¶¡ÏãÔ°AV

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, e.g. Python. The students will be exposed to diverse fields within, and applications of computing science. Topics will include: pseudocode; data types and control structures; fundamental algorithms; recursion; reading and writing files; measuring performance of algorithms; debugging tools; basic terminal navigation using shell commands. Treatment is informal and programming is presented as a problem-solving tool. Prerequisite: BC Math 12 or equivalent is recommended. Students with credit for CMPT 102, 128, 130 or 166 may not take this course for further credit. Students who have taken CMPT 125, 129, 130 or 135 first may not then take this course for further credit. Quantitative/Breadth-Science.

A second course in computing science and programming intended for students studying mathematics, statistics or actuarial science and suitable for students who already have some background in computing science and programming. Topics include: a review of the basic elements of programming: use and implementation of elementary data structures and algorithms; fundamental algorithms and problem solving; basic object-oriented programming and software design; computation and computability and specification and program correctness. Prerequisite: CMPT 102 or CMPT 120, with a minimum grade of C-. Students with credit for CMPT 125 or 135 may not take this course for further credit. Quantitative.

An introduction to computing science and computer programming, using a systems oriented language, such as C or C++. This course introduces basic computing science concepts. Topics will include: elementary data types, control structures, functions, arrays and strings, fundamental algorithms, computer organization and memory management. Prerequisite: BC Math 12 (or equivalent, or any of MATH 100, 150, 151, 154, or 157, with a minimum grade of C-). Students with credit for CMPT 102, 120, 128 or 166 may not take this course for further credit. Students who have taken CMPT 125, 129 or 135 first may not then take this course for further credit. Quantitative/Breadth-Science.

A second course in systems-oriented programming and computing science that builds upon the foundation set in CMPT 130 using a systems-oriented language such as C or C++. Topics: a review of the basic elements of programming; introduction to object-oriented programming (OOP); techniques for designing and testing programs; use and implementation of elementary data structures and algorithms; introduction to embedded systems programming. Prerequisite: CMPT 130 with a minimum grade of C-. Students with credit for CMPT 125, 126, or 129 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 or (ENSC 251 and one of MATH 232 or MATH 240). Quantitative.

Using a mathematical software package for doing calculations in linear algebra. Development of computer models that analyze and illustrate applications of linear algebra. All calculations and experiments will be done in the Matlab software package. Topics include: large-scale matrix calculations, experiments with cellular automata, indexing, searching and ranking pages on the internet, population models, data fitting and optimization, image analysis, and cryptography. Prerequisite: One of CMPT 102, 120, 126, 128 or 130 and one of MATH 150, 151, 154 or 157 and one of MATH 232 or 240. MATH 232 or 240 can be taken as corequisite. Students in excess of 80 units may not take MACM 203 for further credit. Quantitative.

Using a mathematical software package for doing computations from calculus. Development of computer models that analyze and illustrate applications of calculus. All calculations and experiments will be done in the Maple software package. Topics include: graphing functions and data, preparing visual aids for illustrating mathematical concepts, integration, Taylor series, numerical approximation methods, 3D visualization of curves and surfaces, multi-dimensional optimization, differential equations and disease spread models. Prerequisite: One of CMPT 102, 120, 126, 128 or 130 and MATH 251. MATH 251 can be taken as a corequisite. Students in excess of 80 units may not take MACM 204 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 with a minimum grade of C-; 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 with a minimum grade of C-; 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, all with a minimum grade of C-. MATH 240 or 232 may be taken concurrently. Students with credit for MATH 254 may not take MATH 252 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 with a minimum grade of C-; or MATH 155 or 158, with a grade of at least B; MATH 232 or 240, with a minimum grade of C-. Students with credit for MATH 310 may not take this course for further credit. Quantitative.

Basic laws of probability, sample distributions. Introduction to statistical inference and applications. Prerequisite: or Corequisite: MATH 152 or 155 or 158, with a minimum grade of C-. Students wishing an intuitive appreciation of a broad range of statistical strategies may wish to take STAT 100 first. 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, Newton's method. Introduction to modeling with differential equations. 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; introduction to functions of several variables with emphasis on partial derivatives and extrema. 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 and growth models. Sequences and series, series tests, power series, convergence and applications of power series. Prerequisite: MATH 150 or 151, with a minimum grade of C-; 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, with a minimum grade of C-; 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.

Designed for students specializing in business or the social sciences. Topics include: theory of integration, integration techniques, applications of integration; functions of several variables with emphasis on double and triple integrals and their applications; introduction to differential equations with emphasis on some special first-order equations and their applications; sequences and series. Prerequisite: MATH 150 or 151 or 154 or 157, with a minimum grade of C-. 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, with a minimum grade of C-; or MATH 154 or 157, both with a grade of at least B. Students with credit for MATH 240 may 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 emphasis and includes proofs of the basic theorems. Prerequisite: MATH 150 or 151 or MACM 101, with a minimum grade of C-; 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.

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 (CMPT 125, CMPT 129 or CMPT 135)) or (ENSC 251 and ENSC 252), all with a minimum grade of C-. Quantitative.

This course is a continuation of STAT 270. Review of probability models. Procedures for statistical inference using survey results and experimental data. Statistical model building. Elementary design of experiments. Regression methods. Introduction to categorical data analysis. Prerequisite: STAT 270 and one of MATH 152, MATH 155, or MATH 158, all with a minimum grade of C-. 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, with a minimum grade of C-. Quantitative.

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

The integers, fundamental theorem of arithmetic. Equivalence relations, modular arithmetic. Univariate polynomials, unique factorization. Rings and fields. Units, zero divisors, integral domains. Ideals, ring homomorphisms. Quotient rings, the ring isomorphism theorem. Chinese remainder theorem. Euclidean, principal ideal, and unique factorization domains. Field extensions, minimal polynomials. Classification of finite fields. Prerequisite: MATH 240 with a minimum grade of C- or MATH 232 with a grade of at least B. Students with credit for MATH 332 may not take this course for further credit. Quantitative.

Finite groups and subgroups. Cyclic groups and permutation groups. Cosets, normal subgroups and factor groups. Homomorphisms and isomorphisms. Fundamental theorem of finite abelian groups. Sylow theorems. Prerequisite: MATH 340 or 342 or 332, with a minimum grade of C-. Students with credit for MATH 339 may not take this course for further credit.

Students will develop skills required for mathematical research. This course will focus on communication in both written and oral form. Students will write documents and prepare presentations in a variety of formats for academic and non-academic purposes. The LaTeX document preparation system will be used. Course will be given on a pass/fail basis. Corequisite: MATH 499W. Students must have an approved project prior to enrollment.

An honours research project in mathematics is an original presentation of an area or problem in mathematics. A typical project is an original synthesis of knowledge generated from students research experience. A project can contain substantive, original mathematics, but need not. The presentation consists of a written report and an oral presentation both of which must be completed before the end of the exam period. Prerequisite: 18 units of upper division MATH or MACM courses. Must be in an honours program with a GPA of at least 3.0. Corequisite: MATH 498. Students must have an approved project prior to enrollment. Writing.

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.

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 with a minimum grade of C-. 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, with a minimum grade of C- and MACM 201 with a grade of at least B-. 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, with a minimum grade of C-. Quantitative.

Data structures and algorithms for mathematical objects. Topics include long integer arithmetic, computing polynomial greatest common divisors, the fast Fourier transform, Hensel's lemma and p-adic methods, differentiation and simplification of formulae, and polynomial factorization. Students will use a computer algebra system such as Maple for calculations and programming. Prerequisite: CMPT 307 or MATH 332 or MATH 340. 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.

Linear Algebra. Vector space and matrix theory. Prerequisite: MATH 340 or 332, with a minimum grade of C- 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, with a minimum grade of C-, and one additional 200 level MATH or MACM course. Quantitative.

An introduction to the theory of fields, with emphasis on Galois theory. Prerequisite: MATH 340 or 332, with a minimum grade of C-. Quantitative.

A study of ideals and varieties. Topics include affine varieties, ideals, Groebner bases, the Hilbert basis theorem, resultants and elimination, Hilbert's Nullstellensatz. irreducible varieties and prime ideals, decomposition of varieties, polynomial mappings, quotient rings, projective space and projective varieties. Prerequisite: MATH 340 with a minimum grade of C-. Students who have taken this course as MATH 439 Special Topics may not complete this course for further credit.

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, with a minimum grade of C- and MACM 201 with a grade of at least B-. 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, with a minimum grade of C-. Quantitative.

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.

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, all with a minimum grade of C-. 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, all with a minimum grade of C-. 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 260 or MATH 310, with a minimum grade of C-; and one of MATH 251 with a grade of B+, or one of MATH 252 or 254, with a minimum grade of C-. 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 with a minimum grade of C-. 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 260 or MATH 310) and one of MATH 314, MATH 320, MATH 322, PHYS 384, all with a minimum grade of C-. An alternative to the above prerequisite is both of (MATH 252 or MATH 254) and (MATH 260 or MATH 310), both with grades of at least A-. 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, all with a minimum grade of C-. Students with credit for MATH 420 or MATH 719 may not complete this course for further credit. Quantitative.

Metric spaces, normed vector spaces, measure and integration, an introduction to functional analysis. Prerequisite: MATH 320 with a minimum grade of C-. Quantitative.

An introduction to probability from the rigorous point of view. Random variables. Generating functions. Convergence of random variables. The strong law of large numbers and the central limit theorem. Stochastic processes. Stationary process and martingales. Prerequisite: MATH 242 and (MATH 348 or STAT 380), all with a minimum grade of C-.

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 (CMPT 125, CMPT 129 or CMPT 135)) or (ENSC 251 and ENSC 252), all with a minimum grade of C-. Quantitative.

Design and analysis of efficient data structures and algorithms. General techniques for building and analyzing algorithms (greedy, divide & conquer, dynamic programming, network flows). Introduction to NP-completeness. Prerequisite: CMPT 225, MACM 201, (MATH 150 or MATH 151), and (MATH 232 or MATH 240), all with a minimum grade of C-. MATH 154 or MATH 157 with a grade of at least B+ may be substituted for MATH 150 or MATH 151.

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

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.

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.

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 with a minimum grade of C-. 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, with a minimum grade of C- 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 with a minimum grade of C-. 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, with a minimum grade of C-. 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 with a minimum grade of C-. Recommended: MATH 345. Quantitative.

Examines central philosophical issues related to mathematics. Topics may include the metaphysical status of mathematical entities, mathematical knowledge, set theory and others. Prerequisite: One of PHIL 110, 210, 314, 315 or MACM 101; and one of PHIL 100W, 201 or 203. Writing.

Central forces, rigid body motion, small oscillations. Lagrangian and Hamiltonian formulations of mechanics. Prerequisite: PHYS 384, with a minimum grade of C- or permission of the department. Non-physics majors may enter with MATH 252; MATH 260 or MATH 310; PHYS 211. All prerequisite courses require a minimum grade of C-. 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, or all of: STAT 285, MATH 208W, and MATH 251, all with a minimum grade of C-. Quantitative.