Course Descriptions - Undergraduate Calendar 2014-2015

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Note

See also Actuarial Science, Applied Mathematics, Combinatorics and Optimization, Computer Science, Mathematics Electives, Pure Mathematics, Statistics.

MATH 00s


MATH 51 LEC 0.00Course ID: 010374
Pre-University Algebra and Geometry
Topics covered in the course include operations with vectors, scalar multiplications dot and cross products, projections, equations of lines and planes, systems of equations, Gaussian elimination, operations with matrices, determinants, binomial theorem, proof by mathematical induction, complex numbers.
Only offered Online

MATH 52 LEC 0.00Course ID: 010375
Pre-University Calculus
The concepts included are limits, derivatives, antiderivatives and definite integrals. These concepts will be applied to solve problems of rates of change, maximum and minimum, curve sketching and areas. The classes of functions used to develop these concepts and applications are: polynomial, rational, trigonometric, exponential and logarithmic.
Only offered Online

MATH 97 LEC 2.50Course ID: 010113
Study Abroad
For studies at other universities under approved exchange agreements.
Department Consent Required

MATH 100s


MATH 103 LEC,TUT 0.50Course ID: 006847
Introductory Algebra for Arts and Social Science
An introduction to applications of algebra to business, the behavioural sciences, and the social sciences. Topics will be chosen from linear equations, systems of linear equations, linear inequalities, functions, set theory, permutations and combinations, binomial theorem, probability theory. [Offered: F,W,S]
Prereq: Open only to students in the following Faculties: ARTS, AHS, ENV or IS.
Antireq: 4U Advanced Functions, 4U Geometry and Discrete Mathematics, MATH 114, 115, 125, 136, 146, NE 112
Also offered Online

MATH 104 LEC,TUT 0.50Course ID: 006848
Introductory Calculus for Arts and Social Science
An introduction to applications of calculus in business, the behavioural sciences, and the social sciences. The models studied will involve polynomial, rational, exponential and logarithmic functions. The major concepts introduced to solve problems are rate of change, optimization, growth and decay, and integration. [Offered: F,W]
Prereq: Open only to students in the following Faculties: ARTS, AHS, ENV, SCI.
Antireq: MATH 127, 137, 147
Also offered Online

MATH 106 LEC,TUT 0.50Course ID: 006869
Applied Linear Algebra 1
Systems of linear equations. Matrix algebra. Determinants. Introduction to vector spaces. Applications. [Offered: F,W,S]
Prereq: MATH 103 or (4U Advanced Functions and 4U Calculus and Vectors).
Antireq: MATH 114, 115, 136, 146, NE 112
Also offered Online

MATH 109 LEC,TUT 0.50Course ID: 006853
Mathematics for Accounting
Review and extension of differential calculus for functions of one variable. Multivariable differential calculus. Partial derivatives, the Chain Rule, maxima and minima and Lagrange multipliers. Introduction to matrix algebra.
Prereq: MATH 104 or 4U Advanced Functions or 4U Calculus and Vectors; Accounting and Financial Management or Science Biotechnology/CA students only.
Antireq: ECON 211, MATH 116, 117, 124, 127, 137, 147

MATH 114 LEC,TUT 0.50Course ID: 011645
Linear Algebra for Science
Vectors in 2- and 3-space and their geometry. Linear equations, matrices and determinants. Introduction to vector spaces. Eigenvalues and diagonalization. Applications. Complex numbers. [Offered: F]
Prereq: 4U Advanced Functions and 4U Calculus and Vectors; Science students only.
Antireq: MATH 125, 115, 136, 146, NE 112

MATH 115 LEC,TST,TUT 0.50Course ID: 006862
Linear Algebra for Engineering
Linear equations, matrices and determinants. Introduction to vector spaces. Eigenvalues and diagonalization. Applications. Complex numbers. [Offered: F]
Prereq: 4U Calculus and Vectors or 4U Geometry and Discrete Mathematics; Engineering students only.
Antireq: MATH 106/125, 114, 136, 146, NE 112

MATH 116 LEC,TST,TUT 0.50Course ID: 006865
Calculus 1 for Engineering
Functions: review of polynomials, exponential, logarithmic, trigonometric. Operations on functions, curve sketching. Trigonometric identities, inverse functions. Derivatives, rules of differentiation. Mean Value Theorem, Newton's Method. Indeterminate forms and L'Hopital's rule, applications. Integrals, approximations, Riemann definite integral, Fundamental Theorems. Applications of the integral. [Offered: F]
Prereq: 4U Advanced Functions and Intro Calculus or 4U Calculus and Vectors; Open to students in Engineering excluding Electrical and Computer Eng, Nanotechnology Eng, Software Eng and Systems Design Eng.
Antireq: MATH 117, 124, 127, 137, 147

MATH 117 LEC,TST,TUT 0.50Course ID: 006866
Calculus 1 for Engineering
Functions of engineering importance; review of polynomial, exponential, and logarithmic functions; trigonometric functions and identities. Inverse functions (logarithmic and trigonometric). Limits and continuity. Derivatives, rules of differentiation; derivatives of elementary functions. Applications of the derivative, max-min problems, Mean Value Theorem. Antiderivatives, the Riemann definite integral, Fundamental Theorems. Methods of integration, approximation, applications, improper integrals. [Offered: F]
Prereq: 4U Advanced Functions and Introductory Calculus or 4U Calculus and Vectors; Open only to students in Electrical and Computer Engineering or Software Engineering or Nanotechnology Engineering.
Antireq: MATH 116, 124, 127, 137, 147

MATH 118 LEC,TST,TUT 0.50Course ID: 006867
Calculus 2 for Engineering
Methods of integration: by parts, trigonometric substitutions, partial fractions; engineering applications, approximation of integrals, improper integrals. Linear and separable first order differential equations, applications. Parametric curves and polar coordinates, arc length and area. Infinite sequences and series, convergence tests, power series and applications. Taylor polynomials and series, Taylor's Remainder Theorem, applications. [Offered: W,S]
Prereq: One of MATH 116, 117, 127, 137, 147; Open only to students in Engineering excluding students in Electrical and Computer Eng, Nanotechnology Eng, Software Eng and Systems Design Eng.
Antireq: MATH 119, 128, 138, 148

MATH 119 LEC,TST,TUT 0.50Course ID: 006868
Calculus 2 for Engineering
Elementary approximation methods: interpolation; Taylor polynomials and remainder; Newton's method, Landau order symbol, applications. Infinite series: Taylor series and Taylor's Remainder Theorem, geometric series, convergence test, power series, applications. Functions of several variables: partial derivatives, linear approximation and differential, gradient and directional derivative, optimization and Lagrange multipliers. Vector-valued functions: parametric representation of curves, tangent and normal vectors, line integrals and applications. [Offered: W,S]
Prereq: One of MATH 116, 117, 127, 137, 147; Open only to students in Electrical and Computer Engineering or Software Engineering or Nanotechnology Engineering.
Antireq: MATH 118, 128, 138, 148

MATH 124 LEC,TUT 0.50Course ID: 012879
Calculus and Vector Algebra for Kinesiology
Review of trigonometry and basic algebra. Introduction to vectors in 2- and 3-space: sums, addition, dot products, cross products and angles between vectors. Solving linear systems in two and three variables. Functions of a real variable: powers, rational functions, trigonometric, exponential and logarithmic functions, their properties. Intuitive discussion of limits and continuity. Derivatives of elementary functions, derivative rules; applications to curve sketching, optimization. Relationships between distance, velocity and acceleration. The definite integral, antiderivatives, the Fundamental Theorem of Calculus; change of variable and integration by parts; applications to area, centre of mass. [Offered: F]
Prereq: 4U Advanced Functions; Kinesiology students only.
Antireq: MATH 109, 116, 117, 127, 137, 147

MATH 127 LEC,TUT 0.50Course ID: 006871
Calculus 1 for the Sciences
Functions of a real variable: powers, rational functions, trigonometric, exponential and logarithmic functions, their properties and inverses. Intuitive discussion of limits and continuity. Definition and interpretation of the derivative, derivatives of elementary functions, derivative rules and applications. Riemann sums and other approximations to the definite integral. Fundamental Theorems and antiderivatives; change of variable. Applications to area, rates, average value. [Offered: F,W,S]
Prereq: MATH 104 or 4U Advanced Functions and Introductory Calculus or 4U Calculus and Vectors.
Antireq: MATH 109, 116, 117, 124, 137, 147
Also offered Online

MATH 128 LEC,TUT 0.50Course ID: 006872
Calculus 2 for the Sciences
Transforming and evaluating integrals; application to volumes and arc length; improper integrals. Separable and linear first order differential equations and applications. Introduction to sequences. Convergence of series; Taylor polynomials, Taylor's Remainder Theorem, Taylor series and applications. Parametric/vector representation of curves; particle motion and arc length. Polar coordinates in the plane. [Offered: F,W,S]
Prereq: One of MATH 117, 127, 137, 147.
Antireq: MATH 118, 119, 138, 148
Also offered Online

MATH 135 LEC,TST,TUT 0.50Course ID: 006878
Algebra for Honours Mathematics
An introduction to the language of mathematics and proof techniques through a study of the basic algebraic systems of mathematics: the integers, the integers modulo n, the rational numbers, the real numbers, the complex numbers and polynomials.
[Note: Offered: F,W,S]
Prereq: 4U Calculus and Vectors or 4U Geometry and Discrete Mathematics; Honours Mathematics or Mathematics/ELAS or Software Engineering students only.
Antireq: MATH 145
Also offered Online

MATH 136 LAB,LEC,TST,TUT 0.50Course ID: 006879
Linear Algebra 1 for Honours Mathematics
Systems of linear equations, matrix algebra, elementary matrices, computational issues. Real n-space, vector spaces and subspaces, basis and dimension, rank of a matrix, linear transformations and matrix representations. Determinants, eigenvalues and diagonalization, applications.
[Note: Offered: F,W,S]
Prereq: MATH 135 with a grade of at least 60% or MATH 145; Honours Mathematics or Mathematics/ELAS or Mathematical Physics students only.
Antireq: MATH 125, 114, 115, 146, NE 112
Also offered Online

MATH 137 LAB,LEC,TST,TUT 0.50Course ID: 006880
Calculus 1 for Honours Mathematics
Rational, trigonometric, exponential, and power functions of a real variable; composites and inverses. Absolute values and inequalities. Limits and continuity. Derivatives and the linear approximation. Applications of the derivative, including curve sketching, optimization, related rates, and Newton's method. The Mean Value Theorem and error bounds. Introduction to the Riemann Integral and approximations. Antiderivatives and the Fundamental Theorem. Change of variable, areas and rate integrals. Suitable topics are illustrated using computer software.
[Note: Offered: F,W,S]
Prereq: 4U Advanced Functions and Introductory Calculus or 4U Calculus and Vectors; Honours Mathematics or Mathematics/ELAS or Mathematical Physics students only.
Antireq: MATH 116, 117, 124, 127, 147

MATH 138 LEC,TST,TUT 0.50Course ID: 006881
Calculus 2 For Honours Mathematics
Review of the Fundamental Theorem. Methods of integration. Further applications of the integral. Improper integrals. Linear and separable differential equations and applications. Vector (parametric) curves in R2. Convergence of sequences and series. Tests for convergence. Functions defined as power series. Taylor polynomials, Taylor's Theorem, and polynomial approximation. Taylor series. Suitable topics are illustrated using computer software.
[Note: Offered: F,W,S]
Prereq: MATH 127 with a grade of at least 70% or MATH 137 with a grade of at least 60% or MATH 147; Honours Mathematics or Mathematics/ELAS or Mathematical Physics students only.
Antireq: MATH 118, 119, 128, 148

MATH 145 LEC,TST,TUT 0.50Course ID: 006886
Algebra (Advanced Level)
MATH 145 is an advanced-level version of MATH 135. [Offered: F]
Department Consent Required
Prereq: 4U Calculus and Vectors or 4U Geometry and Discrete Mathematics; Honours Mathematics students only.
Antireq: MATH 135

MATH 146 LAB,LEC,TST,TUT 0.50Course ID: 006887
Linear Algebra 1 (Advanced level)
MATH 146 is an advanced-level version of MATH 136. [Offered: W]
Prereq: MATH 145; Honours Mathematics students only.
Antireq: MATH 106/125, 114, 115, 136, NE 112

MATH 147 LAB,LEC,TST,TUT 0.50Course ID: 006888
Calculus 1 (Advanced Level)
MATH 147 is an advanced-level version of MATH 137. [Offered: F]
Department Consent Required
Prereq: 4U Advanced Functions and Introductory Calculus or 4U Calculus and Vectors; Honours Mathematics students only.
Antireq: MATH 116, 117, 124, 127, 137

MATH 148 LEC,TST,TUT 0.50Course ID: 006889
Calculus 2 (Advanced Level)
MATH 148 is an advanced-level version of MATH 138. [Offered: W]
Prereq: MATH 147; Honours Mathematics students only.
Antireq: MATH 118, 119, 128, 138

MATH 200s


MATH 207 LEC,TST,TUT 0.50Course ID: 013105
Calculus 3 (Non-Specialist Level)
Multivariable functions and partial derivatives. Gradients. Optimization including Lagrange multipliers. Polar coordinates. Multiple integrals. Surface integrals on spheres and cylinders. Introduction to Fourier Series. [Offered: F,W,S]
Prereq: MATH 128 or 138 or 148.
Antireq: AMATH 231, MATH 212, 212N, 217, 227, 237, 247

MATH 211 LAB,LEC,TST,TUT 0.50Course ID: 006891
Advanced Calculus 1 for Electrical and Computer Engineers
Fourier series. Ordinary differential equations. Laplace transform. Applications to linear electrical systems. [Offered: F,W]
Prereq: MATH 119; Not open to Mathematics students.
Antireq: AMATH 350, MATH 218, 228
(Cross-listed with ECE 205)

MATH 212 LAB,LEC,TST,TUT 0.50Course ID: 006892
Advanced Calculus 2 for Electrical Engineers
Triple integrals, cylindrical and spherical polar coordinates. Divergence and curl, applications. Surface integrals, Green's, Gauss' and Stokes' theorems, applications. Complex functions, analytic functions, contour integrals, Cauchy's integral formula, Laurent series, residues. [Offered: F,S]
Prereq: MATH 211/ECE 205; Not open to Mathematics students.
Antireq: AMATH 231, MATH 207, 217, 227, 237, 247
(Cross-listed with ECE 206)

MATH 213 LEC,TUT 0.50Course ID: 011849
Advanced Mathematics for Software Engineers
Fourier series. Differential equations. Laplace transforms. Applications to circuit analysis. [Offered: S]
Prereq: MATH 119; Software Engineering students only.
Antireq: AMATH 250, MATH 211/ECE 205, MATH 212N, 218, 228

MATH 215 LAB,LEC,TUT 0.50Course ID: 013464
Linear Algebra for Engineering
Systems of linear equations; their representation with matrices and vectors; their generalization to linear transformations on abstract vector spaces; and the description of these linear transformations through quantitative characteristics such as the determinant, the characteristic polynomial, eigenvalues and eigenvectors, the rank, and singular values. [Offered F,W]
Prereq: Level at least 2A Computer Engineering or Electrical Engineering students only.
Antireq: MATH 114, 115, 106/125, 136, 146, NE 112

MATH 217 LEC,TUT 0.50Course ID: 006897
Calculus 3 for Chemical Engineering
Curves and surfaces in R3. Multivariable functions, partial derivatives, the chain rule, gradients. Optimization, Lagrange Multipliers. Double and triple integrals, change of variable. Vector fields, divergence and curl. Vector integral calculus: Green's theorem, the Divergence theorem and Stokes' theorem. Applications in engineering are emphasized. [Offered: F,W]
Prereq: MATH 118; Not open to Mathematics students.
Antireq: AMATH 231, CIVE 221, ENVE 221, MATH 207, 212/ECE 206, MATH 212N, 227, 237, 247, ME 201

MATH 218 LEC,TUT 0.50Course ID: 006898
Differential Equations for Engineers
First order equations, second order linear equations with constant coefficients, series solutions, the Laplace transform method, systems of linear differential equations. Applications in engineering are emphasized. [Offered: F,S]
Prereq: One of MATH 118, 119, 128, 138, 148, SYDE 112; Engineering or Earth Science students only.
Antireq: AMATH 250, 251, 350, 351, CIVE 222, ENVE 223, MATH 211/ECE 205, MATH 212N, 228, ME 203, SYDE 211

MATH 225 LEC,TUT 0.50Course ID: 006870
Applied Linear Algebra 2
Vector spaces. Linear transformations and matrices. Inner products. Eigenvalues and eigenvectors. Diagonalization. Applications. [Offered: F,S]
Prereq: MATH 106/125 or 136 or 146.
Antireq: MATH 235, 245
Also offered Online

MATH 227 LEC,TUT 0.50Course ID: 006907
Calculus 3 for Honours Physics
Directional derivative and the chain rule for multivariable functions. Optimization, Lagrange multipliers. Double and triple integrals on simple domains; transformations and Jacobians; change of variable in multiple integrals. Vector fields, divergence and curl. Vector integral calculus: Line and surface integrals, Green's Theorem, Stokes' Theorem, Gauss' Theorem, conservative vector fields.
Prereq: MATH 128 or 138; Not open to Mathematics students.
Antireq: AMATH 231, MATH 207, 212/ECE 206, MATH 212N, 217, 237, 247

MATH 228 LEC,TUT 0.50Course ID: 006908
Differential Equations for Physics and Chemistry
First-order equations, second-order linear equations with constant coefficients, series solutions and special functions, the Laplace transform method. Applications in physics and chemistry are emphasized. [Offered: F,W]
Prereq: MATH 128 or 138; Not open to Mathematics students.
Antireq: AMATH 250, 251, 350

MATH 229 LEC,TUT 0.50Course ID: 013104
Introduction to Combinatorics (Non-Specialist Level)
Introduction to graph theory: colourings, connectivity, Eulerian tours, planarity. Introduction to combinatorial analysis: elementary counting, generating series, binary strings. [Offered: F,W]
Prereq: (MATH 106/125 or 136 or 146) and (MATH 135 or 145).
Antireq: CO 220, MATH 239, 249

MATH 235 LEC,TST,TUT 0.50Course ID: 006913
Linear Algebra 2 for Honours Mathematics
Orthogonal and unitary matrices and transformations. Orthogonal projections, Gram-Schmidt procedure, best approximations, least-squares. Inner products, angles and orthogonality, orthogonal diagonalization, singular value decomposition, applications.
[Note: Offered: F,W,S]
Prereq: MATH 106/125 with a grade of at least 70% or MATH 136 with a grade of at least 60% or MATH 146; Honours Mathematics or Mathematical Physics students.
Coreq: MATH 128 or 138 or 148.
Antireq: MATH 225/126, 245
Also offered Online

MATH 237 LEC,TST,TUT 0.50Course ID: 006914
Calculus 3 for Honours Mathematics
Calculus of functions of several variables. Limits, continuity, differentiability, the chain rule. The gradient vector and the directional derivative. Taylor's formula. Optimization problems. Mappings and the Jacobian. Multiple integrals in various co-ordinate systems.
[Note: MATH 247 may be substituted for MATH 237 whenever the latter is a plan requirement. Offered: F,W,S]
Prereq: (MATH 106/125 with at least 70% or MATH 136 with at least 60% or MATH 146) and (MATH 128 with at least 70% or MATH 138 with at least 60% or MATH 148); Honours Math or Math/Physics students.
Antireq: MATH 207, 212/ECE 206, MATH 212N, 217, 227

MATH 239 LEC,TST,TUT 0.50Course ID: 006915
Introduction to Combinatorics
Introduction to graph theory: colourings, matchings, connectivity, planarity. Introduction to combinatorial analysis: generating series, recurrence relations, binary strings, plane trees.
[Note: Offered: F,W,S]
Prereq: ((MATH 106/125 with a grade of at least 70% or MATH 136 or 146) and (MATH 135 with a grade of at least 60% or MATH 145)) or level at least 2A Software Engineering; Honours Mathematics students only.
Antireq: CO 220, MATH 229, 249

MATH 245 LEC,TST 0.50Course ID: 006920
Linear Algebra 2 (Advanced Level)
MATH 245 is an advanced-level version of MATH 235. [Offered: F,S]
Prereq: MATH 146; Honours Mathematics students only.
Antireq: MATH 225/126, 235

MATH 247 LEC,TST 0.50Course ID: 006921
Calculus 3 (Advanced Level)
Topology of real n-dimensional space: completeness, closed and open sets, connectivity, compact sets, continuity, uniform continuity. Differential calculus on multivariable functions: partial differentiability, differentiability, chain rule, Taylor polynomials, extreme value problems. Riemann integration: Jordan content, integrability criteria, Fubini's theorem, change of variables. Local properties of continuously differentiable functions: open mapping theorem, inverse function theorem, implicit function theorem. [Offered: F,W,S]
Prereq: MATH 146, 148; Honours Mathematics students only

MATH 249 LEC,TST 0.50Course ID: 006922
Introduction to Combinatorics (Advanced Level)
MATH 249 is an advanced-level version of MATH 239. [Offered: F,W]
Prereq: (MATH 136 or 146) and (MATH 138 or 148); Honours Mathematics students only.
Antireq: CO 220, MATH 229, 239