?
SiMON FRASER UNIVERSITY
?
s .
MEMORANDUM
To
...........ENATE
?
IFrom. . ?
COMMITTEE. .?
?
.... • STUDIES
Subject. ?
NEW COURSE
?
MATHEMATICS AN
?
Date. . .
.9S'9P.. .7.'. .?
STATISTICS
Action undertaken by the Senate Committee on Undergraduate Studies at
its meeting of October 16, 1984 gives rise to the following motion:
MOTION: "That Senate approve and recommend approval to the
Board of Governors, as set forth in S.84-58, the
MATH 309-3 Continuous Optimization"
FOR INFORMATION
Acting under delegated authority at its meeting of October 16, 1984 the
Senate Committee on Undergraduate Studies approved the following:
1) Change of course number MATH 194-3 to MATH 113-3
ii)
Change of course number MATH 196-3 to MATH 213-3
iii) Change of prerequisites for MACM 216-3
iv) Change of prerequisites for MATH 404-3
v)
Change in description MATH 151-3 and MATH 152
vi)
Change in description and prerequisite for MATH 251-3 and
MATH 252-3 and title of MATH 252-3
vii)
Change in prerequisite for MATH 310-3
viii)
Change of title, calendar description and prerequisites
for MATH 313-3.
F-1
SiMON FRASER UNIVERSITY
?
MEMORA1DUM
SCVS ?Ir
Dd
To
...........
ii9t
.
.
.
.............................
.
e9istrar
.
Subject. .
From.....
. ?
P.
...
Dobud
:..^ ...... ?
...
6
...
6 . ?
.....................
Assisant to
?
e ean
aqyy 9f Science
?
.............
Date ......
Qc
p be ?
/4,
1984
?
........................
Please find attached the documentation relating to calendar changes
approved in our Faculty of Science meting held Monday, October 1, 1984.
1 would appreciate it very much if you would place these items on the
agenda of the
?
and approval..
f) To approve the new
course
MATH 309-3
Continuous Optimization.
Theoretical and computational methods fur investigating the
minimum of a function of several real vcriables with and without
.
?
inequality constraints. Applications tc operations research,
model fitting and economic theory.
Prerequisites: MATH 251 and 308.
Paper F-84-9
Appendix B3
SENATE COMMITTEE ON UNDERGRADUATE STUDIES
COURSE PROPOSAL FORM
.L.
Calendar Information
?
Department: Mathematics
?
-
Abbreviation Code:
MATH
Course Number:
309 ?
Credit Hours:3
?
Vector:3-1-0
Title of Course: Continuous Optimization
Calendar Description of Course: 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.
Nature of Course
Prerequisites (or special instructions):
?
MATH 251 and 308
What course (courses), if any, is being dropped from the calendar if this course is
approved: none (The frequency of offering of MATH 313 will be reduced.)
2. Scheduling
How frequently will the course be offered? Once per year.
Semester in which the course will first be offered? Fall 1985
Which of your present faculty would be available to make the proposed offering
possible: G. Bojadziev, R. Routledge, R. Russell, and others.
Objectives of the Course
To teach students computational and theoretical techniques for maximizing functions
of continuous variables possibly subject to constraints, and to show how these
techniques can be used in such fields as operations research, resource management,
engineering, and mathematical economics.
4. Budgetary and Space Requirements (for information only)
What additional resources will be required in the following areas:
Faculty
?
none
Staff
?
none
Library ?
a. few books
Audio Visual none
Space
?
none
Equipment none
S. Approva'.
Date:
Department thairman
?
77
?
Dean ?
. ?
Chairman,
SCUS
SCUS 73-34b:- (When completing this form, for instructions see Memorandum SCUS 73-34a.
Attach course outline).
Course Description
Calendar Description: MATH 309-3 Continuous Optimization
?
(3-1-0)
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.
Prerequisites: MATH 251 and 308.
Detailed Description:
Unconstrained Optimization
Necessary and sufficient conditions for a minimum, with special
reference to convex and concave functions.
Numerical techniques for functions of one variable.
Coordinate descent, steepest descent, and Newton's method for
functions of several variables.
Introduction to conjugate direction and modified Newton's method.
Constrained Optimization
Review of duality in linear programming.
Necessary and sufficient conditions for a minimum of a function
subject to constraints with special reference to convexity.
The Kuhn-Tucker conditions and their economic interpretation.
A survey of some computational methods.
Applications to operations research and model fitting.
Text: ?
Introduction to Linear and Nonlinear Programming, by
D.C. Luenberger, Addison-Wesley.
SiMON FRASER UNIVERSITY
MEMORANDUM ?
SC. cj
S
1Q
To ......W. Heath
?
From ...... ....Dobud
Assistant to the Dean
egtra-
?
F .c
y
A
y .
.cfl
.
.
Sp.i.nce.......................
Subject. .
?
Date ...... ..cpj• .&,. .
?
•84
Please find attached the documentation relating to calendar changes
approved in our Faculty of Science meeting held Monday, October 1, 1984.
1 would appreciate it very much if you would place these items on the
agenda of the next SCUS meeting for consideration and approval.
[*PARTP(NT OF MATHEMATICS
&
STATISTICS
)
To approve the change of course number for the following courses:
From:
MATH 194-3 Euclidean Geometry
To: ?
MATH 113-3 Euclidean Geometry
and
From:
MATH 196-3 Modern Geometry
To: ?
Math 213-3 Modern Geometry
0
W.R. Heath
• ?
Registrar
•
?
He:
?
CALENDAR CHANGES
?
-2-
b) To approve the change of prerequisites for MACM 216-3,
Introduction to Computational Methods:
From:
MATH 151 or 154 or 157 (formerly 150), CMPT 101 or 103
(except COBOL). Students who have obtained credit for MATH
104 may not receive credit for MACM 216.
Students who have taken the former MATH 216 or who have
taken or who are taking MACN 316 (formerly MATH 316) may
not take
MAClI
216 for further credit.
To: ?
CMPT 1U1 or 102 or 103 (except COBOL); MATH 152 or 155 or
158 should precede or be taken concurrently.
Stüdits who have obtained ere drtfor MATH 104 may not
receive credit for MACM 216.
Students who have taken the former MATH 216 or who have
taken or are taking MACM 316 (formerly MATH 316) may
?
not
take MACh 216 for further credit.
Paper F-84-8
c) ?
To approve the change of prerequisite for MATH 404-3 ?
Statistical Design and Analysis of Experiments.
From:
MATH 272 (or 371) or 302. Permission will be given to
students from other Departments, with suitable backgrounds.
To: ?
MATH 372 or 302. Permission will be given to students from
other departments, with suitable backgrounds.
Paper F-84-8
d) To approve the change in description for MATH 151-3,
Calculus I and MATH 152 Calculus II:
Calendar Description for MATH 151
From:
Real number, functions and graphs, conic sections, limits
and continuity, derivatives, techniques and application of
differentiation, trigonometric functions, logarithms and
exponentials, extrema, the mean value theorem.
W.R. Heath
Registrar
Re:
CALENDAR CHANGES
?
-3 -
To: Real number, functions and graphs, conic'sections, limits and
continuity, derivatives, techniques and applications of
differentiation, trigonometric functions, loc
'
arithms and
exponentials, extrema, the mean value theorerr., polar
coordinates and complex numbers.
Calendar description, for WiTH 152
From:
Integrals, techniques and applications of integration,
approximations, sequences and series.
To: ?
Integrals, techniques and applications of integration,
approximations, sequences and series, area and arc length in
polar coordinates.
Paper F-84-9
e) -To approve the change in calendar description and prerequisite for
MATH 251-3 and MATH
252-3
and the title of MATH 252-3.
From: MATH 251-3 Calculus III
Polar co-ordinates, vectors, solid analytic geometry,
differential calculus of several variables, multiple
integrals, line integrals, Complex numbers.
Prerequisites: MATH 152 or 155; or MATH 158 with a grade of
A or B.
To: ?
MATH
2 51-3 Calculus III
Vectors, solid analytic geometry, differential calculus of
several variables, Lagrange multipliers, multiple integrals,
cylindrical and spherical coordinates, line integrals.
Prerequisites: MATH 152 or 155; or MATH 158 with a grade of
A or B. It is recommended that MATH 232 be completed before
this course is attempted.
Paper 1-84-9
. . . . /
[1
W.R. heath
Registrar
Re: ?
CALENDAR
CHANGES
From: MATH 252-3 Vector Calculus I
Differentials, Jacobians, tranbformation of multiple
integrals, differentiation and integration of vector
functions, integral theorems and their applications.
Prerequisites
MATH 251
or
253.
It is recommended that
MATH
232
precede or be taken
concurrently. Students with credit for
MATH 312
may not
receive credit for
MATH 252.
To: ?
MATH 252-3 Vector Calculus
Vector functions of a single vriab1e, space curves,
scalar
and volume
and
integrals,
vectrftelds,
and
cuns€rvalive
theoiems of Gauss,
fie±ds-jstxrfaee
Green and
--
Stokes.
Prerequisites:
MATH 232
and
MATH 251
(or
MATH 253).
Students with credits for
MATH 312
may not receive
credits for
MATH 252.
g)
To approve the change in prerequisite fcr
MATH 31U-3.
From: ?
MATH 152
or
155;
or
MATH 158
with a grade of
A
or B.
To:
?
MATH 152
or
155;
or
MATH 18
with a grade of
A
or B. It
is strongly recommended that
MATH 232
be completed before
this course is attempted.
Paper F-84-9
h)
To approve the change on Title, Calendar description and pre-
requisites for
MATH 313-3.
From:
?
MATH 313-3
Vector Calculus II
Extrema of functions of several variables, Lagrange
multipliers, curvilinear co-ordinates and vector differ-
ential calculus; space curves. Frente formulae;
surfaces, curvature, Christoffel symbols.
Prerequisites
MATH 232
and
252
(or
253).
Students with credit for
MATH 312
may not receive credit
for
MATH 313.
To: ?
MATH 313-3
Differential Geometry
Curvature and torsion for space curves, Frenet formulae,
tangents and normals to surfaces, curvatures of a sur-
f
g
e, mpeciu1 püirit n and curves or surfaces, calculus (in
surfaces.
Prerequisites
MATH 232
and 2Z.
RATIONALE FOR PREREQUISITE CHANGES
.
MATH 404 (Statistical Design and Analysis of Experiments) formerly had
as prerequisite one of MATH 272 or 302 or suitable background
from another department. Students with no background In
statistics beyond MATH 272 have been inadequately prepared
for the material in MATH 404. For this reason, it is
proposed that the 272 prerequisite be upgraded to MATH 372.
MACM 216 (Introduction to Computational Methods) contains a discussion
of numerical integration. It seems logical to require one of
MATH 152, 155, or 158 at least as a corequisite. The
?
9
Computing Science department have been consulted, and have
agreed to the proposal to upgrade the calculus prerequisite.
RATIONALE FOR CHANGES TO GEOMETRY COURSES
The material, in MATH 196 (Modern Geometry) relies
heavily on ideas in MATH 194 (Euclidean Geometry). Furthermore,
the material has been judged by instructors and students to be
substantially harder than that in most 100-level courses. hence,
it is proposed that MATH 196 be given a 200-level number, and that
a course in Euclidean Geometry be made a prerequisite. We are
also taking this opportunity to renumber these courses to emphasize
the common geometric flavour of what we hope will become MATH 113,
213, and 313.
Brief Rationale for Course Proposals
Revisions to Calculus Sequence: Our existing calculus sequence has become
out of step with most calculus sequences in North America. The problem,
which has been particularly acute at the second-year level, has led to
difficulties for transfer students and problems selecting appropriate
textbooks. Following discussions with students, instructors, and faculty
in departments whose students frequently take these courses, we believe that
the proposed revisions will solve the above mentioned problem without
unduly inconveniencing students or faculty involved in related programs.
_In fac t---we—he-l-i-ev
benefit our major clients. At the request of the Chemistry Department,
•
?
complex numbers will be treated in MATIL 151 for the first time, and to
better serve the needs of physicists, Green's theorem will now be treated
in MATH 251...
MATII 313 and 309: The old syllabus for MATH 313 contained a mixture of
material now included in MATH 251 and 252, continuous optimization, and
differential geometry. We propose to provide a more solid treatment of
these latter two topics by splitting the existing course into two courses.
NM11 313 will become a bona fide course in differential geometry; MATH 309
will discuss continuous optimization. We are able to offer this new course
by reducing the frequency of offering of MATH 313.
Prerequisite Statements Involving MAIl! 232: Instructors in MATH 251, 252,
and 310 have repeatedly found that students in these courses can grasp
the multidimensional concepts much more readily if they have taken or arc
taking linear algebra (MATh! 232). We have resisted the temptation to add
MATh! 232 as a formal prerequisite for 251 and 310 because we realize that
it would create difficulties for chemistry students. We nonetheless would
like to formally advise students about the advantages of taking MAT!! 232.
•
Other Proposals not in this Package: Our department has also approved in
principle a course in numerical linear algebra, but is not bringing it forth
as a formal proposal at this time because we do not have the resources to
mount it on a continuing basis. We would also like to offer courses in
coding theory, applied algebra, and the theory of interest to enhance our
programs to students with an interest in business and computing.
