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A rigorous introduction to computing science and computer programming, suitable for students who already have substantial programming background. This course provides a condensed version of the two-course sequence of CMPT 120/125, with the primary focus on computing science and object oriented programming. Topics include: fundamental algorithms and problem solving; abstract data types and elementary data structures; basic object-oriented programming and software design; elements of empirical and theoretical algorithmics; computation and computability; specification and program correctness; and history of computing science. Prerequisite: BC Math 12 (or equivalent, or any of MATH 100, 150, 151, 154, or 157). Students with credit for CMPT 120, 125, 128, 130, 135 or higher may not take CMPT 126 for further credit. Quantitative/Breadth-Science.

An introduction to computing science and computer programming, suitable for students wishing to major in Engineering Science or a related program. This course introduces basic computing science concepts, and fundamentals of object oriented programming. Topics include: fundamental algorithms and problem solving; abstract data types and elementary data structures; basic object-oriented programming and software design; elements of empirical and theoretical algorithmics; computation and computability; specification and program correctness; and history of computing science. The course will use a programming language commonly used in Engineering Science. Prerequisite: BC Math 12 (or equivalent, or any of MATH 100, 150, 151, 154, or 157). Students with credit for CMPT 125, 126, 130 or CMPT 200 or higher may not take for further credit. Quantitative/Breadth-Science.

An elementary introduction to computing science and computer programming, suitable for students with little or no programming background. Students will learn fundamental concepts and terminology of computing science, acquire elementary skills for programming in a high-level language and be exposed to diverse fields within, and applications of computing science. Topics will include: pseudocode, data types and control structures, fundamental algorithms, computability and complexity, computer architecture, and history of computing science. Treatment is informal and programming is presented as a problem-solving tool. Students should consult with the self-evaluation on the School of Computing Science website to decide whether they should follow the CMPT 120/125 course sequence or enrol in CMPT 126. Prerequisite: BC Math 12 or equivalent is recommended. Students with credit for CMPT 102, 125, 126, 128 or CMPT 200 or higher may not take this course for further credit. Quantitative/Breadth-Science.

A rigorous introduction to computing science and computer programming, suitable for students who already have some backgrounds in computing science and programming. Intended for students who will major in computing science or a related program. Topics include: fundamental algorithms; elements of empirical and theoretical algorithmics; abstract data types and elementary data structures; basic object-oriented programming and software design; computation and computability; specification and program correctness; and history of computing science. Prerequisite: BC Math 12 (or equivalent, or any of MATH 100, 150, 151, 154, or 157) and CMPT 120. Students with credit for CMPT 126, 128, 135 or CMPT 200 or higher may not take for further credit. Quantitative.

Introduction to a variety of practical and important data structures and methods for implementation and for experimental and analytical evaluation. Topics include: stacks, queues and lists; search trees; hash tables and algorithms; efficient sorting; object-oriented programming; time and space efficiency analysis; and experimental evaluation. Prerequisite: MACM 101 and one of CMPT 125, 126 or 128; or CMPT 128 and approval as a Biomedical Engineering Major. Students with credit for CMPT 201 may not take this course for further credit. Quantitative.

Mathematical induction. Limits of real sequences and real functions. Continuity and its consequences. The mean value theorem. The fundamental theorem of calculus. Series. Prerequisite: MATH 152; or MATH 155 or 158 with a grade of B. Quantitative.

Rectangular, cylindrical and spherical coordinates. Vectors, lines, planes, cylinders, quadric surfaces. Vector functions, curves, motion in space. Differential and integral calculus of several variables. Vector fields, line integrals, fundamental theorem for line integrals, Green's theorem. Prerequisite: MATH 152; or MATH 155 or MATH 158 with a grade of at least B. Recommended: It is recommended that MATH 240 or 232 be taken before or concurrently with MATH 251. Quantitative.

Vector calculus, divergence, gradient and curl; line, surface and volume integrals; conservative fields, theorems of Gauss, Green and Stokes; general curvilinear coordinates and tensor notation. Introduction to orthogonality of functions, orthogonal polynomials and Fourier series. Prerequisite: MATH 240 or 232, and 251. MATH 240 or 232 may be taken concurrently. Students with credit for MATH 254 may not take MATH 252 for further credit. Quantitative.

Newtonian mechanics and special relativity for students with good preparation in physics and mathematics. Topics include Newtonian particle mechanics, angular momentum, torque, conservation laws, gravitation, and special relativity. Prerequisite: Greater than 85% in both BC Pre-Calculus 12 & BC Physics 12, or a grade of A in PHYS 100, or equivalent. Co-requisite: MATH 150 or 151 or 154 must precede or be taken concurrently. Students with credit for PHYS 101, 120 or PHYS 140 may not take PHYS 125 for further credit. Quantitative.

Electricity, magnetism, and the electromagnetic character of light for students with good preparation in physics and mathematics. Topics include waves, simple electrical circuits, electricity, magnetism, the unifications of electromagnetism in relativity, light as an electromagnetic wave, and photons. Prerequisite: PHYS 125 or a grade of A or better in PHYS 120 or 140. Corequisite: MATH 152 or 155 must precede or be taken concurrently. Students with credit in PHYS 102, 121 or 141 may not take this course for further credit. Quantitative.

An intermediate mechanics course covering kinematics, dynamics, calculus of variations and Lagrange's equations, non-inertial reference frames, central forces and orbits, and rigid body motion. Prerequisite: PHYS 126 or 121 or 141. Corequisite: MATH 251; MATH 232 or 240. Recommended: MATH 310 and PHYS 255. Quantitative.

Basic laws of probability, sample distributions. Introduction to statistical inference and applications. Corequisite: MATH 152 or 155 or 158. Students wishing an intuitive appreciation of a broad range of statistical strategies may wish to take STAT 100 first. Quantitative. Prerequisite: COREQ-MATH 152 or 155 or 158. Students wishing an intuitive appreciation of a broad range of statistical strategies may wish to take STAT 100 first. Equivalent Courses: STAT102 STAT103 STAT201 STAT203 STAT301. Quantitative.

Designed for students specializing in mathematics, physics, chemistry, computing science and engineering. Topics as for Math 151 with a more extensive review of functions, their properties and their graphs. Recommended for students with no previous knowledge of Calculus. In addition to regularly scheduled lectures, students enrolled in this course are encouraged to come for assistance to the Calculus Workshop (Burnaby), or Math Open Lab (Surrey). Prerequisite: Pre-Calculus 12 (or equivalent) with a grade of at least B+, or MATH 100 with a grade of at least B-, or achieving a satisfactory grade on the ¶¡ÏãÔ°AV Calculus Readiness Test. Students with credit for either MATH 151, 154 or 157 may not take MATH 150 for further credit. Quantitative.

Designed for students specializing in mathematics, physics, chemistry, computing science and engineering. Logarithmic and exponential functions, trigonometric functions, inverse functions. Limits, continuity, and derivatives. Techniques of differentiation, including logarithmic and implicit differentiation. The Mean Value Theorem. Applications of Differentiation including extrema, curve sketching, related rates, Newton's method. Antiderivatives and applications. Conic sections, polar coordinates, parametric curves. Prerequisite: Pre-Calculus 12 (or equivalent) with a grade of at least A, or MATH 100 with a grade of at least B, or achieving a satisfactory grade on the ¶¡ÏãÔ°AV Calculus Readiness Test. Students with credit for either MATH 150, 154 or 157 may not take MATH 151 for further credit. Quantitative.

Designed for students specializing in the biological and medical sciences. Topics include: limits, growth rate and the derivative; elementary functions, optimization and approximation methods, and their applications; mathematical models of biological processes. Prerequisite: Pre-Calculus 12 (or equivalent) with a grade of at least B, or MATH 100 with a grade of at least C, or achieving a satisfactory grade on the ¶¡ÏãÔ°AV Calculus Readiness Test. Students with credit for either MATH 150, 151 or 157 may not take MATH 154 for further credit. Quantitative.

Designed for students specializing in business or the social sciences. Topics include: limits, growth rate and the derivative; logarithmic exponential and trigonometric functions and their application to business, economics, optimization and approximation methods; functions of several variables. Prerequisite: Pre-Calculus 12 (or equivalent) with a grade of at least B, or MATH 100 with a grade of at least C, or achieving a satisfactory grade on the ¶¡ÏãÔ°AV Calculus Readiness Test. Students with credit for either MATH 150, 151 or 154 may not take MATH 157 for further credit. Quantitative.

Riemann sum, Fundamental Theorem of Calculus, definite, indefinite and improper integrals, approximate integration, integration techniques, applications of integration. First-order separable differential equations. Sequences and series, series tests, power series, convergence and applications of power series. Prerequisite: MATH 150 or 151; or MATH 154 or 157 with a grade of at least B. Students with credit for MATH 155 or 158 may not take this course for further credit. Quantitative.

Designed for students specializing in the biological and medical sciences. Topics include: the integral, partial derivatives, differential equations, linear systems, and their applications; mathematical models of biological processes. Prerequisite: MATH 150, 151 or 154; or MATH 157 with a grade of at least B. Students with credit for MATH 152 or 158 may not take this course for further credit. Quantitative.

Theory of integration and its applications; introduction to multivariable calculus with emphasis on partial derivatives and their applications; introduction to differential equations with emphasis on some special first-order equations and their applications to economics and social sciences; continuous probability models; sequences and series. Prerequisite: MATH 150 or 151 or 154 or 157. Students with credit for MATH 152 or 155 may not take MATH 158 for further credit. Quantitative.

Linear equations, matrices, determinants. Introduction to vector spaces and linear transformations and bases. Complex numbers. Eigenvalues and eigenvectors; diagonalization. Inner products and orthogonality; least squares problems. An emphasis on applications involving matrix and vector calculations. Prerequisite: MATH 150 or 151; or MACM 101; or MATH 154 or 157, both with a grade of at least B. Students with credit for MATH 240 make not take this course for further credit. Quantitative.

Linear equations, matrices, determinants. Real and abstract vector spaces, subspaces and linear transformations; basis and change of basis. Complex numbers. Eigenvalues and eigenvectors; diagonalization. Inner products and orthogonality; least squares problems. Applications. Subject is presented with an abstract emphais and includes proofs of the basic theorems. Prerequisite: MATH 150 or 151; or MACM 101; or MATH 154 or 157, both with a grade of at least B. Students with credit for MATH 232 cannot take this course for further credit. Quantitative.

A variety of continuous and discrete models such as difference equations, differential equations, networks, cellular automata, and fractals are introduced. Students will develop mathematical models for physical phenomena, and use the computer to simulate and analyze the models. A mathematical software package, such as Maple or Matlab, will be extensively used in a laboratory setting. Prerequisite: MATH 152 (or MATH 155 or 158), and CMPT 125 (or CMPT 101 or 104 or 126) and MATH 240 or 232 (co-requisite). Quantitative.

Development of computer models that analyze and illustrate applications of linear algebra. Topics include: large-scale matrix calculations, experiments with cellular automata, population models, data fitting and optimization, image analysis. Prerequisite: One of CMPT 125, 126 or 128 and one of MATH 150, 151, 154, or 157. Students in excess of 75 units may not take MACM 203 for further credit. MATH 232 or 240 (can be taken as corequisite). Quantitative.

Development of computer models that analyze and illustrate applications of multi-variable calculus. Topics include: 3D visualization of curves and surfaces, disease spread models, multi-dimensional optimization and probability models. Prerequisite: One of CMPT 125, 126 or 128. Students in excess of 75 units may not take MACM 204 for further credit. MATH 251 (can be taken as a corequisite). Quantitative.

Independent study of computational models in a specialized area of mathematics. Course plans, made in consultation with a supervising instructor, should cover a broad computational perspective, and involve at least three distinct modelling or computational approaches. Prerequisite: One of MATH 232 or 240; and MATH 251. Written permission of the department undergraduate studies committee.

A first course in computer algebra also called symbolic computation. It covers data-structures and algorithms for mathematical objects, including polynomials, general mathematical formulae, long integer arithmetic, polynomial greatest common divisors, the Risch integration algorithm. Other topics include symbolic differentiation, simplification of formulae, and polynomial factorization. Students will learn Maple for use on assignments. Prerequisite: CMPT 307 or MATH 332 or MATH 340. Quantitative.

Development of numerical methods for solving linear algebra problems at the heart of many scientific computing problems. Mathematical foundations for the use, implementation and analysis of the algorithms used for solving many optimization problems and differential equations. Prerequisite: MATH 251, MACM 316, programming experience. Quantitative.

The numerical solution of ordinary differential equations and elliptic, hyperbolic and parabolic partial differential equations will be considered. Prerequisite: MATH 310 and MACM 316. Quantitative.

Formulation, analysis and numerical solution of continuous mathematical models. Applications may be selected from topics in physics, biology, engineering and economics. Prerequisite: MATH 310 and one of MATH 314, MACM 316, MATH 418, PHYS 384. An alternative to the above prerequisite is both of MATH 251 and MATH 310, both with grades of at least B+. Students with credit for MATH 361 or MATH 761 may not complete this course for further credit. Quantitative.

Incompressible fluid flow phenomena: kinematics and equations of motion, viscous flow and boundary layer theory, potential flow, water waves. Aerodynamics. Prerequisite: one of MATH 314, MATH 418, PHYS 384. An alternative to the above prerequisite is both of MATH 251 and MATH 310, both with grades of at least B+. Quantitative.

Stability and bifurcation in continuous and discrete dynamical systems, with applications. The study of the local and global behaviour of linear and nonlinear systems, including equilibria and periodic orbits, phase plane analysis, conservative systems, limit cycles, the Poincare-Bendixson theorem, Hopf bifurcation and an introduction to chaos. Prerequisite: MATH 310. Quantitative.

Procedures of Euler, Lagrange and Hamilton. Extremum problems, stationary values of integrals. Canonical equations of motion, phase space, Lagrangian and Poisson brackets. Prerequisite: MATH 310 and one of MATH 314, 320, 322, PHYS 384. An alternative to the above prerequisite is both of MATH 254 and MATH 310, both with grades of at least A-. Quantitative.

The topics included in this course will vary from term to term depending on faculty availability and student interest. Prerequisite: Will be specified according to the particular topic or topics offered under this course number.

A presentation of the problems commonly arising in numerical analysis and scientific computing and the basic methods for their solutions. Prerequisite: MATH 152 or 155 or 158, and MATH 232 or 240, and computing experience. Quantitative.

First-order differential equations, second- and higher-order linear equations, series solutions, introduction to Laplace transform, systems and numerical methods, applications in the physical, biological and social sciences. Prerequisite: MATH 152; or MATH 155/158 with a grade of at least B, MATH 232 or 240. Quantitative.

Fourier series, ODE boundary and eigenvalue problems. Separation of variables for the diffusion wave and Laplace/Poisson equations. Polar and spherical co-ordinate systems. Symbolic and numerical computing, and graphics for PDEs. Prerequisite: MATH 310; and one of MATH 251 with a grade of B+, or one of MATH 252 or 254. Quantitative.

Sequences and series of functions, topology of sets in Euclidean space, introduction to metric spaces, functions of several variables. Prerequisite: MATH 242 and 251. Quantitative.

Functions of a complex variable, differentiability, contour integrals, Cauchy's theorem, Taylor and Laurent expansions, method of residues. Prerequisite: MATH 251. Students with credit for MATH 424 may not take this course for further credit. Quantitative.

First-order linear equations, the method of characteristics. The wave equation. Harmonic functions, the maximum principle, Green's functions. The heat equation. Distributions and transforms. Higher dimensional eigenvalue problems. An introduction to nonlinear equations. Burgers' equation and shock waves. Prerequisite: MATH 310 and one of MATH 314, 320, 322, PHYS 384. An alternative to the above prerequisite is both of MATH 254 and MATH 310, both with grades of at least A-. Quantitative.

Formulation, analysis and numerical solution of continuous mathematical models. Applications may be selected from topics in physics, biology, engineering and economics. Prerequisite: MATH 310 and one of MATH 314, MACM 316, MATH 418, PHYS 384. An alternative to the above prerequisite is both of MATH 251 and MATH 310, both with grades of at least B+. Students with credit for MATH 361 or MATH 761 may not complete this course for further credit. Quantitative.

Incompressible fluid flow phenomena: kinematics and equations of motion, viscous flow and boundary layer theory, potential flow, water waves. Aerodynamics. Prerequisite: one of MATH 314, MATH 418, PHYS 384. An alternative to the above prerequisite is both of MATH 251 and MATH 310, both with grades of at least B+. Quantitative.

Stability and bifurcation in continuous and discrete dynamical systems, with applications. The study of the local and global behaviour of linear and nonlinear systems, including equilibria and periodic orbits, phase plane analysis, conservative systems, limit cycles, the Poincare-Bendixson theorem, Hopf bifurcation and an introduction to chaos. Prerequisite: MATH 310. Quantitative.

The numerical solution of ordinary differential equations and elliptic, hyperbolic and parabolic partial differential equations will be considered. Prerequisite: MATH 310 and MACM 316. Quantitative.

Stability and bifurcation in continuous and discrete dynamical systems, with applications. The study of the local and global behaviour of linear and nonlinear systems, including equilibria and periodic orbits, phase plane analysis, conservative systems, limit cycles, the Poincare-Bendixson theorem, Hopf bifurcation and an introduction to chaos. Prerequisite: MATH 310. Quantitative.

A first course in computer algebra also called symbolic computation. It covers data-structures and algorithms for mathematical objects, including polynomials, general mathematical formulae, long integer arithmetic, polynomial greatest common divisors, the Risch integration algorithm. Other topics include symbolic differentiation, simplification of formulae, and polynomial factorization. Students will learn Maple for use on assignments. Prerequisite: CMPT 307 or MATH 332 or MATH 340. Quantitative.

Development of numerical methods for solving linear algebra problems at the heart of many scientific computing problems. Mathematical foundations for the use, implementation and analysis of the algorithms used for solving many optimization problems and differential equations. Prerequisite: MATH 251, MACM 316, programming experience. Quantitative.

Linear programming modelling. The simplex method and its variants. Duality theory. Post-optimality analysis. Applications and software. Additional topics may include: game theory, network simplex algorithm, and convex sets. Prerequisite: MATH 150, 151, 154, or 157 and MATH 240 or 232. Quantitative.

Theoretical and computational methods for investigating the minimum of a function of several real variables with and without inequality constraints. Applications to operations research, model fitting, and economic theory. Prerequisite: MATH 232 or 240, and 251. Quantitative.

Linear Algebra. Vector space and matrix theory. Prerequisite: MATH 340 or 332 or permission of the instructor. Students with credit for MATH 438 may not take this course for further credit. Quantitative.

Structures and algorithms, generating elementary combinatorial objects, counting (integer partitions, set partitions, Catalan families), backtracking algorithms, branch and bound, heuristic search algorithms. Prerequisite: MACM 201 (with a grade of at least B-). Recommended: knowledge of a programming language. Quantitative.

Fundamental concepts, trees and distances, matchings and factors, connectivity and paths, network flows, integral flows. Prerequisite: MACM 201 (with a grade of at least B-). Quantitative.

Convergence in Euclidean spaces, Fourier series and their convergence, Legendre polynomials, Hermite and Laguerre polynomials. Prerequisite: MATH 232 or 240 and one of MATH 314, 320, 322, PHYS 384. Students with credit for MATH 420 or MATH 719 may not complete this course for further credit. Quantitative.

Conformal mapping, Cauchy Integral Formula, Analytic Continuation, Riemann Mapping Theorem, Argument Principle. Prerequisite: MATH 320 and either MATH 322 or 254, or permission of the instructor. Quantitative.

Metric spaces, normed vector spaces, measure and integration, an introduction to functional analysis. Prerequisite: MATH 320. Quantitative.

Formulation, analysis and numerical solution of continuous mathematical models. Applications may be selected from topics in physics, biology, engineering and economics. Prerequisite: MATH 310 and one of MATH 314, MACM 316, MATH 418, PHYS 384. An alternative to the above prerequisite is both of MATH 251 and MATH 310, both with grades of at least B+. Students with credit for MATH 361 or MATH 761 may not complete this course for further credit. Quantitative.

Incompressible fluid flow phenomena: kinematics and equations of motion, viscous flow and boundary layer theory, potential flow, water waves. Aerodynamics. Prerequisite: one of MATH 314, MATH 418, PHYS 384. An alternative to the above prerequisite is both of MATH 251 and MATH 310, both with grades of at least B+. Quantitative.

Stability and bifurcation in continuous and discrete dynamical systems, with applications. The study of the local and global behaviour of linear and nonlinear systems, including equilibria and periodic orbits, phase plane analysis, conservative systems, limit cycles, the Poincare-Bendixson theorem, Hopf bifurcation and an introduction to chaos. Prerequisite: MATH 310. Quantitative.

Procedures of Euler, Lagrange and Hamilton. Extremum problems, stationary values of integrals. Canonical equations of motion, phase space, Lagrangian and Poisson brackets. Prerequisite: MATH 310 and one of MATH 314, 320, 322, PHYS 384. An alternative to the above prerequisite is both of MATH 254 and MATH 310, both with grades of at least A-. Quantitative.

The topics included in this course will vary from term to term depending on faculty availability and student interest. Prerequisite: Will be specified according to the particular topic or topics offered under this course number.

Computer based approaches to the solution of complex physical problems. A partial list of topics includes: Monte-Carlo and molecular dynamics techniques applied to thermal properties of materials; dynamical behavior of conservative and dissipative systems, including chaotic motion; methods for ground state determination and optimization, including Newton-Raphson, simulated annealing, neural nets, and genetic algorithms; the analysis of numerical data; and the use of relevant numerical libraries. Prerequisite: MATH 310, PHYS 211, CMPT 101 or 102. Recommended: PHYS 344 or equivalent. Quantitative.

Central forces, rigid body motion, small oscillations. Lagrangian and Hamiltonian formulations of mechanics. Prerequisite: PHYS 384 or permission of the department. Non-physics majors may enter with MATH 252, 310 and PHYS 211. Quantitative.

Nonlinear mechanics, nonlinear lattice dynamics, competition phenomena, applications in optics and chemistry, forced oscillations, chaos. Prerequisite: PHYS 384 or permission of the department. Quantitative.

Review of discrete and continuous probability models and relationships between them. Exploration of conditioning and conditional expectation. Markov chains. Random walks. Continuous time processes. Poisson process. Markov processes. Gaussian processes. Prerequisite: STAT 330. Quantitative.