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## Department of Mathematics

K10512 Shrum Science Centre, 778.782 3331/3332 Tel, 778.782 4947 Fax, www.math.sfu.ca

- Chair
A.H. Lachlan BA, MA, PhD (Camb), FRSC

- Professors Emeriti
B.R. Alspach BA (Wash), MA, PhD (Calif)

G. Bojadziev PhD (Sofia Mech Eng Inst)

A. Das BSc, MSc (Calc), PhD (NUI), DSc (Calc)

R.W. Lardner BA, PhD, ScD (Camb)

M. Singh AB, MA (Punj), MSc, PhD (Brown)

S.K. Thomason BS (Oregon), PhD (C'nell)

B.S. Thomson BSc (Tor), MA, PhD (Wat)

- Professors
J.L. Berggren BS, MS, PhD (Wash)

J.M. Borwein BSc (WOnt), MSc, PhD (Oxf), FRSC

P.B. Borwein BSc (WOnt), MSc, PhD (Br Col)

T.C. Brown BA (Reed), AM, PhD (Wash U)

G.A.C. Graham BA (Dub), MS (Brown), PhD (Glas)

P. Hell BSc (Prague), MSc (McM), PhD (Montr)*

A.H. Lachlan BA, MA, PhD (Camb), FRSC

R.D. Russell BS, BA, MA, PhD (New Mexico)

C.Y. Shen BS, MS, PhD (Oregon State)

- Associate Professors
L. Goddyn BSc (S Fraser), MMath, PhD (Wat)

M.B. Monagan BSc (Massey), MMath, PhD (Wat)

D. Muraki BSc, MSc (Calif Inst Tech), PhD (Northwestern)

K. Promislow BSc (N Carolina), PhD (Indiana)

M.R. Trummer Dipl Math ETH, PhD (Zurich)

- Assistant Professors
R. Choksi BSc (Tor), MS, PhD (Brown)

K-K.S. Choi BSc, MPhil (HK), PhD (Texas)

M.C.A. Kropinski BSc (Qu), MMath (Wat), PhD (Rensselaer)

K. Promislow, BSc (N Carolina), PhD (Indiana)

S. Ruuth BMath (Wat), MSc, PhD (Br Col)

- Adjunct Professors
H.H. Bauschke Dipl-Math (Goethe), PhD (S Fraser)

R. Brewster BSc, MSc (Vic, BC), PhD (S Fraser)

D. Hare BSc (Vic, BC) MSc (Alta), PhD (S Fraser)

L. Jorgenson BSc (Qu), MSc, PhD (McG)

V. Jungic BSc (Sarajevo) MSc (Croatia), PhD (S Fraser)

G. Reid BSc (Otago), PhD (Waik)

M. Rosenfeld MSc, PhD (Hebrew University)

N. Tariq BSc, MSc (KCNS), PhD (New Br)

J. Vanderwerff MSc, PhD (Alta)

M.L. Yu BSc (Fundan, Shanghai), MSc, PhD (S Fraser)

Q. Yu BSc, MSc (Shandong), PhD (S Fraser)

R. Zahar BASc, MA (Br Col), MS (Purdue), MA (Camb), PhD (Purdue)

- Associated Faculty

- Senior Lecturers
J.C. Arya BSc (Agra), MA ( Punjab), MSc, PhD (S Fraser)

T.M. Berggren BA (Wash), MSc (S Fraser)

*joint appointment with computing science

- Advisor
Mrs. M. Fankboner BA (Occidental), MSc (S Fraser), K10511 Shrum Science Centre, 778.782 4849

The department also maintains a committee of faculty advisors each year and their office hours are available through the Department of Mathematics general office. Students wishing to major in any of the programs sponsored by the Department of Mathematics should seek advice early in their academic careers about program planning from departmental faculty advisors.

Students are also invited to apply to enter the Cooperative Education program in mathematics and statistics, which integrates work experience with academic study. For further details, students should see "Cooperative Education". and they should also consult with the mathematical sciences coop coordinator, Mr. E. Simons, in K10507, telephone 778.782 4123, esimons@sfu.ca.

The major and minor programs listed below lead to a Bachelor of Science degree in the Faculty of Science. Students interested in a Bachelor of Arts degree in mathematics or should see "Mathematics Program". in the Faculty of Arts section.

Students interested in mathematics may also wish to consider related programs detailed under the sections on programs in statistics, applied mathematics, mathematics and computing, mathematical physics, management and systems science, and actuarial science.

## General Regulations

Students will not be permitted to enroll in any course for which a D grade or lower was obtained in any prerequisite course.

Major or honors students must satisfy Faculty of Science requirements. They must also satisfy general University CGPA and credit hour requirements. Please see "Mathematics". for entry level course requirements and department workshops.

## Prerequisite Grade Requirement

Without at least a C- or higher in each prerequisite course, or a special waiver from the department, a student may not register in any department course.

## Applied Mathematics Major Program

Applied mathematics consists of areas of mathematics which are closely related to such traditional fields as the physical sciences and engineering, but nowadays sophisticated mathematical tools are used over a wide spectrum of disciplines. With the rapid development of computers, applied mathematics is increasingly computationally oriented. Applied mathematicians are in demand and the good student in the field is virtually sure of an interesting career whether she/he chooses industrial research, government laboratory or university.

The Department of Mathematics offers sufficient undergraduate courses to specialize in applied mathematics. Details for applied mathematics of physics and engineering are given below. Also, there are joint honors in mathematics and computer science and in mathematical physics. Both include a substantial number of applied mathematics courses. A concentration in applied mathematics will provide an excellent basis for a career in engineering, and Simon Fraser's engineering science program make considerable use of courses in this area.

Required courses are as follows.

## Lower Division Requirements

(36-37 credit hours plus electives)

CMPT 101-4 Introduction to Computer Programming

CMPT 102-3 Introduction to Scientific Computer Programming

MACM 202-4 Mathematical Modeling and Computation

MATH 232-3 Elementary Linear Algebra

MATH 242-3 Introduction to Analysis*

PHYS 120-3 Modern Physics and Mechanics

PHYS 121-3 Optics, Electricity and Magnetism

PHYS 211-3 Intermediate Mechanics

STAT 270-3 Introduction to Probability and Statistics

*to be completed by end of year 2

## Upper Division Requirements

(30 credit hours plus electives)

MACM 316-3 Numerical Analysis I

MATH 310-3 Introduction to Ordinary Differential Equations

MATH 313-3 Differential Geometry

MATH 314-3 Boundary Value Problems

MATH 320-3 Advanced Calculus of One Variable

MATH 309-3 Continuous Optimization

MATH 408-3 Discrete Optimization

MATH 415-3 Ordinary Differential Equations

MATH 416-3 Numerical Analysis II

MATH 418-3 Partial Differential Equations

MATH 424-3 Applications of Complex Analysis

STAT 380-3 Introduction to Stochastic Processes

MATH 361-3 Mechanics of Deformable Media

MATH 470-3 Variational Calculus

Choices from the above must include at least three courses at the 400 level and the credit hours must total at least 120, of which at least 12 must be taken outside the Faculty of Science, including a minimum of six hours in the Faculty of Arts. At least 44 hours must be at the upper division.

## Applied Mathematics Honors Program

## Lower Division Requirements

(36-37 credit hours plus electives)

CMPT 102-3 Introduction to Scientific Computer Programming

MACM 202-4 Mathematical Modeling and Computation

MATH 232-3 Elementary Linear Algebra

MATH 242-3 Introduction to Analysis

PHYS 120-3 Modern Physics and Mechanics

PHYS 121-3 Optics, Electricity and Magnetism

PHYS 211-3 Intermediate Mechanics

STAT 270-3 Introduction to Probability and Statistics

## Upper Division Requirements

(48 credit hours plus electives)

MATH 310-3 Introduction to Ordinary Differential Equations

MATH 313-3 Differential Geometry

MATH 314-3 Boundary Value Problems

MATH 320-3 Advanced Calculus of One Variable

MATH 361-3 Mechanics of Deformable Media

MACM 316-3 Numerical Analysis I

MATH 416-3 Numerical Analysis II

STAT 380-3 Introduction to Stochastic Processes

MATH 309-3 Continuous Optimization

MATH 408-3 Discrete Optimization

MATH 415-3 Ordinary Differential Equations

MATH 418-3 Partial Differential Equations

MATH 424-3 Applications of Complex Analysis

STAT 330-3 Linear Models in Applied Statistics

MATH 470-3 Variational Calculus

Choices from the above must include at least five 400 level courses and total at least 132 credit hours, of which at least six must be in the Faculty of Arts. At least six further hours must be in a faculty other than science, and at least 60 must be at the upper division.

## Management and Systems Science Program

- Co-ordinator
D. Muraki BSc, MSc (Calif Inst Tech), PhD (Northwestern), 778.782 4814

The Department of Mathematics and the Department of Statistics and Actuarial Science, in conjunction with the Faculty of Business Administration, the School of Computing Science and Department of Economics, offers a major and honors in management and systems science (MSSC) leading to a BSc degree. These are highly structured programs providing a multidisciplinary approach to quantitative methods to business and industry in an environment of expanding computerization. A seminar in which problems requiring a broad perspective are presented and discussed has been designed for upper division students.

The management and systems science program coordinator is selected from the associated faculty.

The program cooperates with the School of Computing Science regarding program admission. Students formally apply to be admitted into the program. Acceptance will be based on overall academic performance as measured by the cumulative grade point average (CGPA). The CGPA is calculated based on all work completed at SFU as described in the General Regulations section.

A student may apply for program acceptance during the semester in which she/he is completing all lower division requirements. Transfer and second degree students who have credit for all lower division requirements may apply for special admission consideration based on transcripts from other post-secondary institutions. To remain in the program, students must maintain a 2.5 CGPA. It is strongly recommended that you contact the program advisor or coordinator early about admission and scheduling.

## Management and Systems Science Major Program

- · Under program and University regulations a general degree requires a minimum of 44 upper division credits in courses numbered 300 and above, completion of at least 120 credit hours, and completion of the major program.
- · Six elective credit hours must be completed in courses taken from outside the Faculty of Business Administration, School of Computing Science, Departments of Economics, Mathematics, and the Department of Statistics and Actuarial Science.
- · Completion of all lower and upper division courses shown below is required. However, students should be aware of the requirements for entrance into business administration, computing science and economics courses. Contact those departments for further information.
BUS 207-3 Managerial Economics

ECON 301-5 Intermediate Microeconomic Theory

BUS 251-3 Financial Accounting I Computing Science

BUS 272-3 Behavior in Organizations

- Computing Science
CMPT 101-4 Introduction to Computer Programming

CMPT 150-3 Introduction to Computer Design

CMPT 201-4 Data and Program Abstraction

CMPT 275-4 Software Engineering

- Economics
ECON 103-3 Principles of Economics (I) Microeconomics

ECON 105-3 Principles of Economics (II) Macroeconomics

- Mathematics and Computing Science
MACM 101-3 Discrete Mathematics I

MACM 201-3 Discrete Mathematics II

- Mathematics and Statistics
MATH 232-3 Elementary Linear Algebra

STAT 270-3 Introduction to Probability and Statistics

- Upper Division Requirements
For the BSc degree in management and systems science, all of the upper division courses listed below are required.

Students must take a minimum of 34 upper division credit hours, such that at least nine are taken from each of the groups under business administration (excluding ECON 301), computing science, and mathematics and statistics. Those credit hours taken beyond 34 can be applied to other major or minor programs. Only one of ECON 301 and BUS 207 is required for the Management and Systems Science major program.

- Business Administration
BUS 343-3 Introduction to Marketing

BUS 364-3 Information Systems in Organization and Society

BUS 473-4 Operations Management

- Computing Science
CMPT 305-3 Computer Simulation and Modelling

CMPT 307-3 Data Structures and Algorithms

CMPT 354-3 File and Database Structures

CMPT 370-3 Information System Design

- Economics
BUS 207-3 Managerial Economics

ECON 301-5 Intermediate Microeconomic Theory

- Mathematics and Statistics
MATH 343-3 Applied Discrete Mathematics

MATH 408-3 Discrete Optimization

STAT 330-3 Introduction to Statistical Inference

- Management and Systems Science
MSSC 480-1 Undergraduate Seminar in Management and Systems Science

MSSC 481-1 Undergraduate Seminar in Management and Systems Science

Students should note the prerequisites for these courses.

Note: BUEC 232, BUEC 333 and ECON 331 will not be accepted towards the 120 or 132 hours required for the MSSC major or honors degree.

## Management and Systems Science Honors Program

- · Under University regulations, an honors degree requires completion of a minimum of 60 upper division credit hours in courses numbered 300 and above, including at least 50 upper division credit hours in the honors program, and completion of at least 132 credit hours. Honors students require a graduation grade point average of not less than 3.00.
- · Students must complete all of the requirements as specified above for the degree with the major program. In addition, the student must complete the following upper division courses.
CMPT 405-3 Design and Analysis of Computing Algorithms

STAT 350-3 Linear Models in Applied Statistics

MATH 443-3 Combinatorial Theory

MATH 445-3 Introduction to Graph Theory

- · Students must also complete at least three credit hours in business administration or in economics at the 400 division.
For major or honors, the following upper division courses are recommended.

BUS 488-3 Human Relations in Business

CMPT 405-3 Design and Analysis of Computing Algorithms

BUEC 396-3 The Structure of Industry

ECON 431-5 Intermediate Mathematical Economics

MACM 316-3 Numerical Analysis I

MATH 310-3 Introduction to Ordinary Differential Equations

MATH 443-4 Combinatorial Theory

STAT 410-3 Statistical Analysis of Sample Surveys

STAT 430-3 Statistical Design and Analysis of Experiments

Note: Students who wish to combine the MSSC honors program with another major or minor should consult with the MSSC program co-ordinator for details.

## Mathematics Major and Honors Programs

The requirements of the department are as follows.

## Lower Division Requirements

CMPT 101-4 Introduction to Computer Programming

CMPT 201-4 Data and Program Abstraction

MACM 101-3 Discrete Mathematics I

MACM 201-3 Discrete Mathematics II

MACM 202-4 Mathematical Modeling and Computation

MATH 232-3 Elementary Linear Algebra

MATH 242-3 Introduction to Analysis*

STAT 270-3 Introduction to Probability and Statistics

*to be completed either as part of the student's first 60 credit hours or as soon as possible after the student declares the major.

Note: With a grade of C or better in the relevant course, the following substitutions are permitted: CMPT 104 for CMPT 101, MATH 154 or MATH 157 for MATH 151, MATH 155 or MATH 158 for MATH 152. However, where possible, students should take MATH 151 and MATH 152.

## Upper Division Requirements

All students must take at least one from each of the following four pairs of courses.

MATH 343-3 Applied Discrete Mathematics

MATH 320-3 Advanced Calculus of One Variable

MATH 332-3 Introduction to Applied Algebraic Systems

MATH 342-3 Elementary Number Theory

MATH 310-3 Introduction to Ordinary Differential Equations

MACM 316-3 Numerical Analysis I

BSc math major students must obtain at least 30 credit hours in upper division mathematics (MATH), statistics (STAT*), actuarial (ACMA), or mathematics/computing science (MACM), or PHYS 413.

Of the 30 credit hour minimum total requirement for the mathematics major, at least 15 must come from MATH courses. At least three of the courses used to satisfy the 30 credit hour requirement must be at the 400 division level, of which at least two must be 400 division MATH courses. Students may not use a directed studies, job practicum, or honors essay course to fulfil the 400 division requirement.

## Honors Program Specific Requirements

In addition requirements for the major, honors students must obtain at least 18 additional credit hours in upper division mathematics (MATH), statistics (STAT*), actuarial mathematics (ACMA), or mathematics/computing science (MACM) courses, or PHYS 413. Of this minimum 48 upper division credit hours, at least 24 must come from MATH courses.

At least five of the courses used to satisfy the 48 credit hour requirement must be at the 400 division level, of which at least three must be 400 division MATH courses. Students may not use a directed studies, job practicum, or honors essay course to fulfil the 400 division requirement.

*None of STAT 301, 302 and 403 may be counted toward the 30 credit hours requirement for a major, or towards the 48 credit hours requirement for an honors, although they may be counted as upper division elective credits.

Note: Major or honors mathematics students are advised to take an upper division statistics course and an upper division MACM or CMPT course.

## Major and Honors Program Electives

Students must obtain at least six credit hours in courses offered by the Faculty of Science outside the Department of Mathematics. Students must obtain at least six credit hours in Faculty of Arts courses. (The two required CMPT courses and the six credit hour requirement in Faculty of Arts courses fulfil the Faculty of Science requirement that students take 12 credit hours from outside the Faculty of Science.)

Major program students must complete at least 44 upper division credit hours, including the requirements for the major. Honors program students must complete at least 60 upper division credit hours, including the requirements for honors.

## Mathematics Minor Program

Students completing a minor in mathematics are subject to the general regulations of the faculty in which they are registered. Students normally are required by the Department of Mathematics to

- i) obtain at least 11 mathematics or statistics credit hours (MATH 100, 110, 190 may not be included) or mathematics/computing science (MACM) courses numbered 101-299 inclusive. These courses normally will include MATH 151 (or 154 or 157), 152 (or 155 or 158), and 232.
- ii) obtain credit in at least 15 credit hours of upper division mathematics (MATH) or statistics (STAT) or mathematics/computing science (MACM) or actuarial mathematics (ACMA) courses. These courses may not include PHYS 413 or STAT 301 or STAT 403.
## Mathematics and Computing Science Honors Program

This honors program is offered jointly by the Department of Mathematics and the School of Computing Science. Entry requires permission of both the department and the school. Graduates may proceed to graduate work in either mathematics or computing science. (Depending on the particular area of interest of the student, a small amount of additional undergraduate work in either mathematics or computing science may be required.)

Normally, students apply for acceptance upon completion of the lower division requirements for the program. Early acceptance is available for SFU students and transfer students with high cumulative GPAs and program related GPAs. Direct acceptance is also possible for secondary school students with strong university admission GPAs.

Students must complete 132 credit hours, as specified below.

- Lower Division Requirements
CMPT 101-4 Introduction to Computer Programming

CMPT 150-3 Introduction to Computer Design

CMPT 201-4 Data and Program Abstraction

CMPT 250-3 Introduction to Computer Architecture

CMPT 275-4 Software Engineering

MACM 101-3 Discrete Mathematics I

MACM 201-3 Discrete Mathematics II

MACM 202-4 Mathematical Modeling and Computation

MATH 232-3 Elementary Linear Algebra

MATH 242-3 Introduction to Analysis

STAT 270-3 Introduction to Probability and Statistics

*a 100 division English course may be substituted

Note 1: A student who, in satisfaction of upper division requirements (see below), wishes to use group e) as one of the two upper division required groups taken from the list a), b), c), d), e) must also obtain credit for the lower division course MATH 252.

Note 2: A student wishing to use courses from group a) to satisfy requirements is advised that STAT 280 is a prerequisite for STAT 380.

- Upper Division Requirements
MACM 316-3 Numerical Analysis I

CMPT 307-3 Data Structures and Algorithms

CMPT 405-3 Design and Analysis of Computing Algorithms

MATH 343-3 Applied Discrete Mathematics

- · the required courses in two of the groups a), b), c), d), e) below and in two of the groups f), g), h), i), j) below.
- · additional courses as required taken from any of the lists a) - k) below to bring the total upper division credits in MATH or STAT to at least 25 and the total credits in upper division CMPT to at least 25 where, for this purpose, credit obtained in MACM courses is divided evenly between MATH and CMPT.
- · the Social Aspects of Computing requirement of the computing science major and honors program
- · additional courses as required to bring the total number of upper division credits to at least 60.
STAT 330-3 Introduction to Statistical Inference

STAT 350-3 Linear Models in Applied Statistics

STAT 380-3 Introduction to Stochastic Processes

- Other courses
STAT 402-3 Generalized Linear and Nonlinear Modelling

STAT 460-3 Bayesian Statistics

- b) Discrete Mathematics

- Required courses
MATH 343-3 Applied Discrete Mathematics

MATH 408-3 Discrete Optimization

MATH 443-3 Combinatorial Theory

- c) Algebra

- Required courses
MACM 401-3 Introduction to Computer Algebra

- d) Numerical Analysis

- Required courses
MATH 310-3 Introduction to Ordinary Differential Equations

MATH 416-3 Numerical Analysis II

- e) Applied Mathematics

- Required course
MATH 310-3 Introduction to Ordinary Differential Equations

MATH 314-3 Boundary Value Problems

MATH 415-3 Ordinary Differential Equations

MATH 418-3 Partial Differential Equations

MATH 470-3 Variational Calculus

- f) Computer Graphics and Multimedia

- Required course
CMPT 361-3 Introduction to Computer Graphics

CMPT 363-3 User Interface Design

- Other courses
CMPT 461-3 Advanced Computer Graphics

CMPT 468-3 Scientific Visualization

CMPT 469-3 Special Topics in Computer Graphics

- g) Computing Systems

- Required course
CMPT 300-3 Operating Systems I

CMPT 371-3 Data Communications and Networking

- Other courses
CMPT 400-3 High Performance Computer Architecture

CMPT 401-3 Operating Systems II

CMPT 402-3 Operating Systems Software Laboratory

CMPT 479-3 Special Topics in Computing Systems

CMPT 499-3 Special Topics in Computer Hardware

- h) Programming Languages and Software

- Required course
CMPT 379-3 Principles of Compiler Design

CMPT 383-3 Comparative Programming Languages

- Other courses
CMPT 475-3 Software Engineering II

CMPT 480-3 Foundations of Programming Languages

CMPT 481-3 Functional Programming

CMPT 487-3 Software Engineering Tools and Environments

CMPT 489-3 Special Topics in Programming Languages

- i) Information Systems

- Required course
CMPT 301-3 Information Systems Management

CMPT 370-3 Information System Design

CMPT 454-3 Database Systems II

CMPT 459-3 Special Topics in Database Systems

- Other courses
CMPT 302-3 System Development Projects

CMPT 470-3 Advanced Application Development Tools

- j) Artificial Intelligence

- Required course
CMPT 310-3 Artificial Intelligence Survey

CMPT 412-3 Computational Vision

CMPT 413-3 Computational Linguistics

CMPT 417-3 Intelligent Systems

- Other courses
CMPT 411-3 Knowledge Representation

CMPT 414-3 Model Based Computer Vision

CMPT 419-3 Special Topics in Artificial Intelligence

- k) Theoretical Computing Science
CMPT 308-3 Computability and Complexity

CMPT 406-3 Computational Geometry

CMPT 407-3 Computational Complexity

CMPT 408-3 Theory of Computer Networks/Communications

CMPT 409-3 Special Topics in Theoretical Computing Science

MACM 300-3 Introduction to Formal Language and Automata with Applications

## General Requirements

The program is subject to Faculty of Science and University general regulations. Admission to courses and prerequisites are subject to departmental requirements. Admission to and continuation in the program requires an overall GPA of at least 3.00.

## Mathematical Physics Honors Program

This program, offered jointly with the Department of Physics, consists of theoretical and laboratory physics and applied and pure mathematics courses. See "Mathematical Physics Program".

## Cooperative Education Program

Students are encouraged to enter cooperative education, a program which integrates work experience with academic study. For further details, see "Cooperative Education".

Students should contact the mathematical sciences coop coordinator at 778.782 4123, K10507, for admission requirements and information.

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Index : searchable with the Find function in your web browser | Calendar.pdfs | Office of the Registrar / SFU |

Table of Contents : searchable with the Find function in your web browser | Course Database or Course Outlines (opens in new window) |
Financial Assistance |