SiMON FRASER UNIVERSITY
MEMORANDUM
To ?
SENATE
?
From
S7.2-1.11
Date ?
DECEMBER 16, 1971
Subject
CURRICULUMANDCALENDARCHANGES
-
?
DEPARTMENT OF MATHEMATICS
• ?
MOTION: ?
"That Senate approve, as set forth in S.72
.
-14
PROPOSAL I.
?
Degree Requirements for Majors and Honors in
Mathematics.
PROPOSAL II. • Degree Requirements for a Minor Program in
Mathematics.
PROPOSAL III. Adjustment to the Calculus Sequence - with
discontinuance of Mathematics 251-3, replaced?
?
•
?
by Mathematics 253-4.
PROPOSAL IV.
?
Discontinuance of Mathematics 411-4, replaced
?
•
?
by Mathematics 311-4 (renumbering).
PROPOSAL V. ?
Change in Prerequisite for Mathematics 422-4.
?
•
? PROPOSAL VI.
?
New Course Proposal - Mathematics 302-3 - with
discontinuance of Mathematics 102-3."
0
?
SiMON FRASER UNIVERSITY
?
S
72 -1
. ?
MEMORANDUM
To
?
SENATE ?
From
SENATE COMMITTEE ON UNDERGRADUATE
_STUDIES
• ?
Subiect
CUR.RICULUN_AND_CALENDAR_
CHANGES
_- ?
Date
_
DECEMBER-16. 1971
•S
DEPARTMENT OFMATHEMATICS
?
S ? • ?
•
The Senate Committee on Undergraduate Studies approved
•
?
S •
the.submissiôn of the Department of Mathematics, as set
•
?
S.
forth in SCIJS 71-27, and recommends approval to Senate.
40
SIMON FRASER UNIVERSITY
?
SC..L)c
'1l-7i
MEMORANDUM
fl
10 ?
II. Evans, Secretary
Studies
Subject
................................................................................................................
Agenda Item for SCUS:
Faculty of
g cienec ?
Propoualo
for-Changes in Mathematics Under-
graduate Calendar Submission
(including new course proposal).
From ....... ........ S.
?
Aronoff,... Chairman.... ..........................
Faculty. of. .S.c.i.ence..Executi.vc. Committee
Date...... ......... November23,. .1971......................................
Enclosed please find the paper entitled "Proposals for Changes in
Mathematics Undergraduate Calendar Submission". These proposals
have been approved by the Faculty of Science Undergraduate Curriculum
Committee and the Executive
Committee,
acting on behalf of the
Faculty.
The paper is now being forwarded for the approval of the Senate
Committee on Undergraduate Studies and Senate. .
SA: la
Enclosure
cc: J. Chase, Chairman of SCUS
R. Lardner, Acting Chairman of Mathematics
41
SIMON FRASER UNIVERSITY
?
(1-71-2,+
•
?
.
MEMORANDUM
W
,o
-
. Dr.
• S. ..Arono.ff,.. Chairman
?
.
Undergraduate Studies Committee
lty....of....S.c.i.eic.e................................................
Subject.
...........
PROPOSALS
.
FORC flANGES IN MATHEMATICS
UNDERGRA[)UATE GAPT1)iFSUBMISSION
From
?
Dr..
R
...
IV. La.dner .
..
Acting head
Date.
............ .Septçmbe.r21
?
1971 ?
.
.
The Mathematics Department wishes to recommend that
'a number
of changes be made in its undergraduate calendar submission.
?
They are:
I.
?
Degree requirements for Majors and Honors in Mathematics
II. ?
Degree requirements for Minors in Mathematics
III. ?
Adjustment to the calculus sequene
IV. ?
Renumbering of Mathematics 411-4
V. ?
Change in prerequisite for Mathematics 422-4
VI. . New course proposal - Mathematics 302-3.
The first is a proposal to change the degree requirements for
students majoring or taking honors in mathematics.
?
It is the result
of a critical evaluation of the Department's present degree requirements,
combinOd with a comparison of mathematics degree requirements at the
Universities of British Columbia and Victoria.
?
The Department wishes
to adopt these new requirements in order to increase the flexibility for
undergraduate students who complete all of their mathematics degree
requirements here, and in order to make it easier for students to transfer
to this University from the B.C. regional colleges.
?
Details of the other
proposals appear on the attached pages.
ii ?
L
R.W.
?
Lardncr
RWL/ses ?
•. ? .
?
.
?
.
Mathematics Department
September 21, 1971
PROPOSAL I
.
??
it is proposed that the requirements for undergraduate students majoring
or taking honors in Mathematics be changed to read as follows:
REQUIREMENTS FOR STUDENTS MAJORING OR TAKING HONORS IN MATHEMATICS
Students majoring or taking honors in Mathematics are subject to the
general regulations, of the Faculty of Science. . They will normally be required
by the Mathematics Department -
(i)
to obtain credit by the end of the fourth level for the following
lower division Mathematics courses:
151-3, 152-3, 232-3,. 2S3J
and, at least three of the following courses:
106-3, 141-2, 142-2, 161-3, 180-3, 195-3, 241-2, 261-3
(In choosing courses from this list students should note that
106-3, 241-2 and, 261-3 are prerequisites for certain upper
division mathematics courses.
?
In particular, honors students
are advised to note that 241-2 is a prerequisite for 421-4.)
(ii)
to obtain at least six semester hours of credit in Science courses
other than Mathematics. ' (Physics courses which are required for
the Applied Mathematics option, see "Programs of Study" below, can
be used if desired for the satisfaction of this requirement.)
(iii)
in the case of major students - to obtain a total of at least 44
semester hours of credit in upper division courses of which at
least thirty must be in upper division Mathematics courses.
(iv)
in the case of honors students - to obtain credit in the following
upper division
Mathematics
Mathematics
courses:
352-2, 411-4, 421-4, 422-4, and
one of 431-4, 432-4
?
.
(NOTE: Any student with honors standing may, 'on application to
the Departmental Undergraduate Studies Committee, be permitted
to complete a program of studies in a specialized area, for which
one or more of the above courses may be waived.)
Honors students will be required to obtain a total of at least
60 semester hours of credit in upper division courses of which at
least 50 hours (including those specified above) must be in upper
division Mathematics courses.
For. the purposes of the
411-4 may be counted as
to obtain a grade of C-
S ?
permitted to enroll in
any prerequisite.
satisfaction of conditions (iii) and (iv) above, Physics
a Mathematics course.
?
Mathematics students are expected
or better in their courses
,
,*\i they will not normally be
any course for whici
?
D grade or lower was obtained in
U.B.C. ?
.
U. VIC.
S.F.U.
Present
New
1.
No.
of required hours of
100 and
200
level Math courses -
MAJORS
18
18
21
19-22
2.
No.
of required hours of
100 and
0
200
level Math courses -
HONORS
20
18
21
19-22
3.
No.
of required hours of
300 and
400
level Math courses -
MAJORS
24
30
30
30
4.
No.
of required hours of
.300 and
400
level Math courses -
HONORS
42
. ?
48
50
50
.
SiMON FRASER UNIVERSITY
MEMORANDUM
?
0
Dr.
?
S. ?
Aronoff
...................................From.........Dr.
?
R.W. ?
Lardner ?
....................................
?
Acting Head
Dean
?
of ?
Science ?
.........................................
....
.Matm.aticS..
...
1eprtnen
. t
?
..................
Subject
..............CHANGES IN
?
....PQR..
?
Date ......
........Nove
mb e r1
8 ...... 1971
?
MAJORS AND HONORS STUDENTS IN MATH
At the Executive Committee Meeting on Tuesday you requested a
brief summary of our reasons for proposing a change in the degree
requirements for undergraduate students majoring or taking honors in
Mathematics. These are as follows:
It has become apparent that difficulties were being created for
students who transferred from regional colleges in this province, since
none of these colleges offer courses similar to our Mathematics 161
and/or 261. Douglas College, potentially our largest source of transfer
students, attempted to mount a course similar to our Math 161 and were
forced to cancel it since no students registered for the course. The
proposed changes will now make it possible for transfer students to
complete all of their lower level mathematics requirements before
transferring to this University to complete a BSc. in Mathematics.
In addition enrollments in 161 and 261 at this University have never
been very large, and there has been pressure to remove their. status
as required courses.
The proposed changes were also the result of a comparison of this
Department's requirements with those of the Mathematics Departments of
the Universities of B.C. and Victoria. The changes reflect an attempt
to align this Department's requirements with those of the other
mathematics departments in the other B.C. universities. A comparison
of the requirements for undergraduates majoring or taking honors in
Mathematics atthe three B.C. Universities is as follows:
...2
-2-
• S
??
In addition the other universities allow their mathematics majors
much greater freedom in their choice of mathematics courses than we
have done in the past. The new degree requirements we are proposing
will give our students a flexibility in this respect which will match
that of U.B.C. Hopefully they will put us in a more competitive
position as regards attracting transfer students from the junior
colleges.
• ?
•
?
•
• • Dr. R.W. Lardner
/
Sc
I-iS
',7
* ?
7 ,-'
• ?
. ?
.S1MON FRASER UNIVERSITY
MMORAUM
o
...............................•1l.
?
Evans
?
. ?
.:...........................................From.................Aronoff
?
..........................
Secretary
?
Senate
?
Dea
?
.................
ary toSen
n of Science
Subject. ?
.
?
Paper SCUS 71-27, Proposals
?
November
?
..........................
Changes in ftith.ematics Undergra uate
Attached please find a memo from the Department of Mathematics
relating to the Proposals for Changes in Mathematics Undergraduate
Calendar Submission (Paper SCIJS 71-27), specifically Proposal I
of that paper.
May we request that this memo be included as supplementary material
in the submission which goes to Senate.
la
Enclosure
71..27/
MATH1MATICS DEPARTMENT
November 30, 1971
PROPOSAL II (Revised)
The Mathematics Department wishes to implement a minor program in Mathematics.
The following would be the calendar entry for such a program:
REQUIREMENTS FOR STUDENTS COMPLETING A MINOR PROGRAM IN MATHEHATICS
Students completing a minor program in Mathematics are subject to the
?
?
general regulations of the Faculty in which they are registered.
?
They will
normally be required by the Mathematics Department -
(i) to obtain
,
predit for 11 emepter. hours of mathematics courses
numbered bet eh
?
IW"these would normally consist of
the following courses:
1513 and 152-3 and 232-3, and
either 106-3 or
161-3
or 241-2 or
25-I.(i
?
25/J1
•
?
?
(ii) to obtain credit in at least 15 semester hours of upper
?
division Mathematics courses. (Physics 411-4 may not be
used to satisfy this requirement.) (Students will be
expected to complete all of the prerequisites for those
upper level mathematics courses they wish to include in
;their minor programs.)
Students will be expected to obtain a grade of C- or better in their
courses. They will not normally be permitted to enroll in any course for
which a grade of D or lower was obtained in any prerequisite.
Students may specialize in Applied Mathematics, Probability and
Statistics, or Pure Mathematics. Further information is available
from the Mathematic5 Departmental Office.
An advisory service will be available to assist students in the
selection of courses most appropriate to their programs.
0
Mathematics Department
September
21, 1971
PROPOSAL III
The Mathematics Department requests that 1 semester hour of credit be
added to the course Mathematics 251-3, Calculus III, which would then become
Mathematics 25.-4, Calculus III. The topic 'infinite series', which is
now
taught in Mathematics 152-3, Calculus II,
would
then be taught in Mathematics
253-4. ?
More material on applications of differentiation and integration of
?
functions of one variable would then be taught in Mathematics 151-3 and 152-3.
The reasons for the proposed change are:
(a)
The inclusion of infinite series in Mathematics 152-3 has
resulted in severe limitations on the time spent on
applications of integration.
?
The proposed change would
permit more applications of calculus of one variable to
be taught in Mathematics 151-3 and 152-3 and allow a
fuller exposition of infinite series in Mathematics 253-4
for those students (particularly in Mathematics, Physics,
and Chemistry)whose work requires this topic.
(b)
It would ease transfer arrangements for students coming
from junior colleges, since infinite series are not
taught in first year calculus courses in many colleges.
0...
Finally, it should be noted that the proposed changes in the syllabuses
for these calculus courses have been discussed with representatives, of the
Biology, Chemistry and Physics Departments, and that they were amenable to
these changes.
.ci
XAC ?
t\A ?
3
?
"t
^',
?
- ?
/-'
--4
?
.
S
lI--3
'lEXT
?
Purcell
- CALCULUS
?
lTl
ANALYTIC GEOlii'fR\'
Chapter
1 ?
- ?
NUN}ik5
Section ?
1 . I
Real Numbers
•
1.2
Scis
1.3
J11eqL11.it1Cs
1 .4
Bounded Sets
1 .
S
The coord
nate
line
•
?
1.6
Absolute val.ue
1.7
I)irected di st:ncc
Estimated
time 4 hours.
Chapter
2 ?
?
-
CARTESIAIN
Section 2. 1
Rctangular cuordi nates
-
1
.2
Distance hctecn
twO p01 it5
2.3
Directed distances .
?
Midpoint
fOl
?
a
2.4
Slope
2.5
The graph
of an equation
2.7
sketch iii" graphs
2.8
The
straight line
2.9
Distance between a point and a line
2.10
Ta circle
Estimated
time ?
4
?
iou.rs .
Chapter
3
-
?
THEIR GRAPHS
Section
3.1
Functions
3.2
Oeerat ions on functions
3.3
Special functions
Estimated
time 2 ligurs.
•
Chapter
4
?
-
?
LIMITS AND CONTINUITY
•
Section 4 ..i
The Limit of a function
•
•
1
1,2
•
?
Dofi.niti.n of
?
unit
•
4.3
Theorems on iilts
4.4
Continuity
4.5
Limits as x
?
. ?
One-sided ?
limits
4.6
Asymptotes
4.7
Increments
Sections
4.S, ?
4.6 done
very brcf1y ci.' possibly oni ttcd
Esti mated
time 3 hours
I
-
A
Chapter 5 -
. ?
Section S. I.
5.2
5.3
5.'l
5.5
Tangeat to a curve
Instantaneous velocity
The derivative
Rate of Chai;c
The dcri vati
y
e and continuity
Estiinit.ed tine 3
hours.
Chapter 6 - FORMULAS FOR D1.FFI;RENT
Section 6.1
6.2
•
?
6.3
6.4
6.5
6.6
6.7
6.8
[ATION OF ALThlA1C
FUNCTIONS
Derivative of polynomial function
Derivative of a product or quot i.nt of
functions
Chain rule
for differentiating ceuposite
functions
Derivative of any rational power of a func.ci
Derivatives of
higher
order
Implicit, differentiation
Differential',;
Differentials as approximations
Proofs not clone in detail.
Estiirated time S hours.
Chapter 7 - APPLICATIONS OF
DER1VVIiVLS
Section 7.1
7.2
7.3
7.4
7.5
7.6
7.7
7.8
7.9
7.10
7.11
7.12
7.13
Estimated time 12 hours
Tangents and normals
Acceleration in straight line :oti.on
Related rates
Newton's inthod for determining the roots
of f(x) = 0.
Absolute, maximum and minimum values of a
function
Extreiia
The
first derivative test for c
Rolle' s
theorem and the mean
Va
lie the.i
Second den vative test for cxtrc :n
Applied problems in max-i ia and a n ia
Maxima and minima b
y
implicit di licrenri :t
çoncavi tv
?
Points of inflection
Curve sketching
Chapter 12 - TflANSCENDFNTAL FUNCTIONS
•'
?
Section 12.7
?
Trigonometric functions
?
12.8 ?
o'ue tn
?
:nc'.ati'i c I imi t.
?
12.9 ??
Derivatives of the tr.i gononetr i c fua
istimated
t
ime, 3
hoofs
• ?
-3-
The chief
change from the prcviou syl I ahus is the inciiseJ
material md cstiiited t i
?
n Ch ptc r 7 ai d the oii' ion of
?
t of
Cw
)tc
i
S
,\1.),l
JLtIS ?
ITI I ,\'\LYI1 C
tEf
Chapter 8 -
?
Section 8.1
?
Tntroduti on
?
8.2 ?
Finding antiderivativcs
?
8.3 ?
Gcnc:ra ii :ed
.
powee formula for aiitidcri vat ive:
?
8.4
?
Some appii cati.oas of anti.dri vatives
Estimated ti.r.e 2 - 3 hours.
Chaptcr 9
Section 9.1
• ?
9.2
9.3
9.4
9.5
9.6
9.7
9.8
9
.
9
Estimated time S hours
Area
The sigma no1:rtiOn
The definite integral
Approximate i.ntcgrat on.. by t.ie traj:e:o d:i
Properties of definite i.n.eirls
The mean vallie theorem for . a tecral.s.
integrals wi-th variable un'c :
r 1i.i:!c
The fundamenia 1. theorem of i.ntcgn1
c,-,!- I
Finding the exact value of a dcfi.ni
I e in'-e.r
Chapter 10 -
?
Section 10.1
?
Plane 'yç
?
10.2 ?
Volume of a solid revoliii ion
?
10.6 ?
Centroid of a
p
lane
re:iOfl
?
10
.
8
?
Moment
of
inert i a of a
p
lane reg ion
10. 10 Arc length and d:t ffcrev.ti.al
of arc in
rectangui ci coerd I nate:;
Estimated time 5 hours.
Chapter 1] - coNIc;
?
Section 11.3
?
. The parabola (c
?
1)
?
11.7
?
The e1 lipse (c < 1)
?
1.9
?
The
hyperbola (e > 1)
Only the standard forms of parabola , elI. apse and hyporbo .1 a
Since these sections ave ciosc ly connctcJ to others .-I: ma:
:
nul be
advisable to folio: the hook.
Estima ted time 3 - 4 hours.
0
• ?
. Chtcr U - ri• ::sci
?
TAI. FTlN;
•
?
. Section 12.1
12.2
S
.12.3
12.4
12.5
• ? . .
?
12.6
•
?
.
?
. ?
12.1()
12.11
12.12
• ? 12.13
• . ?
Equation 1216.5 may he o:
•
?
. ?
.
?
ESti.lfl2ted time 7 hours.
The natural logarithmic Function
Graph
of the natural logarithmic function
Logarithmic differentiation
Inverse of a. function
The exponent.] a 1 function
Exponential and logarithmic functiens
with bases other than e
Inverse
tr.i.ontaaetric functions.
Graphing by addition of ordinates
Hyperbolic functions
Inverse hyperno].i.c functions
titted.
Chapter 13 - TECHNIqUP OF INTEGRATION
Section 13.1
?
Introduction
13.2
The basic i.ntcration formulas
•
.
13.413.3 The
Integration
first
four
by substitution
basic formulas of
integration
13.5
The basic trigonometric formulas
13.6
The basic inverse trigonometric
forms
13.7
integration by parts
13.8 integrals involving
v+.b
13.9
Definite
?
i.nt-5ra1s .
?
Chnuc ?
of
?
1
4
.:71-1
ts
5
.
?
.
13.
10
Some trigonometric intcgyals
13.11
Integrals involving / a 2 - ?
, ?
I a' ?
4 U2
or,
?
U.
?
- ?
a2
(Ax + )3)dx
1:3.12
Integrals of
?
f
------------
(ax
?
+bx+c)
13.13
Integration of rational fun'tions
.
by partial..
fractions
•
. ?
. ?
.
?
.
1304
Integration b
y
partial fractic.;
(continued)
13.1S
Rational functions of sin x and
cos
?
X.
13.16
Tables of integrals
13.17
Simpson's rule
Section
?
13.13 done
briefl y .
' ?
•. ?
:
Estimated time 10
hours.
.
?
. ?
. ?
. .
• Chapter 14 -
?
COORDINATES
Section 14.1
Polar coord:inatcs of a
point •
?
•
•
•
14.2
Graph of a pol
ar
equation
14.3
ReiaJons •bet,ccm Cartonion and
polar
• ?
.
?
.
.
coordinates
The sti'n',ht
?
line and ?
cftcie ii1ciar
S
.14.4
• ?
• .
?
,
?
AMU
t i.Iie ?
..')
?
hours.
• C:er ?
15 ?
-.
?
P. ?
ui'1•tr(;
EQUATIONS ti
\CTc;L; 1N
?
fffl ?
PI.t
Section
15.1
1ari
p
trjc equations of
?
i curve
:
iS. 2
The cy ci o (1
.
15.3
Functions defined b
y
paramc:tri c equations
•
?
15.2 ?
d o n c
hrj en'.
Estimated
t. inc
?
2 hours.
• ?
The chief
changes
from the
previous syi lahus are the increased
• ?
material ?
and. time in Chapter
lo,
the inc usion oC Chapter 32 and the omission
of Chapter 16 and 21.
Chapter 16 -
• ?
Section 16.1
16.2
36.3
16.5
16.6
Estimated time 4 hours.
lrtf:i i. t.e limits of
Infinite i ntcrn1)JS
Exi•ondd mean va Inc
I ndctereiflte forma
L
t
lIonital ?
rules
Other indeterminate
i t•c,rai:i on
the
or
em
forms
Chapter 17 -. ANALYTIC GEOMETA
OF THRVE-DIMENSIONAL SPACE
Section 17.1
17.2
17.3
17.4
17.5
17.6
17.7
1
• ?
-,
17.9
17.10
17.31
17.13
17 .34
17.15
3.7.16
17 J7
1/.18
37.19
17.20
17.21
Cartesian coordinates in three-space
Distance formulas
?
.
?
.
Direct:ion angles and di rccticn cas.i ;e
Direction numbers
The two fundnmerital . orohi ens in space.
Lcivati.on of a
p
lane par11cl to a
coordinate plane
Normal equation of a plane
Graph of a first-degree equation
Parallel, and
perpendicular ni.ancs
Conditions that determine a piano
General equations of a line in sacc
SVITn;etI'lC
OCuatiOT5
of a 1. inc
Para:not: c. (c.uat. Ions of a I inc in spat,:,
he shore i
f;n'faces ?
1 curves
Ci
iflJe3's ?
.
Surfaccs
of
revolt ion
S'.n'nCtry, traces
and plane sections
Q a
surface
Qi'adri c. surfaces
Procedure for sketching surface
1716 should perhaps be augmented with other natc;ri a] s
1istia.:oi time 12 hciirs
Chapter I - VFCTOnG IN THREE-DIMENSIONAL SPACE,
1
Section 13.1
13.2
.L').
1.4
18.0
Vectors in space
Cross product
Vcctor
(;qUt.,j
ens of pianos and ii nas
Vector functions in t.i'e dii cas
.i 0;
Veloci
ty
and aced etal ion
Are length,
?
Curvztt.ire
.
Two dimensional vetors (15.5 Vectors in the plane, 35.
6
5¼alnr.s,
dot product,
and
Us is vcctors • 15.7 Vector fuc.l.i.'n. 15
-S
('nv 1 ' ri:nr motion.
Vc:trr
arc 3 e;n
.
th . ) should b'
WO
also.
:_!
timeLiars.
.
(';hu pter 19 -
?
P.JT IAL 1)1 FIRF']' I AT.! (
Section 19.1
19.2
19.3
19.4
19.5
19.6
19.7
19.6
19.9
Func ions of t'.'o or
m
o
re
variables
Parti a] derivatives
Limits
JId cont. i.flUi
tv
InCfem_']It S
and (I it
i.et'ent.i al s oi
'
1:UnCt1OnS
of two variables
Chain rule
I). vectiona 1 derivative
(;rnd .i cat . Tangent r1 ano
to
a, surface
Extreia of a Ei.mction of tue variables
Line i.flt(ra1S
.
Estimated time S hours.
(:Ftr 20 -
?
IJLTI PIE I ?FE,PJ.I.S
Section 201
20.2
20.3
20.4
20.5
20.
20.7
20.5
UnIv •th. 'birea'a nd "vol
need be done
Estimated time 8 hours.
Double integrals ?
.
Iterated i tera is
Evaluation of double integrals by mens
iterated integrals
Other app].icrt ions
of double integrals
Polar coordinates
Triple integrals
A11)i1Cat1O1) in rCCt!UiU
coordinates
Cylindrical and spherical
ccerdi.natcs
u!c" sect.ons of 20.4, 20.7 repcctiVe).y
• C]Ia1tCT
21 -
?
INFINITE
.
?
.
?
.
?
.
?
Section 21.1
?
Sequences ?
.
?
0
-1.2
?
Infinite. sC)IC5
?
21.3
?
Tests for convergnce of series of positive
tcrns ? .
?
21.4
?
Alternating series.
Absolute convergncC
?
21.5
?
Power se)'ics
?
.
?
21 . C. ?
1:w ) ct i ons ecta nd by power series
?
21.7 ?
Tavlcr's formula
?
2.1 .3
?
Other fonn of the re aindar in Taylor's
iheor€i
?
21
.9
?
Comp cx van aM c'
?
.
Estimated time 10 hours, .
Chanters 1, 21 were p:cvi
ill nth
ously
1.52-3.
tat.tjt
To enable
stndets
to
take Kith W-2 conciurent.Iy, Chapter. 21 would have
0
?
to he tuht
?
ti Cit.:':' 16.
I
MathcmatiCs Department
September 21, 1971
PROPOSAL IV
ow
The Mathematics Department wishes to recommend that Mathematics 411-4,
Methods I, be renumbered and noted in the undergraduate calendar as Mathematics.
311-4.
?
The reason for this request is that a change in number as is proposed
would encourage students to take this course early in their upper level course
work.
?
This is particularly necessary for applied mathematics students since
Mathematics 411-4 is a prerequisite for many of the upper division applied
mathematics courses.
?
In addition, we wish to make Mathematics 311-4 an?
alternate prerequisite for Mathematics 422-4 to allow more flexibility for
mathematics students and for majors and honors students in Physics.
?
There
will be no change in the syllabus for this course.
?
.
0
0
- ?
-
?
.
MATH 311-4 ADVANCED CALCULUS
1. Quick review of functions of several variables.
?
(1½-i week)
2 .
. Vector field theory: Differentialoperator V, Gradient,
divergence and curl of vector valued functions, the directional
- ?
derivative, applications to analytic geometry.
?
(1½ weeks)
3. Extrema of functions of several variables, extrema under
constraints. ?
.
?
.
?
. ? . ?
. (1 week)
ii. Multiple. integrals: Iterated integrals, double and triple
integrals, Jacobians change of variable in multiple integrals
cylindrical and spherical coordinates.
?
(2 weeks)
5.
Line and surface integrals: Simply or multiply connected
regions, independence of the path. Green's Theorem, the
divergence theorem, Stoke's theorem.
?
(2
'weeks)
•
?
6.
Infinite series: Review of tests for absolute and conditional
convergence of the series of constants,.operatiOfl with series
(Addition, multiplication, rearrangement, etc.), sequence and
series of functions, absolute and uniform convergence, tests
for convergence. ?
.
?
.
?
. .
?
(1-111 weeks)
7.
Power series: Radius and interval of convergence, the Taylor
and MacLaurin series, forms of the remainder.
?
(1 week)
8.
Tproper Integrals: Integrals of discontinuous functions,
infinite integrals, absolute conditional and uniform convergence,
Tts for convergence. ?
0 ?
(2 weeks)
9. ?
Curvilinear coordinates:
Coordinate curves and coordinate
surfaces, the base vectors,
orthogonal curvilinear coordinates.
(2 weeks).
TEXT: ?
1.
?
Advanced Calculus
by
Watson Fuiks
'. ?
Mvnced Calculus.
by
J.M.H. ?
Olmsted
?. ?
Avaiced Calculus
by
D.V. ?
Widder
Mathematics Department
September 21, 1971
PROPOSAL V
. ?
The Mathematics Department wishes to request that the prerequisite for?
Mathematics 422-4, Complex Variable I, be changed to read as follows:
FROM: Mathematics 251-3 and 241-2 (or Mathematics 214-3 and 22172).
jj
?
/y
Zi
-4
• ?
TO : Mathematics 311-4
1
or Mathematics -2-sand 241-2(or
Mathematics 214-3 and 221-2).
?
1
?
•
•
?
• ?
The reasons for this request are that more flexibility would exist
• • for Mathematics and Physics .students who either wish to, or are required to •
take Mathematics 422-4 as a part of their degree-requirements.
?
•
0 ;
S
.
.ç C
LA
S. 71-
27 C
FACULTY OF SCIENCE
NEW COURSE PROPOSAL
I ?
CALENDAR INFORMATION
Department: Mathematics
?
Course Number: 302-3
Title: Statistical Methods
Sub-title or Description:
Non-parametric statistics, analysis of variance and related topics which
are intended to help the students understand the uses of statistics in
experimental research.
Credit Hours: 3 ?
Vector Description: 3-0-1
rre-requisite(s): Mathematics 101-3 or Mathematics 371-3
(Mathematics major and honor students may not use this course to satisfy
the required number of semester hours of uppr division mathematics
courses-
1-lnvr..
they
ma
y
include the course to satisfy the total
number of required hours of upper division credit.)
?
1
--/
i
?
/
•
1
") , ?
.
...
.
0e. e.
II ?
ENROLMENT AND SCHEDULING
• Estimated Enrollment: 20 per offering
Semester Offered (e.g. Yearly, every Spring; twice yearly, Fall and
•
?
Spring):
Yearly, every Spring
When course will, first be offered: Spring 1973
III
?
JUSTIFICATION
A.
What is the detailed description of the course including differentiation
from lower level courses, from similar courses in the same department
and from courses in other departments in the University?
It is a course in statistical methods with emphasis
in
the design and analysis of experiments, 'which is primarily designed
to satisfy the needs of students
in
other departments of SFU.
B.
What is the range of topics that may be dealt with in the course?
Analysis of variance, regression, correlation and non-parametric
methods.
3.
Page 2
•
?
. .
?
C. How does this course fit the goals of the department?
It is primarily a service course which will be offered to
students of other departments.
D. How does this course affect degree requirements?
This course is not required for any Mathematics, degree program.
B. What are the calendar changes necessary to reflect the addition of
this course?
New entry and deletion of mathematics l023.
F.
What course, if any, is being dropped from the calendar if this
course is
approved? ? .
Mathematics 102-3.
G.
What is the nature of student demand for this course?
It will fill out the demand for a course in statistical methods
by upper level students, in areas other than mathematics. These
students would not get full value from such a course if it were
taken too early in their degree programs. One of the groups
to which this case would be particularly beneficial is the Bioscience
tpdents. ?
. ?
. ? .
H.
. otner reasons for introducing the course.'
See the attached sheet.
I.
IV ?
BUDGETARY'ANDSPACE'FACTORS ?
.,
A. Which
faculty will be available to teach this course?
Dr. R. Rennie, Dr. C. Villegas, Dr. .D. Mallory
Page 3
B.
What are the special space and/or equipment requirements for
this course?
The existing statistical laboratory facilities will suffice.
C.
Any other budgetary implications of mounting this course:
None.
OTHER REASONS FOR INTRODUCING MATH1ATICS
302-3
Mathematics 302 is intended to be a statistical methods course which
will cover the same topics as Mathematics 102, but in more depth.
Through teaching Mathematics 102 and advising advanced students on their
statistical problems we have come to the conclusion that an upper levels service
course is more desirable than a first year course. There are two basic reasons:
students are usually not motivated towards the use of statistical methods until
they reach upper levels and many of their problems need a deeper understanding
than that which has been obtained in Mathematics 102.
Instead of performing a brief review of Mathematics 101 as we did in
Mathematics 102, we shall, in reviewing Mathematics 101, place emphasis on a
rigorous understanding of sample space, random variables, probability, expectation
and distributions. In addition to providing a better base for discussion of all
statistical problems this technique will allow us to deal with the more sophisti-
cated and general approach to analysis of variance using linear models and
expected mean squares.
Hence, the adoption of this course should attract more students to using
correct statistical proceedure and give these students a deeper understanding
than is now available.
S
Mathematics 302-3
STATISTICAL METHODS
?
• ?
1. Review of Math 101 with emphasis on a rigorous understanding of
probability, random variables, expectation and distribution as
applied to statistical understanding.
• 2. Analysis of variance - Linear models approach with E.M.S. calculations.
One way, Two way, Factorial and Latin Square Designs,
?
•
?
Fixed, Random, Mixed Models;
Multiple Comparisons
? • ?
•
?
• - ?
• ?
3. Bivariate Linear Regression and correlation.
? •
4 ?
Analysis of Covariance
? •
?
•
?
•.
?
•
?
S
S. Non-parametric Statistics
?
S
Sign, Run, Rank-sum tests, Rank correlation,
Tests of Randomness ?
S
?
•
?
S.
SUGGESTED TEXTBOOKS:
?
S
?
•
?
•
? 1•
Dixon and Massey: Introduction to Statistical Analysis
Fryer: Concepts and Methods of Experimental Statistics
