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.Off.lce .o.f . the. Dean. of. Graduate. Studies 

New Graduate Courses, Math 850-4, 

Subject.. ?

7A. 0114. .84.............................

Date ......

eb.rury..14.,.).984

......................... 

r

Action undertaken by the Executive Committee, Senate Graduate Studies 

Committee, gives rise to the following motion:- 

MOTION: "That Senate •approve and recommend approval 

to the Board of Governors, as set forth in 

S.84-23, the proposed new graduate courses: 

MATH 850-4 Numerical Linear Algebra 

MATH 851-4 Numerical Solution of Ordinary 

Di fferential Equations 

MATH 852-4 Selected Topics in Numerical Analysis 

These courses were approved by the Executive Committee, Senate 

Graduate Studies Committee at its meeting on February 13, 1984. 

John 

M.

Webster 

C it 

Dean of Graduate Studies. 

mm/

SiMON FRASER UNIVERSITY

MIMORANDUM

To ....... ... 

M

...ebst..      

............ 

an

•

of ... 

Subj.d .... .RIcL

AN1SLYI5, .CQU.ILE.S......

From ...... .3.,F.,.. 

go.ctir.an

,...en..................

...

F.acu.lty. .o.f. .S.cLexce..................... 

Date... J.anuar.y.. 24.,. .1981e........................ 

Dear John: 

I am replying to your memo of January 13, 1984 concerning 

the Faculty approval of Mathematics graduate courses: 

MATH 850-4 

MATH 851-k 

MATH 852-4 

These courses were approved by the Faculty of Science at Its 

meeting on Monday, October 18, 1982. A copy of the appropriate 

motion is attached. Note that two Items were approved 

Independently in that motion: 

(1)  the M.Sc. Program In Applied Statistics; 

(2)

the new graduate courses In Mathematics. 

Subsequent to the Faculty Meeting I wished to assure myself 

that everyone had been clear on what we had passed at that meet- 

ing. ? 

I therefore distributed the memo of October 26, 1982 to the 

Chairmen (copy attached). My memo made It very clear that we had 

passed the adoption of new math graduate courses independent of 

the new Applied Statistics Program. ? 

1 received no representa- 

?

tions that anyone wanted the matter of the Math graduate courses 

to be reconsidered. In my view, these new courses have been 

approved on the basis of their intrinsic merit. 

/ mq j 

?

JOhn F. Cochra#O. 

cc:

?

Chairmen, Faculty of Science 

JAN 25 1984

DEAN OF GRADUATE

STUDIES OFFICE

of the Ficn1ty of Sr.ience 

1iig•

of Mond,jv, Octoh.r 18. 1992. . ...Page 

2. ? 

MATHEMATICS 

New

Project Option in 

statistics (Paper F-82-2) 

Tticr& was considerable discussion On the proposed project 

option In statistics and questions were raised as to whether 

this woiihj he 

prnfe;sj one I derue or an academic degree 

and would this option not be changing the pattern of 

originni work carrI'(1 out for a Master's thesis. 

?

FacuLty 

were advised that an M.S. in Mathematics does not have 

to ?

?

t'r I g I na 

I

r!c ? 

It. can he expositor y . 

?

The M. Sc . In 

M t.herni t. i (:': 1

not.

I1f,CesSfi

ri ly 

resea 

rch

degree 

the

major ts-sueN ra ist'd was the 

lahe] ii

ng of

the

dl

program 

-

t2ifld

tfr

as

r't.

a;

such 

Iv.

nfl

?

'l'h 

?

M .

?

and

.

the

Is a 

poss 

research 

bill 

y

degree 

of labelling

and should 

it

?

r

cl 'CUSS

tn

the

following was

moved by G . A .C. (',ratim 

s Cflfl(Jf!(

j

t)V M . 

S

t ph ii s 

MOTION ? 

"That the M.c. Program in Applied Statis_tjcand 

P

robability with a project requirement 

&dditIo1 new course* Presented Is the

docIseetatjon he approved." 

MOTION CARRIEP. 

The meeting was adjour, 

p

d at 5:45 p.m. 

$iPlI YPA$t*

vN1vv'clrv ?

$ivCtaduat. 

Curs*

PronuRl f 

j.F

Ajt

Nj,hrt 

Math

850-4

Titleg 

?

Numerical Linear Algebra -

Description:

Direct 

methods

for

n*znerical_solution of

linear-systems of 

euationi

are

considered with emphasis on various applications such as statistical 

computing.

4

?

Vsctort___                   

_

Credit Hours: ? 

_______________________

4-0-0 

?

Prerequisite(n) If 

e

Inroilmuntl 

?

When 

ill

the

course

first 

be off.r.dx_____________________

be off.r.ds 

Once

every two years. 

JUSTTFICAfl ?

(see attached) 

The course has been regularly offered (4 times in the last 5 years) 

under

"Selected 

Topics

in Applied 

Mathematics", and

it is desireable to give the course a 

accurate 

normally teach the covye.mR. Russell, B. Bhattacharya 

(Cainpt.

Sc.) 

ht

the

bud

g etar y 

Imp lications 

p wt1ni the courser 

?

1/6 of 

faculty

member.

Ii,

Ard

chcr.

seffictcnt Library resources 

(a ?

oend

.I

.tail.Y:'S 

indication of 

the conetence of 

the

Faculty 

penber 

to tive the

course.

c) Library resources 

Approved:

Dr

^ p

artnental 

Graduate Studies

Costtt

Mote 

I

Tacuty 

Graduate

flnt•t

Cu

1 t7

I

?

flt.i

M,vltf2

Senate Graduate Studies

Date l_____

MATHF21ATICS 850-4

NUMERICAL LINEAR ALGEBRA

Course Outline 

(a) ? 

i. Errors in Floating Point Computation 

Number representatives, truncation error, 

roundoff error, ill-posed (ill-conditioned) 

problems, inverse error analysis. 

II. Direct Methods for Solving Linear Systems 

(a)

Special matrices and matrix properties, vector 

and matrix norms, error analysis of Gaussian 

elimination, iterative improvement. 

(b)

Orthogonal Factorizations-Householder and Givens 

transformations, modified Gram-Schmidt, singular 

value decomposition. 

II. Linear Least Squares 

Methods using orthogonal factorization, sweep 

operations and normal equations, iterative refinement 

low rank changes and singular value decomposition, 

all possible regressions, stepwise regression, 

regression under linear equality/inequality 

constraints. 

IV. Special Topics 

Chosen from among the following: 

A. Computational, methods for classification models 

fixed-effect, models (special case of balance and 

completeness and general problem), computing 

expected mean squares and estimates of variance 

Components. 

.

(2 weeks) 

(4 weeks) 

(2 1/2 weeks) 

(4 1/2 weeka) • 

B.

Selected Multivariate Methods 

canonical correlations, principal components 

Factor analysis, multivariate analysis of variance. 

C.

Algebraic elgenvalue problem 

Similarity transformations, reduction to canonical form,. 

sensitivity of eigenvalues and eigenvectors, QR 

algorithm, computation of singular value decomposition. 

D.

Unconstrained optimization and nonlinear regression 

steepest descent, Newton's method and variants 

conjugate gradients, modified Gauss-Newton and 

Le venberg-Ma.rqurdt, 

?

alternative gradient methods, 

minimization without derivatives. 

(b) ? 

The material 

covered in this course is standard in the backgrounds of 

those doing 

research in numerical analysis. 

? -

(c) ?

The

library 

is well-supplied with texts in this area and subscribes 

to most major 

numerical analysis journals. 

•

ITY

Câsdat.CevrS.ProoaaI'or.

Dcp.rtn.nt: ? 

_i_

CflUTIC w

up6ero________________

Title:

Nuzzrical Solution

of

Ordinary

Differential 

Equations

Description

Study 

of the practical numerical methods for solving initial 

and

boundary value problems for

ordinary

differential equations.

Credit Hours:

y.etors_ 

?

400 ? 

Prer.qui.ftc(A) if an:_

INOhtMt.XT

AND

ciatc'

Will

COunt

firAt

be of(ar.dt____________________

Hc'i

t

en will the course

off.rdi

Once every two

years.

JUST I 

f

I CAT 101: 

This 

c?uroe 

has previously 

been

offered as Selected

Topics in Applied 

m a thematics

and it is expected that numerical analysis, applied 

mathematics.

and r

hysicalEciences

students

will 

regularly

take the 

course.

JSOURC(S: 

Which 

will

pro

the

bud&.tary Implications of momitine et*

cour.1L!_ot_a

faculty member.

/.rPrc v .d

Dcrtntl Graduate Studies

Faculty

Grad a a

stud

).te)4T)

SfieIt Graduate Studies

_____________

J-t^ 

vLz

p

tvf

enhtuI_

fln?pi________

MATHEMATICS 851-4

NUMERICAL SOLUTI4 0? ORDINARY DIFFERENTIAL EQUATIONS 

Course Outline 

(a)

?

i. introduction to Ordinary Differential Equation. 

model problems, general let order systems, 

existence and uniqueness, problem stability, 

GreeflS functions. 

II. Initial Value problems 

Euler's iethod for illustration, higher order one-step 

methods (Taylor series method and explicit/implicit 

Runge Kutta), convergence and stability, error bounds 

and error estimates, step size choice, extrapolation 

methods, multistep methods (Mama methods, predictor' 

(2 weeks) 

(5 1/2 weeks) 

corrector methods). 

iii. -Boundary Value Problems 

?

(5 1/2 weeks) 

initial value approaches Csimple end multiple shooting), 

finite difference methods, stability and convergence, 

acceleration methods, collocation methods, mesh selection, 

special methods for solution of linear and nonlinear 

systems. 

(b)

The material covered in this course is standard in the backgrounds of 

those doing research in numerical analysis. 

(c)

The library is well-supplisd with texts in this area and subscribes 

to most major numerical analysis journals. 

.

.

)

(

sz?Mr

VN%1.'ITY 

New croduater-c-Mrs — 

a

Prcmosal Tom 

CALENDAR 1N1ORMATI1.

mathematics 

?

.

? Math 

852-4 

Dep.rtTeft

Title: ?

Selected Topics in Nterica1 

Malysia

Study of a specialized area of numerical analysis such as partial 

differential 

flescriptiont 

equations, continuous optimization, or approximation theory. 

Credit IorPt 

?

V.ctort ? 

4-0-0 ? 

Prerequisite(s) If anv________ 

1NT10L1Y'T A

sc,IFI'ItL!?IC.!

rstjnbLed Enrollments 

?

5-

?

When 

will the 

course first be offeredi_____________________ 

Had

of tcn 

will

the course be off.red* ? 

Once every 

.two years. 

?

- -

JusnrlCATTo:: 

?

.

With an increasing number 

of students doing mathematical computation orstudying 

nunerica1 analysis, 

there is need to provide regularly what have previously 

L.ccn 

reading 

courses. 

urcn(IR( 

R. Russell, .hattacharYa (pt. Sci.) 

Which Faculty

utc&er will nor*ally teach th course 

1/6 of a 

faculty 

member. 

61i&t

are ? 

o

bud*

t

y

I

?

It1

?

Of

moun1flI 

rn.

caurr

If1

eulfictent Library resources 

(sf5054

dstatIs) ? 

Yea.. 

Apptflded$. a)

Outline of the Course 

?

.

b)

An Indication of the comnetsnes of the Faculty ,entsr to give the course. 

c)

Library rO.ourcse 

Approved: Departmental Craduste Studies comsittt..ijc/ 

ye

}sculiy Cr.d(: 

r1stes ? 

es

Pecu 

ity I

Senate Craduts Studies 

Cewustttii 

Senat.i 

&LhYl-.._Th%t.l 

Akt..

/q/9'_.

4t•1

(4/L$4

fl,tet

rurther information. reqarding 

MATH 8524 

?

ToptCB

in Numerical My) 

(a)

Course outline varies with topic selected. 

(b)

The materialcovered in this course is standar 

d

in the backgrounds of 

those doing research in numerica 

l

anft1YBt'

(ç) 

his area and subscribes 

The library is ilsupPhi with texts Lis t 

to most major numerical analysts journals. 

-

?

- ?

-

?

-

?

-

?

0 ?

--.