MATH 103 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 set theory, permutations and combinations, binomial theorem, probability theory, systems of linear equations, vectors and matrices, mathematical induction.
MATH 104 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.
MATH 106 Applied Linear Algebra 1
Systems of linear equations. Matrix algebra. Determinants. Introduction to vector spaces. Applications.
MATH 109 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.
MATH 114 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.
MATH 115 Linear Algebra for Engineering
Linear equations, matrices and determinants. Introduction to vector spaces. Eigenvalues and diagonalization. Applications. Complex numbers.
MATH 116 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.
MATH 117 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.
MATH 118 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.
MATH 119 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.
MATH 124 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.
MATH 125 Applied Linear Algebra 1
Systems of linear equations. Matrix algebra. Determinants. Introduction to vector spaces. Applications.
MATH 126 Applied Linear Algebra 2
Vector spaces. Linear transformations and matrices. Inner products. Eigenvalues and eigenvectors. Diagonalization. Applications.
MATH 127 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.
MATH 128 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. Functions of two variables, partial derivatives, the linear approximation/tangent plane.
MATH 135 Algebra for Honours Mathematics
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.
MATH 136 Linear Algebra 1 for Honours Mathematics
Systems of linear equations, matrix algebra, elementary matrices, computational issues. Real and complex n-space, vector spaces and subspaces, basis and dimension, rank of a matrix, linear transformations and matrix representations. Inner products, angles and orthogonality, applications.
MATH 137 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.
MATH 138 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.
MATH 207 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.
MATH 211 Advanced Calculus 1 for Electrical and Computer Engineers
Fourier series. Ordinary differential equations. Laplace transform. Applications to linear electrical systems.
MATH 212 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.
MATH 212N Advanced Calculus 2 for Nanotechnology Engineering
Gradient, Divergence and Curl: Applications. Line and Surface Integrals. Green's, Gauss', and Stokes' Theorems: Applications to electromagnetism and fluid mechanics. Numerical solution of partial differential equations.
MATH 213 Advanced Mathematics for Software Engineers
Fourier series. Differential equations. Laplace transforms. Applications to circuit analysis.
MATH 217 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.
MATH 218 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.
MATH 225 Applied Linear Algebra 2
Vector spaces. Linear transformations and matrices. Inner products. Eigenvalues and eigenvectors. Diagonalization. Applications.
MATH 227 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.
MATH 228 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.
MATH 229 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.
MATH 235 Linear Algebra 2 for Honours Mathematics
Orthogonal and unitary matrices and transformations. Orthogonal projections, Gram-Schmidt procedure, best approximations, least-squares. Determinants, eigenvalues and diagonalization, orthogonal diagonalization, singular value decomposition, applications.
MATH 237 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.
MATH 239 Introduction to Combinatorics
Introduction to graph theory: colourings, matchings, connectivity, planarity. Introduction to combinatorial analysis: generating series, recurrence relations, binary strings, plane trees.
MATH 247 Calculus 3 (Advanced Level)
Topology of real n-dimensional space: completeness, closed and open sets, connectivity, compact sets, continuity, uniform
MATH 249 Introduction to Combinatorics (Advanced Level)
MATH 249 is an advanced-level version of MATH 239.