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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.

Introduction to counting, induction, automata theory, formal reasoning, modular arithmetic. Prerequisite: BC Math 12 (or equivalent, or any of MATH 100, 150, 151, 154, 157. Quantitative/Breadth-Science.

A continuation of MACM 101. Topics covered include graph theory, trees, inclusion-exclusion, generating functions, recurrence relations, and optimization and matching. Prerequisite: MACM 101. Quantitative.

Introduction to methods of operations research: linear and nonlinear programming, simulation, and heuristic methods. Applications to transportation, assignment, scheduling, and game theory. Exposure to mathematical models of industry and technology. Emphasis on computation for analysis and simulation. Prerequisite: MATH 150 or 151 or 154 or 157. Students with credit for MATH 208 may not take this course for further credit. Writing/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.

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.

This course is a continuation of STAT 270. Review of probability models, procedures for statistical inference from survey results and experimental data. Statistical model building. Elementary design of experiments and regression methods. Introduction to categorical data analysis. Prerequisite: STAT 270. Prerequisite or corequisite MATH 232 or MATH 240. This course may not be taken for credit by students who have credit for STAT 330 prior to Fall 2003. 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.

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.

Inventory theory, Markov decision process and applications, queuing theory, forecasting models, decision Analysis and games, probabilistic dynamic programming, simulation modeling, project planning using PERT/CPM, sequencing and scheduling. Prerequisite: STAT 270. Pre-/Co-requisite: MATH 308. Quantitative.

Problems from operations research will be presented and discussed in class. Students will also work on a problem of their choice and present their solution in report form as well as a presentation. Prerequisite: MATH 308 and STAT 285. Writing/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.

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.

Model building using integer variables, computer solution, relaxations and lower bounds, heuristics and upper bounds, branch and bound algorithms, cutting plane algorithms, valid inequalities and facets, branch and cut algorithms, Lagrangian duality, column generation of algorithms, heuristics algorithms and analysis. Prerequisite: MATH 308. Quantitative.

Applications of network flow models; flow decomposition; polynomial algorithms for shortest paths, maximum flows and minimum costs flows; convex cost flows; generalized flows, multi-commodity flows. Prerequisite: MATH 308. Recommended: MATH 345. Quantitative.

Theory and application of linear regression. Normal distribution theory. Hypothesis tests and confidence intervals. Model selection. Model diagnostics. Introduction to weighted least squares and generalized linear models. Prerequisite: STAT 285 and MATH 251. 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.

Quality of an estimator: unbiasedness, asymptotic unbiasedness, consistency, means squared error, uniform minimum variance. Confidence interval. Tests of hypotheses. Estimation for complete data. Estimation for grouped data. Estimation for modified data: Kaplan-Meier estimator, variances and confidence intervals of the empirical estimator, kernel density estimator. Parameter estimation. Variance of the estimators and confidence intervals. Model selection: graphical procedures, goodness-of-fit test, likelihood ratio test. Interpolation and smoothing. Covers part of the syllabus for Exam C of the Society of Actuaries and Exam 4 of the Casualty Actuarial Society. Prerequisite: ACMA 320. Quantitative.

Modern techniques of statistical, econometric, population and technological forecasting are presented along with discussions of a wide range of topics including Box-Jenkins methods, leading indicators, survey data, world models and the use of information sets of increasing size. Applied work on the Canadian and BC economies. Prerequisite: BUEC 333, 60 units.

Statistical computing in R and SAS. Data management: reading, editing and storing statistical data; querying databases with SQL. Data exploration and representation: summarizing data with tables, graphs and other statistical tools. Data simulation: model-based and empirical. The SAS component of the course will give students a good start for writing the SAS programming certification exams. Prerequisite: STAT 285 or STAT 302 or STAT 305 or equivalent. Quantitative.

An introduction to the major sample survey designs and their mathematical justification. Associated statistical analyses. Prerequisite: STAT 350. Quantitative.

An extension of the designs discussed in STAT 350 to include more than one blocking variable, incomplete block designs, fractional factorial designs, and response surface methods. Prerequisite: STAT 350 (or MATH 372). Equivalent Courses: MATH404. Quantitative.

The Bayesian approach to statistics is an alternative and increasingly popular way of quantifying uncertainty in the presence of data. This course considers comparative statistical inference, prior distributions, Bayesian computation, and applications. Prerequisite: STAT 330 and 350. Quantitative.

Introduction to standard methodology for analyzing categorical data including chi-squared tests for two- and multi-way contingency tables, logistic regression, and loglinear (Poisson) regression. Prerequisite: STAT 285 or STAT 302 or STAT 305 or equivalent. Students with credit for the former STAT 402 or 602 may not take this course for further credit. Quantitative.

Topics in areas of probability and statistics not covered in the regular undergraduate curriculum of the department. Prerequisite: Dependent on the topic covered.

This course is an introduction to the modelling, analysis, and computer simulation of complex systems. Topics include analytic modelling, discrete event simulation, experimental design, random number generation, and statistical analysis. Prerequisite: CMPT 225, MACM 101, STAT 270.

Analysis and design of data structures for lists, sets, trees, dictionaries, and priority queues. A selection of topics chosen from sorting, memory management, graphs and graph algorithms. Prerequisite: CMPT 225, MACM 201, MATH 151 (or MATH 150), and MATH 232 or 240.

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.

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.

Graph coloring, Hamiltonian graphs, planar graphs, random graphs, Ramsey theory, extremal problems, additional topics. Prerequisite: MATH 345. Quantitative.

This course is an introduction to the modelling, analysis, and computer simulation of complex systems. Topics include analytic modelling, discrete event simulation, experimental design, random number generation, and statistical analysis. Prerequisite: CMPT 225, MACM 101, STAT 270.

Analysis and design of data structures for lists, sets, trees, dictionaries, and priority queues. A selection of topics chosen from sorting, memory management, graphs and graph algorithms. Prerequisite: CMPT 225, MACM 201, MATH 151 (or MATH 150), and MATH 232 or 240.

This course provides an introduction to the fundamentals of computer graphics. Topics include graphics display and interaction hardware, basic algorithms for 2D primitives, anti-aliasing, 2D and 3D geometrical transformations, 3D projections/viewing, Polygonal and hierarchical models, hidden-surface removal, basic rendering techniques (color, shading, raytracing, radiosity), and interaction techniques. Prerequisite: CMPT 225 and MATH 232 or 240.

Models of computation, methods of algorithm design; complexity of algorithms; algorithms on graphs, NP-completeness, approximation algorithms, selected topics. Prerequisite: CMPT 307.

Covers advanced topics and techniques in computer graphics with a focus on image synthesis. Topics include photorealistic rendering, advanced ray tracing, Monte Carlo methods, photon maps, radiosity, light fields, participating media, as well as tone reproduction. Prerequisite: CMPT 361, MACM 201 and 316. Students with credit for CMPT 451 may not take this course for further credit.

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.

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.

An introduction to the subject of modern cryptography. Classical methods for cryptography and how to break them, the data encryption standard (DES), the advanced encryption standard (AES), the RSA and ElGammal public key cryptosystems, digital signatures, secure hash functions and pseudo-random number generation. Algorithms for computing with long integers including the use of probabilistic algorithms. Prerequisite: (CMPT 201 or 225) and one of (MATH 340 or 332 or 342); or CMPT 405. Students with credit for MACM 498 between Fall 2003 and Spring 2006 may not take this course for further credit. 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.

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.

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.

The prime numbers, unique factorization, congruences and quadratic reciprocity. Topics include the RSA public key cryptosystem and the prime number theorem. Prerequisite: MATH 240 or 232, and one additional 200 level MATH or MACM course. 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.

Inventory theory, Markov decision process and applications, queuing theory, forecasting models, decision Analysis and games, probabilistic dynamic programming, simulation modeling, project planning using PERT/CPM, sequencing and scheduling. Prerequisite: STAT 270. Pre-/Co-requisite: MATH 308. 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.

Design theory: Steiner triple systems, balanced incomplete block designs, latin squares, finite geometries. Enumeration: generating functions. Burnside's Lemma, Polya counting. Prerequisite: MATH 340 or 332, and MACM 201 (with a grade of at least B-). Quantitative.

Graph coloring, Hamiltonian graphs, planar graphs, random graphs, Ramsey theory, extremal problems, additional topics. Prerequisite: MATH 345. Quantitative.

An introduction to the theory and practice of error-correcting codes. Topics will include finite fields, polynomial rings, linear and non-linear codes, BCH codes, convolutional codes, majority logic decoding, weight distribution of codes, and bounds on the size of codes. Prerequisite: MATH 340 or 332. 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.

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.