science majors.
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Mathematics 2331      Introduction to Mathematical Probability
Credit Weight: 0.5
Prerequisite(s): Mathematics 1180
Description: A mathematical introduction to the theory and application of probability. Topics may include distributions and their properties, limit theorems, expectation and simulations.
Offering: 3-1; 0-0
Notes: Only one of Mathematics 2321 and 2331 can be taken for credit.
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Mathematics 2333      Introduction to Mathematical Statistics
Credit Weight: 0.5
Prerequisite(s): Mathematics 2331
Description: A mathematical introduction to statistics, using the probability theory developed in Math. 2331. 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.
Offering: 0-0; 3-1
Notes: Only one of Mathematics 2321 and 2333 can be taken for credit.
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Mathematics 2990      Co-op Work Term II
Credit Weight: 0.5
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Mathematics 2998      Internship Work Term I
Credit Weight: 0.5
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*Mathematics 3012      Vector Analysis
Credit Weight: 0.5
Prerequisite(s): Mathematics 1230
Corequisite(s): Mathematics 2050
Description: 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.
Offering: 3-1; 0-0
Notes: Students who have taken Mathematics 4012 previously may not take Mathematics 3012 for credit.
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*Mathematics 3032      Complex Functions and PDEs
Credit Weight: 0.5
Prerequisite(s): Mathematics 2050, 3012
Description: Power series and series solutions of differential equations. Power series solutions of Bessel's equation. Sturm-Liouville theorem and eigenfunctions. Linear partial differential equations. Fourier Series in one and two variables. Fourier-Bessel solutions of boundary value problems. Complex functions and integrals. Cauchy's integral formula.
Offering: 0-0; 3-1
Notes: Students who have taken Mathematics 4032 previously may not take Mathematics 3023 for credit.
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Mathematics 3050      Numerical Analysis and Computing
Credit Weight: 0.5
Prerequisite(s): Mathematics 2050 and 2070 or permission of the instructor
Description: Error analysis, root finding; numerical integration; solution of linear equations; solution of ordinary and partial differential equations.
Offering: 0-0; 3-1
Notes: Students who have taken Mathematics 4050 previously may not take Mathematics 3050 for credit.
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Mathematics 3071      Discrete Mathematics for Engineers
Credit Weight: 0.5
Description: 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.
Offering: 3-1; 0-0
Notes: Open to students in other programs with permission of the Department. Students who have taken Mathematics 4071 previously may not take Mathematics 3071 for credit.
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Mathematics 3111      Partial Differential Equations I
Credit Weight: 0.5
Prerequisite(s): Mathematics 2111, 2131
Description: A study of partial differential equations (e.g. diffusion, wave, potential); boundary value problems; Sturm-Liouville problems; Fourier series; special functions.
Offering: 3-0; 0-0
Notes: Students who have taken Mathematics 3131 previously may not take Mathematics 3111 for credit.
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Mathematics 3113      Partial Differential Equations II
Credit Weight: 0.5
Prerequisite(s): Mathematics 3111
Description: A study of partial differential equations in polar, cylindrical and spherical co-ordinates; special functions; non-homogeneous problems; Fourier and other transform techniques.
Offering: 0-0; 3-0
Notes: Students who have taken Mathematics 3133 previously may not take Mathematics 3113 for credit.
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Mathematics 3131      Methods of Mathematical Physics I
Credit Weight: 0.5
Prerequisite(s): Mathematics 2111, 2131
Description: A study of partial differential equations (e.g. diffusion, wave, potential); boundary value problems; Sturm-Liouville problems; Fourier series; special functions.
Offering: 3-0; 0-0
Notes: Students who have taken Mathematics 3111 previously may not take Mathematics 3131 for credit.
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Mathematics 3133      Methods of Mathematical Physics II
Credit Weight: 0.5
Prerequisite(s): Mathematics 3131
Description: A study of partial differential equations in polar, cylindrical and spherical co-ordinates; special functions; non-homogeneous problems; Fourier and other transform techniques.
Offering: 0-0; 3-0
Notes: Students who have taken Mathematics 3113 previously may not take Mathematics 3133 for credit.
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Mathematics 3171      Complex Analysis
Credit Weight: 0.5
Prerequisite(s): Mathematics 3231 and 3233 or 2131
Description: The geometry of the complex plane, analytic functions, Moebius transformations, the Cauchy-Goursat theorem, power series, the residue theorem, conformal mapping.
Offering: 3-0; 0-0
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Mathematics 3211      Special Topics I
Credit Weight: 0.5
Prerequisite(s): Permission of the Department
Description: 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.
SpecialTopic: Y
Offering: 3-0; 0-0
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Mathematics 3213      Special Topics II
Credit Weight: 0.5
Prerequisite(s): Permission of the Department
Description: 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.
SpecialTopic: Y
Offering: 0-0; 3-0
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Mathematics 3231      Introductory Analysis I
Credit Weight: 0.5
Prerequisite(s): Mathematics 1180 and either Mathematics 1281 or permission of the Department
Description: 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.
Offering: 3-0; 0-0
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Mathematics 3233      Introductory Analysis II
Credit Weight: 0.5
Prerequisite(s): Mathematics 3231
Description: 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.
Offering: 0-0; 3-0
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Mathematics 3331      Linear Programming and Applications
Credit Weight: 0.5
Prerequisite(s): One of Mathematics 1070, 2255, or 2070; or permission of the Department
Description: 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.
Offering: 3-0; 0-0
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Mathematics 3333      Operations Research
Credit Weight: 0.5
Prerequisite(s): Mathematics 2331 and 3331; or permission of the Department
Description: Topics selected from network algorithms, game theory, inventory models, sequencing and scheduling, dynamic programming, decision-making methods, queuing theory, and simulation.
Offering: 0-0; 3-0
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Mathematics 3335      Sample Survey Methods
Credit Weight: 0.5
Prerequisite(s): A half course in introductory statistics from any discipline
Description: An introduction to the design and analysis of sample surveys. Topics include simple, stratified, cluster and systematic random sampling techniques; ratio and regression estimation methods; multistage and multiphase sampling.
Offering: 3-0; or 3-0
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Mathematics 3351      Applied Numerical Methods
Credit Weight: 0.5
Prerequisite(s): Mathematics 2111, or equivalent
Description: 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.
Offering: 3-1; or 3-1
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Mathematics 3371      Computational Linear Algebra and Numerical Approximation I
Credit Weight: 0.5
Prerequisite(s): Mathematics 2255 and 2275
Description: 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.
Offering: 3-0; 0-0
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Mathematics 3990      Co-op Work Term III
Credit Weight: 0.5
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Mathematics 3992      Co-op Work Term IV
Credit Weight: 0.5
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*Mathematics 4030      Probability and Statistics
Credit Weight: 0.5
Prerequisite(s): Mathematics 2070
Description: 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.
Offering: 3-0; 0-0
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Mathematics 4101      Measure and Integration
Credit Weight: 1
Description: The classical Lebesgue theory.
Offering: 3-0; 3-0
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Mathematics 4151      Advanced Calculus
Credit Weight: 0.5
Prerequisite(s): Mathematics 3231
Description: 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.
Offering: 0-0; 3-0
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Mathematics 4211      Reading and Research in Mathematics
Credit Weight: 0.5
Prerequisite(s): Honours year standing in Mathematics
Description: 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.
SpecialTopic: Y
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Mathematics 4213      Reading and Research in Mathematics
Credit Weight: 0.5
Prerequisite(s): Honours year standing in Mathematics
Description: 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.
SpecialTopic: Y
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Mathematics 4221      Topology
Credit Weight: 1
Prerequisite(s): Mathematics 3231 and 3233
Description: Topological spaces, continuous mappings, metric spaces, separation axioms, metrizability, compactness, product spaces, elements of homotopy theory and homology theory.
Offering: 3-0; 3-0
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Mathematics 4273      Logic in Mathematics and Computer Science
Credit Weight: 0.5
Prerequisite(s): Mathematics 1281 or permission of the Department
Description: Propositional and quantifier logic. Axioms for basic mathematical theories. Formal number theory and completeness/incompleteness phenomena. Introduction to the theory of models.
Offering: 3-0; or 3-0
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Mathematics 4275      Computability in Mathematics
Credit Weight: 0.5
Prerequisite(s): Mathematics 1281 and either Mathematics 3373 or Computer Science 4433
Description: Models of computation. Finite automata and regular languages. Theoretical computability with unbounded resources. Computable sets in mathematics and hierarchies of relatively computable sets. Feasible computability, deterministic and non-deterministic resource-bounded computation. The P/NP problem. Probabilistic computing and classes of computable problems.
Offering: 3-0; or 3-0
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Mathematics 4301      Honours Seminar
Credit Weight: 1
Prerequisite(s): Honours year standing in Mathematics
Description: 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.
Offering: 3-0; 3-0
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Mathematics 4331      Stochastic Processes
Credit Weight: 0.5
Prerequisite(s): Mathematics 2331 and 2333
Description: Random walk and recurrent events; Markov chains; martingales; simple time continuous processes.
Offering: 3-0; or 3-0
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Mathematics 4335      Design of Experiments
Credit Weight: 0.5
Prerequisite(s): Mathematics 2331 and 2333
Description: Introduction to the fundamental statistical concepts required for designing efficient experiments. The roles of replication, blocking and randomization are examined. Various designs are discussed including completely randomized designs, randomized block designs, factorial designs, and split-plot designs.
Offering: 3-0; or 3-0
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Mathematics 4361      Topics in Actuarial Mathematics
Credit Weight: 1
Prerequisite(s): Mathematics 2333
Description: Mathematics of compound interest, mathematics of life contingencies, risk theory, mathematics of demography, mathematics of graduation and mortality table construction. The course content may change from year to year depending on Parts 4 and 5 of the Society of Actuaries examinations.
Offering: 3-0; 3-0
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Mathematics 4382      Topics in the Mathematics of Finance
Credit Weight: 1
Prerequisite(s): Permission of the Department
Description: Content will vary from year to year.
Offering: 3-0; 3-0
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Mathematics 4990      Co-op Work Term V
Credit Weight: 0.5
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Mathematics 4992      Co-op Work Term VI
Credit Weight: 0.5
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