### Please note:

To view the Spring 2020 Academic Calendar go to www.sfu.ca/students/calendar/2020/spring.html

# Mathematics Courses

### MATH 100 - Precalculus (3)

Designed to prepare students for first year Calculus courses. Topics include language and notation of mathematics; problem solving; algebraic, exponential, logarithmic and trigonometric functions and their graphs. Prerequisite: Pre-Calculus 11 or Foundations of Mathematics 11 (or equivalent) with a grade of at least B or Pre-Calculus 12 (or equivalent), with a grade of at least C and SFU FAN credit, or SFU FAN X99 course with a grade of at least B-, or achieving a satisfactory grade on the Simon Fraser University Quantitative Placement Test. Students with credit for MATH 150 or 151 or 154 or 157 may not take MATH 100 for further credit. MATH 100 may not be counted towards the mathematics minor, major or honours degree requirements. Quantitative.

### MATH 113 - Euclidean Geometry (3)

Plane Euclidean geometry, congruence and similarity. Theory of parallels. Polygonal areas. Pythagorean theorem. Geometrical constructions. Prerequisite: Pre-Calculus 11 (or equivalent) with a grade of at least B, or Foundations of Mathematics 11 (or equivalent) with a grade of at least B, or SFU FAN X99 course with a grade of at least C, or achieving a satisfactory grade on the Simon Fraser University Quantitative Placement Test. Intended to be accessible to students who are not specializing in mathematics. Particularly recommended for students considering a career in teaching secondary or middle school mathematics. Quantitative.

### MATH 125 - Introduction to Mathematical Methods in the Physical Sciences-l (3)

Review of limits and differentiation. Complex numbers and link to polar coordinates. Mathematics of kinematics, including vectors and parametrics curves. Area and Riemann sums. Definite and indefinite integration. Fundamental Theorems of Calculus. Techniques of integration and approximation of integrals. Series and tests of convergence. Taylor series. Solution of first and constant-coefficient second order ODE. Prerequisite: MATH 150 or MATH 151 or MATH 154 with a grade of at least B or IB Mathematics HL with a score of 6 or better or AP Calculus AB or BC with a grade of at least 4, or BC Calculus 12 and a pass on the Calculus Challenge Exam. And Permission of the Department. Recommended corequisite: Physics 125.

### MATH 126 - Introduction to Mathematical Methods in the Physical Sciences-ll (3)

Partial differentiation and applications. Taylor series of functions of two variables. Method of characteristics for 1-D transport and wave equations. Similarity solutions including plane waves, traveling waves and scaling solutions, with applications in the physical sciences. Introduction to vector calculus, including differentiation, decompositions via potentials. Curvilinear coordinate systems. Multivariate integration, including Green's, the Stokes and the Divergence theorem. Introduction to abstract vector spaces. Linear independence. Inner products and orthogonality. Fourier Series. Prerequisite: A grade of C+ or higher in Math 125 or Math 152. And Permission of the Department. Recommended corequisite: Physics 126.

### MATH 130 - Geometry for Computer Graphics (3)

An introductory course in the application of geometry and linear algebra principles to computer graphical representation. Vector and matrix algebra, two and three dimensional transformations, homogeneous coordinates, perspective geometry. Prerequisite: Pre-Calculus 12 or Foundations of Mathematics 12 (or equivalent) with a grade of at least B, or MATH 100 with a grade of at least C. Quantitative.

### MATH 150 - Calculus I with Review (4)

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 Simon Fraser University Calculus Readiness Test. Students with credit for either MATH 151, 154 or 157 may not take MATH 150 for further credit. Quantitative.

### MATH 151 - Calculus I (3)

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 Simon Fraser University Calculus Readiness Test. Students with credit for either MATH 150, 154 or 157 may not take MATH 151 for further credit. Quantitative.

### MATH 152 - Calculus II (3)

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; 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.

### MATH 154 - Calculus I for the Biological Sciences (3)

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 Simon Fraser University Calculus Readiness Test. Students with credit for either MATH 150, 151 or 157 may not take MATH 154 for further credit. Quantitative.

### MATH 155 - Calculus II for the Biological Sciences (3)

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.

### MATH 157 - Calculus I for the Social Sciences (3)

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 Simon Fraser University Calculus Readiness Test. Students with credit for either MATH 150, 151 or 154 may not take MATH 157 for further credit. Quantitative.

### MATH 158 - Calculus II for the Social Sciences (3)

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. Students with credit for MATH 152 or 155 may not take MATH 158 for further credit. Quantitative.

### MATH 160W - Mathematics in Action (3)

Students take an active role in modeling mathematics of change through a guided, investigative, discovery-based approach of learning that mimics past and present research methods in mathematics. The course is divided into several modules, each of which centers around a major application in mathematics using calculus such as logistic growth (e.g. spread of diseases), optimization (e.g. cost effective oil pipe line routes), approximation (e.g. security system design), area calculation (e.g. tile design) and volume calculation (e.g. optimal ice cream cone) as well as a function review module and calculus history module. The history module allows students to gain a broad understanding of the developments of calculus and how this branch of mathematics helped to shape other branches of mathematics as well as the sciences. The instructional approach emphasizes conceptual understanding over rote drill and students write, present, and defend their mathematical discoveries. Prerequisite: Pre-Calculus 12 or Foundations of Mathematics 12 (or equivalent) with a grade of at least B, or MATH 100 with a grade of at least C- and SFU FAN credit. Writing/Quantitative/B-Sci.

### MATH 178W - Fractals and Chaos (3)

Introduction to fractal geometry and chaos theory, with a survey of applications of these topics in modern mathematics and in other areas outside of mathematics including music, art, computer graphics, finance, and the sciences. Designed to be accessible to students with only high school mathematics. Prerequisite: Pre-Calculus 12 or Foundations of Mathematics 12 (or equivalent) with a grade of at least B, or MATH 100 with a grade of at least C-. Writing/Quantitative/B-Sci.

### MATH 190 - Principles of Mathematics for Teachers (4)

Designed for students pursuing a career as an elementary school teacher. Topics are drawn from number systems as well as plane, solid, and metric geometry. Examination of the historical and cultural development of mathematical ideas and their place in contemporary mathematics. Emphasis on deep understanding of mathematical concepts and on multiple representations: physical, pictorial, and symbolic. Detailed topics include: problem solving, bases, whole and fractional numbers and their arithmetic operations, number theory, ratios, rates, percent, polygons, polyhedra, symmetries, transformations, and measurements. Prerequisite: Pre-Calculus 11 or Foundations of Mathematics 11 (or equivalent) with a grade of at least B, or SFU FAN X99 course with a grade of at least C, or achieving a satisfactory grade on the Simon Fraser University Quantitative Placement Test. This course may not be counted toward the Mathematics minor, major or honours degree requirements. Students who have taken, have received transfer credit for, or are currently taking MATH 150, 151, 154 or 157 may not take MATH 190 for credit without permission from the Department of Mathematics. Intended to be particularly accessible to students who are not specializing in mathematics. Quantitative.

### MATH 197 - Hitchhiker's Guide to Everyday Math (3)

Should you buy a ticket for 6/49 or Super 7? If you tested positive for a rare disease, what is the chance that you actually do have it? What are likely to be the consequences of moving to a single transferable voting system from a "first past the post" voting system? What is the connection between Chinese dragging noodles, E. coli bacteria and interest on your credit card? These are some of the questions we will be investigating in this course. We will also look into the use, misuse and abuse of mathematics in the media and advertisements. Prerequisite: Pre-Calculus 11 or Foundations of Mathematics 11 (or equivalent) with a grade of at least B, or SFU FAN X99 course with a grade of at least C, or achieving a satisfactory grade on the Simon Fraser University Quantitative Placement Test. Students who have taken, have received transfer credit for, or are currently taking MATH 150, 151, 154 or 157 may not take MATH 197 for credit without permission from the Department of Mathematics. This course may not be counted toward the Mathematics minor, major or honours degree requirements. Quantitative.

### MATH 198 - Introduction to Quantitative Reasoning (4)

Designed specifically for students in the Integrated Studies programs to help them develop their abilities to interpret and reason with quantitative information. Topics covered include logical reasoning and problem solving, counting and probability, mathematics of finance, and linear and exponential modeling. Prerequisite: Pre-Calculus 11 or Foundations of Mathematics 11 (or equivalent) with a grade of at least B, or Simon Fraser University FAN X99 course with a grade of at least C, or achieving a satisfactory grade on the Simon Fraser University Quantitative Placement Test. Quantitative.

### MATH 208W - Introduction to Operations Research (3)

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.

### MATH 232 - Applied Linear Algebra (3)

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.

### MATH 240 - Algebra I: Linear Algebra (3)

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; 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.

### MATH 242 - Introduction to Analysis I (3)

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.

### MATH 251 - Calculus III (3)

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.

### MATH 252 - Vector Calculus (3)

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.

### MATH 254 - Vector and Complex Analysis for Applied Sciences (3)

Designed for students in the Engineering Science program. Combines a continuation of the study of vector calculus from MATH 251 with an introduction to functions of a complex variable. Vector functions of a single variable, space curves, scalar and vector fields, conservative fields, surface and volume integrals, and theorems of Gauss, Green and Stokes. Functions of a complex variable, differentiability, contour integrals, Cauchy's theorem. Taylor and Laurent expansion, method of residues, integral transform and conformal mapping. Prerequisite: MATH 240 or 232; and 251. MATH 240 or 232 may be taken concurrently. Students with credit for MATH 322 or MATH 252 may not take this course for further credit. Quantitative.

### MATH 291 - Selected Topics in Mathematics (2)

Topics will vary from term to term depending on faculty availability and student interest. Prerequisite: Prerequisites will be specified according to the particular topic or topics offered.

### MATH 292 - Selected Topics in Mathematics (3)

Topics will vary from term to term depending on faculty availability and student interest. Prerequisite: Prerequisites will be specified according to the particular topic or topics offered.

### MATH 301 - Mathematical Journeys I (3)

A focused exploration of a special topic (varying from term to term) that builds on mathematical ideas from lower division courses and provides further challenges in quantitative and deductive reasoning. Each Journeys course is designed to appeal particularly to mathematics minor students and others with a broad interest in mathematics. Students may repeat this course for further credit under a different topic. Prerequisite: MATH 152 or 155 or 158, and MATH 232 or 240. There may be additional prerequisites depending on the specific course topic.

### MATH 302 - Mathematical Journeys II (3)

A focused exploration of a special topic (varying from term to term) that builds on mathematical ideas from lower division courses and provides further challenges in quantitative and deductive reasoning. Each Journeys course is designed to appeal particularly to mathematics minor students and others with a broad interest in mathematics. Prerequisite: MATH 152 or 155 or 158, and MATH 232 or 240. There may be additional prerequisites depending on the specific course topic. Quantitative.

### MATH 303 - Mathematical Journeys III (3)

A focused exploration of a special topic (varying from term to term) that builds on mathematical ideas from lower division courses and provides further challenges in quantitative and deductive reasoning. Each Journeys course is designed to appeal particularly to mathematics minor students and others with a broad interest in mathematics. Prerequisite: MATH 152 or 155 or 158, and MATH 232 or 240. There may be additional prerequisites depending on the specific course topic. Quantitative.

### MATH 304 - Mathematical Journeys IV (3)

A focused exploration of a special topic (varying from term to term) that builds on mathematical ideas from lower division courses and provides further challenges in quantitative and deductive reasoning. Each Journeys course is designed to appeal particularly to mathematics minor students and others with a broad interest in mathematics. Prerequisite: MATH 152 or 155 or 158, and MATH 232 or 240. There may be additional prerequisites depending on the specific course topic. Quantitative.

### MATH 308 - Linear Optimization (3)

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.

### MATH 309 - Continuous Optimization (3)

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.

### MATH 310 - Introduction to Ordinary Differential Equations (3)

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.

### MATH 314 - Introduction to Fourier Methods and Partial Differential Equations (3)

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.

### MATH 320 - Introduction to Analysis II (3)

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.

### MATH 322 - Complex Variables (3)

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.

### MATH 336 - Job Practicum I (3)

This is the first term of work experience in a co-operative education program available to mathematics students. Interested students should contact departmental advisors as early in their careers as possible, for proper counselling. Units from this course do not count towards the units required for an SFU degree. Prerequisite: Students must apply to and receive permission from the co-op co-ordinator at least one, preferably two, terms in advance. They will normally be required to have completed 45 units with a GPA of 2.5. This course will be graded on a pass/withdraw basis. A course fee is required.

### MATH 337 - Job Practicum II (3)

This is the second term of work experience in a co-operative education program available to mathematics students. Units from this course do not count towards the units required for an SFU degree. This course will be graded on a pass/withdraw basis. A course fee is required. Prerequisite: MATH 336 and permission of the co-op co-ordinator; students must apply at least one term in advance.

### MATH 338 - Advanced Linear Algebra (3)

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.

### MATH 340 - Algebra II: Rings and Fields (3)

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 (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.

### MATH 341 - Algebra III: Groups (3)

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. Students with credit for MATH 339 may not take this course for further credit.

### MATH 342 - Elementary Number Theory (3)

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.

### MATH 343 - Applied Discrete Mathematics (3)

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.

### MATH 345 - Introduction to Graph Theory (3)

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.

### MATH 348 - Probabilistic Models in Operations Research (3)

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.

### MATH 380W - History of Mathematics (3)

Topics in the history of mathematics from ancient times to the present. Prerequisite: MATH 152, MATH 155 or MATH 158 and at least 6 units from MATH at the 200 division or above (includes STAT 270). Writing/Quantitative.

### MATH 381W - Mathematics Undergraduate Seminar (3)

A writing and presentation-intensive study of an area of mathematics. Students will read and prepare written and oral comments on material in the mathematics literature. Prerequisite: Six units of mathematics at the 200 division or higher. Writing/Quantitative.

### MATH 396 - Selected Topics in Mathematics (3)

Topics in areas of mathematics not covered in the regular undergraduate curriculum of the department. Prerequisite: Prerequisites will be specified according to the particular topic or topics covered.

### MATH 397 - Selected Topics in Mathematics (3)

Topics in areas of mathematics not covered in the regular undergraduate curriculum of the department. Prerequisite: will be specified according to the particular topic or topics covered.

### MATH 398 - Selected Topics in Mathematics (3)

Topics in areas of mathematics not covered in the regular undergraduate curriculum of the department. Prerequisite: Prerequisites will be specified according to the particular topic or topics offered.

### MATH 402W - Operations Research Clinic (4)

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.

### MATH 408 - Discrete Optimization (3)

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.

### MATH 418 - Partial Differential Equations (3)

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.

### MATH 419 - Linear Analysis (3)

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.

### MATH 424 - Complex Analysis (3)

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.

### MATH 425 - Real Analysis (3)

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

### MATH 436 - Job Practicum III (3)

This is the third term of work experience in a co-operative education program available to mathematics students. Units from this course do not count towards the units required for an SFU degree. This course will be graded on a pass/withdraw basis. A course fee is required. Prerequisite: MATH 337 and permission of the co-op co-ordinator; students must apply at least one term in advance.

### MATH 437 - Job Practicum IV (3)

This is the fourth term of work experience in a co-operative education program available to mathematics students. Units from this course do not count towards the units required for an SFU degree. This course will be graded on a pass/withdraw basis. A course fee is required. Prerequisite: MATH 436 and permission of the co-op co-ordinator; students must apply at least one term in advance.

### MATH 439 - Selected Topics in Algebra (3)

Topics in advanced algebra not covered by other courses. Prerequisite: MATH 338 or 340 or 332, according to the particular topic or topics offered.

### MATH 440 - Galois Theory (3)

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

### MATH 441 - Commutative Algebra and Algebraic Geometry (3)

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. Students who have taken this course as MATH 439 Special Topics may not complete this course for further credit.

### MATH 443 - Combinatorial Theory (3)

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.

### MATH 445 - Graph Theory (3)

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

### MATH 447 - Coding Theory (3)

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.

### MATH 448 - Network Flows (3)

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.

### MATH 461 - Continuous Mathematical Models (3)

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.

### MATH 462 - Fluid Dynamics (3)

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.

### MATH 467 - Dynamical Systems (3)

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.

### MATH 470 - Variational Calculus (3)

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.

### MATH 480W - The Art and Craft of Problem Solving (3)

Designed for students with a strong interest in problem solving and the determination to persevere in seeking solutions to highly challenging mathematical problems. Intended as a preparation for the Putnam Competition, the most challenging and prestigious undergraduate mathematics competition in North America, in which effective presentation of solutions is as important as skill in problem solving. Reviews strategic principles, tactical approaches, and specific technical tools for problem solving, and mathematical problem solving folklore. Emphasis is placed on clarity of exposition and persuasiveness of written argument, and on development of communication skills. Students interested in MATH 480W are encouraged to take the course as soon as they meet the prerequisites, since performance in the Putnam Competition often improves with second and subsequent attempts. Prerequisite: MACM 201 with a grade of at least B. At least one of MACM 201, MATH 240, MATH 242, MATH 251, MATH 252 with a grade of at least A, or both of MACM 203, MACM 204 with a grade of at least A. Or permission of the instructor. Students with credit for MATH 370W may not take MATH 480W for credit. Writing/Quantitative.

### MATH 486 - Job Practicum V (3)

This is an optional fifth term of work experience in a co-operative education program available to mathematics and statistics students. Units from this course do not count towards the units required for an SFU degree. This course may be repeated for additive credit. Prerequisite: MATH 437 and permission of the co-op co-ordinator. Students must apply at least one term in advance.

### MATH 491 - Honours Essay (2)

Selected topics. Prerequisite: Written permission of the department undergraduate studies committee.

### MATH 492 - Directed Studies (4)

Independent reading or research in topics selected in consultation with the supervising instructor. Prerequisite: Written permission of the department undergraduate studies committee.

### MATH 493 - Directed Studies (4)

Independent reading or research in topics selected in consultation with the supervising instructor. Prerequisite: Written permission of the department undergraduate studies committee.

### MATH 494 - Directed Studies (4)

Independent reading or research in topics selected in consultation with the supervising instructor. Prerequisite: Written permission of the department undergraduate studies committee.

### MATH 495 - Selected Topics in Applied Mathematics (3)

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.

### MATH 496 - Selected Topics in Mathematics (3)

The topics included in these courses 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.

### MATH 497 - Directed Studies (3)

### MATH 498 - Communication and Research Skills in the Mathematical Sciences (1)

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.

### MATH 499W - Honours Research Project (5)

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 credits of upper division MATH or MACM courses. Must be in an honours program with a GPA of at least 3.0. Corequisite: MATH 498. Writing.

### MATH 603 - Foundations of Mathematics (4)

Crises in mathematics, their historical and philosophical background and their resolution. Prerequisite: Acceptance into the MSc program in mathematics education or permission of the department. Graduate students in the Department of Mathematics cannot take this course to satisfy their degree requirements.

### MATH 604 - Geometry (4)

Euclidean and non-Euclidean geometries. Klein's erlangen program. Prerequisite: Entrance into the MSc in mathematics education program or permission of the department. Graduate students in the Department of Mathematics cannot take this course to satisfy their degree requirements.

### MATH 701 - Computer Algebra (3)

Data structures and algorithms for mathematical objects, including long integers, polynomials, and general mathematical formulae. Topics include 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. Students may not take a 700 division course if it is being offered in conjunction with a 400 division course which they have taken previously.

### MATH 708 - Discrete Optimization (3)

Held jointly with MATH 408-3. See description for MATH 408-3. Students may not take a 700 division course if it is being offered in conjunction with a 400 division course which they have taken previously.

### MATH 709 - Numerical Linear Algebra and Optimization (3)

Held jointly with MACM 409-3. See description for MACM 409-3. Students may not take a 700 division course if it is being offered in conjunction with a 400 division course which they have taken previously.

### MATH 716 - Numerical Analysis II (3)

The numerical solution of ordinary differential equations and elliptic, hyperbolic and parabolic partial differential equations will be considered. Students may not take a 700 division course if it is being offered in conjunction with a 400 division course which they have taken previously.

### MATH 718 - Partial Differential Equations (3)

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. Students may not take a 700 division course if it is being offered in conjunction with a 400 division course which they have taken previously.

### MATH 719 - Linear Analysis (3)

Convergence in Euclidean spaces, Fourier series and their convergence, Legendre polynomials, Hermite and Laguerre polynomials. Students may not take a 700 division course if it is being offered in conjunction with a 400 division course which they have taken previously.

### MATH 724 - Applications of Complex Analysis (3)

Conformal mapping, application to boundary value problems, Schwarz-Christoffel transformation, integral formulas, analytic continuation, argument principle. Students may not take a 700 division course if it is being offered in conjunction with a 400 division course which they have taken previously.

### MATH 725 - Real Analysis (3)

Metric spaces, normed vector spaces, measure and integration, an introduction to functional analysis. Students may not take a 700 division course if it is being offered in conjunction with a 400 division course which they have taken previously.

### MATH 739 - Algebraic Systems - Selected Topics in Algebra (3)

Algebraic systems including, for example, groups, rings. Polynomial theory. Prerequisite: appropriate knowledge of algebraic structures. Students may not take a 700 division course if it is being offered in conjunction with a 400 division course which they have taken previously.

### MATH 740 - Galois Theory (3)

An introduction to the theory of fields, with emphasis on Galois theory. Students may not take a 700 division course if it is being offered in conjunction with a 400 division course which they have taken previously.

### MATH 741 - Commutative Algebra and Algebraic Geometry (3)

A study of ideals and varieties. Topics include affine varieties, ideals, 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. Additional topics depending on the instructor. Groebner bases and automatic theorem proving in geometry, Bezout's theorem, dimension, and elliptic curves.

### MATH 742 - Cryptography (3)

Held jointly with MACM 442-3. See description for MACM 442-3. Students may not take a 700 division course if it is being offered in conjunction with a 400 division course which they have taken previously.

### MATH 743 - Combinatorial Theory (3)

Design theory: Steiner triple systems, balanced incomplete block designs, latin squares, finite geometries. Enumeration: generating functions. Burnside's Lemma, Polya counting. Students with credit for MATH 443 may not take this course for further credit.

### MATH 745 - Graph Theory (3)

Graph coloring, Hamiltonian graphs, planar graphs, random graphs, Ramsey theory, extremal problems, additional topics. Students may not take a 700 division course if it is being offered in conjunction with a 400 division course which they have taken previously.

### MATH 747 - Coding Theory (3)

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. Students may not take a 700 division course if it is being offered in conjunction with a 400 division course which they have taken previously.

### MATH 748 - Network Flows (3)

Held jointly with MATH 448-3. See description for MATH 448-3. Students may not take a 700 division course if it is being offered in conjunction with a 400 division course which they have taken previously.

### MATH 761 - Continuous Mathematical Models (3)

Formulation, analysis and numerical solution of continuous mathematical models. Applications may be selected from topics in physics, biology, engineering and economics. Students may not take a 700 division course if it is being offered in conjunction with a 400 division course which they have taken previously.

### MATH 762 - Fluid Dynamics (3)

Incompressible fluid flow phenomena: kinematics and equations of motion, viscous flow and boundary layer theory, potential flow, water waves. Aerodynamics. Students may not take a 700 division course if it is being offered in conjunction with a 400 division course which they have taken previously.

### MATH 767 - Dynamical Systems (3)

Stability and bifurcation in vector fields and discrete maps. Centre manifold theory and applications of normal forms. Introduction to chaos, Lyapunov exponents, and normal hyperbolicity.

### MATH 770 - Variational Calculus (3)

Held jointly with MATH 470-3. See description for MATH 470-3. Students may not take a 700 division course if it is being offered in conjunction with a 400 division course which they have taken previously.

### MATH 795 - Selected Topics in Applied Mathematics (3)

Held jointly with MATH 495-3. See description for MATH 495-3. Students may not take a 700 division course if it is being offered in conjunction with a 400 division course which they have taken previously.

### MATH 796 - Selected Topics in Mathematics (3)

Held jointly with MATH 496-3. See description for MATH 496-3. Students may not take a 700 division course if it is being offered in conjunction with a 400 division course which they have taken previously.

### MATH 800 - Mathematics: Selected Topics (4)

### MATH 801 - Computer Algebra (4)

Computing with long integers, polynomials, and mathematical formulae. Topics include computing polynomial greatest common divisors, the Fast Fourier Transform, Hensel's Lemma and p-adic methods, differentiation and simplification of formulae, polynomial factorization. Integration of rational functions and elementary functions, Liouville's principle, the Risch algorithm. Students will use a computer algebra system such as Maple for calculations and programming. Students who have credit for either MACM 401 or MATH 701 may not take this course for further credit.

### MATH 804 - Operations Research: Selected Topics (4)

Topics vary depending on faculty availability and student interests. Possible topics include: Applied and Computational Optimization, Approximation Algorithms, Convex Programming, Discrete Convexity and Optimization Methods in Finance.

### MATH 808 - Advanced Linear Programming (4)

Convex geometry, the simplex method and duality, pivot rules, degeneracy, decomposition and column generation methods, the complexity of linear programming and the ellipsoid algorithm, interior point methods for linear programming.

### MATH 817 - Groups and Rings (4)

A survey of graduate group and/or ring theory. Possible topics include generators and relations, composition series, Sylow theory, permutation groups, abelian groups, p-groups, nilpotent and solvable groups, aspects of simple groups, representation theory, group algebras, chain conditions, Jacobson radical, Chevalley-Jacobson density theorem, Wedderburn-Artin theorems.

### MATH 818 - Algebra and Geometry (4)

An introduction to algebraic geometry with supporting commutative algebra. Possible topics include Hilbert basis theorem, Hilbert's Nullstellensatz, Groebner bases, ideal decomposition, local rings, dimension, tangent and cotangent spaces, differentials, varieties, morphisms, rational maps, non-singularity, intersections in projective space, cohomology theory, curves, surfaces, homological algebra.

### MATH 819 - Algebra: Selected Topics (4)

### MATH 820 - Graph Theory (4)

Algebraic graph theory, extremal graph theory, coloring problems, path and cycle structure of graphs, application of graphs, hypergraphs, and current research topics.

### MATH 821 - Combinatorics (4)

An introduction to the theory of incidence structures (finite geometries, block designs) and their relation to linear codes. Algebraic techniques - finite group actions, orbit enumeration, generation of orbit representatives. Exact and asymptotic enumeration of labelled and unlabelled structures.

### MATH 827 - Discrete Mathematics: Selected Topics (4)

### MATH 831 - Real Analysis I (4)

An intensive study of Lebesque measure, integration and the Lebesque convergence theorems together with the treatment of such topics as absolute continuity, the fundamental theorem of calculus, the Lp-spaces, comparison of types of convergence in function spaces, the Baire category theorem.

### MATH 833 - Analysis: Selected Topics (4)

### MATH 841 - Topology: Selected Topics (4)

### MATH 842 - Algebraic Number Theory (4)

Review of Galois theory, integrality, rings of integers, traces, norms, discriminants, ideals, Dedekind domains, class groups, unit groups, Minkowski theory, ramification, cyclotomic fields, valuations, completions, applications.

### MATH 843 - Analytic and Diophantine Number Theory (4)

Arithmetical functions, distribution of prime numbers, theory of Dirichlet characters, Dirichlet series, theory of Riemann Zeta functions and Dirichlet L-functions, exponential sums, character sums, Diophantine equations, Diophantine approximations, applications.

### MATH 845 - Number Theory: Selected Topics (4)

### MATH 846 - Cryptography (4)

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), differential and linear cryptanalysis. RSA and EIGamal 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. Elliptic curve cryptography. Post-quantum cryptography. Students with credit for either MACM 442 or MATH 742 may not take this course for further credit.

### MATH 875 - PhD Preliminary Examination

A preliminary written examination covering a broad range of senior undergraduate material. Graded on a satisfactory/unsatisfactory basis. Prerequisite: Corequisite MATH 876. Only available to students in Mathematics PhD program. Students with credit for MATH 878 may not take this course for further credit.

### MATH 876 - PhD Comprehensive Examination

A comprehensive written examination covering a broad range of graduate material. Graded on a satisfactory/unsatisfactory basis. Prerequisite: Corequisite MATH 875. Only available to students in Mathematics PhD program. Students with credit for MATH 878 may not take this course for further credit.

### MATH 877 - Supplementary Reading (1)

### MATH 878 - PhD Comprehensive Examination

A comprehensive written examination covering a broad range of senior undergraduate and graduate material. Graded on a satisfactory/unsatisfactory basis.

### MATH 879 - PhD Thesis Proposal

An open oral defence of a written thesis proposal presented to the student's supervisory committee. Graded on a satisfactory/unsatisfactory basis.

### MATH 880 - MSc Project (6)

A project leading to research in mathematics completed under the supervision of a faculty member. The project will consist of a written report and a public presentation. This course can only be used for credit towards the MSc project course option. Graded on a satisfactory/unsatisfactory basis.

### MATH 888 - Ph.D. Comprehensive Exam: Operations Research

A written examination covering a broad range of senior undergraduate and graduate mathematical material commonly used in Operations Research. Graded on a satisfactory/unsatisfactory basis.

### MATH 890 - Co-op I

First term of work experience in a co-operative education program. Graded on a satisfactory/unsatisfactory basis.

### MATH 891 - Co-op II

Second term of work experience in a co-operative education program. Graded on a satisfactory/unsatisfactory basis.

### MATH 894 - Reading (2)

### MATH 895 - Reading (4)

### MATH 898 - MSc Thesis (12)

Graded on a satisfactory/unsatisfactory basis.

### MATH 899 - PhD Thesis (12)

Graded on a satisfactory/unsatisfactory basis.