a
SiMON FRASER UNIVERSITY
0
?
MEMORANDUM
From
_SENATE COMMITTEE ON UNDERGRADUATE STUDIES
FACULTY OF SCIENCE -
Subject
DEPARTMENT OF MATHEMATICS -
?
Date
November 14, 1974
PROPOSED CURRICULUM CHANGE
MOTION 1:
?
"That Senate
theBoard, t
in S.74-157
MATH
310-3
MATH
312-4
MATH
320-4
approve - and recommend approval to
e new course proposals, as set forth
for
- Introduction to Ordinary Differential Equations
- Multidimensional Calculus
- Theory of Convergence"
If 1 Is approved
MOTION 2:
?
"That effective September 1975 the following courses
will be discontinued
MATH
352-2 ?
(c.f.
MATH
310-3)
MATH
311-4 ?
(c.f.
MATH
312-4,320-3)"
If 1 is approved
MOTION 3:
?
"That Senate approve - and recommend approval to
the Board - the new course proposal, as set forth
in S.74-157 , for
MATH
420-4 - Linear Analysis
with discontinuation Of
MATH
412-4 effective
September 1975."
S
-
• ?
If 1 and 3 are approved
MOTION 4:
?
"That Senate approve, asset forthin
S.74-
157,
the-proposed-changes in requirements
and in prerequisites"
If 1 is approved
MOTION 5:
?
"That Senateapprove, as set forth in S.74-/57
the proposed changes to Chemical Physics,
Chemistry and Physics."
MOTION 6:
?
"That Senate approve, as set forth in S.74-/.7
the change in Mathematics prerequisite for the
S ?
•
?
Physics Core Program."
SiMON FRASER UNIVERSITY
?
MEMORANDUM
4k
•
?
SENATE ?
From
SENATE CXMI'1Thh ON UNDE1RADUATE S'IIJDIES
Faculty of Science: Prcposed
Subject....
.
T1CU
?
PePa1't1T
11t
of
?
Date..
November 14, 1974
Mathematics.
At its meeting of 12th November, the Senate Committee
on Undergraduate Studies considered the attached curriculum changes
for the Department of Mathematics and allied programs. This
proposal is now forwarded to Senate for its consideration, with
the Committee's recommendation that it be approved.
: ----
I. Mugridge
ams
att.
.
is
rc.141 73^,--wrd
SiMON FRASER UNIVERSITY
MEMORANDUM
...........Senate C.ominit.te.e..on .................................. .......
.
From... ?
A. E.
?
Curzon
...........Unde.r.graduat.e .... S.tudies
...................
..............
?
.....
Acting Dean of Science
Subject ........
MATHEMATICS... ?
Date....
.. ?
November .
?
1974
The following motions were passed by the Faculty of Science at
its meeting of October 31, 1974:
1)
"That the new course proposals for MATH 310-3, 312-4,
and 320-.3 be approved."
?
(See Appendix A)
2)
"That the number and name of MATH 412-4 (Methods II) be
changed to MATH 420-4 (Linear Analysis)." (See Appendix B)
3)
"That the calendar changes outlined in [Appendix C] be
approved."
4)
"That modifications in the Chemical Physics, Chemistry, and
Physics programs be approved, to incorporate the course
changes outlined in [Appendix A]." (See Appendix D)
is
?
5) "That the prerequisite change for MATH 241-2, outlined in
[Appendix E], be approved."
These motions are now submitted to SCUS for its approval.
1w
0
SiMON FRASER UNIVERSITY ?
APPENDIX A
MEMORANDUM
Dr. S. Aronoff ?
From ?
Dr. A. H. Lachlan, Chairman
Dean of Science ,
?
Department of Mathematics
Subject ?
MATHEMATICS 310-3, 312-4, and 320-3 ?
Date
?
August 23, 1974
PROPOSED NEW COURSES
We propose to introduce three new courses, Mathematics 310-3, 312-4,
and 320-3,. and to change the name and number of another.
Mathematics 310-3 (Introduction to Ordinary Differential Equations)?
replaces Mathematics 352-2. The pace will be less hectic, and there will
be time to discuss the Laplace transform and its use in solving differential
equations. Otherwise, the course will be much like 352-2. It will be
,a
required course in the Mathematics Honors Program, as was Mathematics 352-2.
We plan to offer 310-3 quite frequently. There is no reason
why
a fourth
level student who has completed Mathematics 253-4 cannot take this upper
division course, and we would recommend that students planning to take
Mathematics 310-3 do so as early as possible.
Mathematics 312-4 (Multidimensional Calculus) and 320-3 (Theory of
Convergence) together replace Mathematics 311-4, a course which has been
less than completely satisfactory for students and for faculty. Multi-
. ?
dimensional Calculus and the Theory of Convergence traditionally appear
in Advanced Calculus courses, and, except for that fact, have nothing to
do with each other. Mathematics 311-4 tried to cover too much material
(every bit: of it quite essential material) in a four credit course.
Mathematics 312-4 contains the multidimensional calculus portion of
Mathematics 311-4. The four credit hours (rather than approximately 2)
allow proper treatment of the material, much of which was done in cursory
fashion (or omitted completely) when it was part of Mathematics 31i-4.
Mathematics 320-3 contains material on convergence of cquences and series
of r.umber; and of functions, and of improper integrals, from M;tLiiem:Tt,ics
311-4. There is time for a discussion of convergence of Fouri.jr S:ic;,
and additional time for applications. Both courses will be requirtd in
the Mathematics Honors Program. We would expect the
Physics
Departncnt
to replace their Mathematics 311-4 requirement with one for Mathmatics
312-4; in addition we urge them to consider replacing their Mathematics
241-2 requirement for honors students with one for Mathematics 30-3.
Although we only plan to offer 320-3 every other semester initially, if
the course proves to be as popular as we hope, we may then increase its
frequency of offering to twice a year. We are considering making it a
prerequisite for Mathematics 421-4. Mathematics 312-4 and 320-3 could be
taken by properly prepared fourth level students.
tP
I..EASE
READ
?
)74
,
&D INITIAL
rA0Mi
-'-4-
C L[AN
ASST.
-2-
•
??
We will be able to offer the courses as frequently as we have indicated
because we will do several things to make time available for these important
courses. First, if faculty do not handle the tutorials in MTh 310-3, then
a sessional lecturer may be appointed to do so. Since there usually are
several tutorial sections, we will come out ahead this way. Next, we'll
be cutting back slightly on the frequency of offering of some of our applied
courses - in particular, Mathematics 412'-4, 414-4, and 422-4. We ma
y
cut
back on our Real Analysis course, MATH 421-4, especially if we make NIATII 320-3
a prerequisite for it. Though we dislike doing all this, the new courses
are more fundamental than the ones being cut back, and we would rather do
this than stick with the very unsatisfactory MATH 311-4. Finally, we have
made certain cutbacks in our graduate course offerings for faculty teaching
credit (some courses now get taught "for free") and we have come up with a
few hours there. So if you just look at MATH 310-3 versus MAtH 35-2, or
MATH 312-4 and MATH 320-3 versus MATH 311-4, it would appear to be the case
that we can't do it, but if you look at the whole programme you can see that
we'll manage.
.
0
SiMON FRASER UNIVERSITY ?
MEMORANDUM
•.......Dr. S. Aronoff
Dean
?
of Science .................................
Subject
MATHEMATICS 310-3, 312-4, 320-3
AND 420-4 PROPOSED NEW COURSES
From ?
David Ryeburn, Chairman..............
Undergraduate Studies Committee
Department of Mathematics
Date.
?
October 23, 1974
Here is a list of certain mathematics courses, the number of faculty
teaching hours devoted to them for the two periods Fall 1973 - Summer 1975
and Fall 1975 - Summer 1977, and the number of times offered. It makes
sense to look at two-year periods since many of these courses repeat on
a six semester cycle instead of a three semester cycle.
1973 -
1975
1975 - 1977
Course
Hours
Times Offered
Course
Hours
Times Offered
311-4
26
4
312-4
24
4
320-3
20
5
352-2
24
5
310-3
22
4
412-4
15
3
420-4
10
2
414-4
15
3
414-4
10
2
421-4
20
4
421-4
15
3
422-4
16
3
422-4
20
4
433-4
5
1
433-4
0
0
TOTAL
121
TOTAL
121
.1 was mittaken when I said in my October 17 memorandum that we were
planning to cJ:t back on 422-4 -- in fact we'll offer it more often. But
we are going to cut back on 310-3 and 421-4, and have eliminated 433-4.
It should be noted that.to
some extent what we are doing is offering more
hours of applied mathematics and fewer hours of pure mathematics. Our
graduate programme has been cut back from 36 hours per year to 24.
rJ
APLIED MATHEMATICS UNDERGRADUATE COURSE OFFERINGS
July 31, 1974
YEAR I
?
(1976-77)
YEAR II ?
(1975-76)
Fall
Spring
Summer
Fall
Spring
Summer
104-3
104-3
161-3
161-3
308-3
308-3
310-3
310-3
310-3
310-3
310-3
312-4
312-4
312-4
312-4
316-3
316-3
320-3
320-3
320-3
3613
361-3
412'4
412-4
413-4
S
414-4
414-4
416-3
422-4
422-4
422-4
431-4
431-4
431-4
466-4
466-4
471_4*
468_4*
467_3*
469_4*
470_4*
* The order of these courses can be rearranged provided 1) 468 should follow
361, and 2)
469 should follow 422.
TOTAL APPLIED HOURS 69
?
TOTAL APPLIED HOURS 67
Note: For comparison purposes these figures include those courses listed as
"applied" on "Summary of Hours of Course Offerings" table. That is
these totals do not include 104-3, 422-4 and 431-4.
0
SENATE COMMITTEE ON UNDERGRADUATE STUDIES
COURSE PROPOSAL FORM
0
Calendar Information ?
Department:
?
Mathematics
Abbreviation Code:
?
Number:
310
?
Credit Hours: 3
?
Vector: 3-1-0
Title of Course: INTRODUCTIONTOORDINARYDIFFERENTIALEQUATIONS
Calendar Description of Course: First
and higher order differential equations;
linear differential equations; solution by power series; Laplace transform
method; applications to physical, chemical, biological and social science
Nature of Course Lecture/Tutorial
Prerequisites (or special instructions): Math 253-4. Students who have obtained
credit for MATH 352-2 cannot subsequently
obtain credit for MATH 310-3.
What course (courses), if any, is being dropped from the calendar if this course is
approved:
MATH 352-2
2. Scheduling
How frequently will the course be offered? Twice
a
year.
Semester in which the course will first be offered? Fall 1975
Which of your present faculty would be available to make the proposed offering
possible:
I
•
All faculty members.
ObjectivesoftheCourse The purpose of this course is to provide
the students,
mathematics major or otherwise, the basic knowledge about ordinary differential
equations. The emphasis here is on the techniques of solving ordinary differential
equations and on the applications to various diversified fields.
4. BudgetaryandSpaceRequirements (for information only)
What additional resources will be required in the following areas:
Faculty ?
Probably none.
Staff
Library
Audio Visual ?
NONE
Space
Equipment
5. Approval
Date:
?
17/10/74 ?
-7/H/7
W
?
Department Chairman
?
Dean
Chairman, SCUS
SCUS 73-34b:- (When completing this form, for instructions see Memorandum SCUS 73-34a.
Attach course outline).
.
310-3
INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS
1.
First order equations: Equations solved by separation of variables,
exact equations,
integrating
factor, homogeneous equations, higher
order equations reducible to first order, applications of first order
differential equations to geometry and to social, biological, physical
and chemical science. (3 weeks)
2.
Linear differential equations: Existence and uniqueness of solutions,
linear independence and Wronskians, solution of homogeneous equations,
particular solutions of nonhomogeneous equations, method of undetermined
coefficients, method of variation of parameters, applications. (3 weeks)
3.
Systems of linear differential equations: Matrix notation, solution
of systems of
linear differential equations,
applications. (1 1/2 weeks)
4.
Solutions in power series: Power series, solution of differential
equations in power series, regular singular points, method of
Frobenius, numerical solutions. (1 1/2 weeks)
5.
Solution of differential equations
bX
the Laplace transform; Fourier series:
Laplace transform, some supporting t1eory, applying the transform. The
Fourier series concept. Fourier traisform, applications.
?
(3 weeks)
Suggested Textbooks: (The Instructor s]9uld choose any one of the following)
1.
Applied Differential Equations by M.R. Spiegel.
2.
Ordinary Differential Equations, a first course by F. Brauer and A. Noble.
3.
Introduction to Ordinary Differential Equations by A.L. Rabenstein.
4.
Differential Equations with Applications and Historical Notes by G.F. Simmons.
.
0
SENATE COMMITTEE ON UNDERGRADUATE STUDIES
COURSE PROPOSAL FORM
Calendar Information
?
Department:
?
Mathematics
Abbreviation Code:
?
Number: 312 ?
Credit Hours: 4
?
Vector: 4-1-0
?
Title of Course: MULTIDIMENSIONAL CALCULUS
Calendar Description of Course:
Functions of several variables; gradient, divergence and curl; extrema; multiple
integrals; line and surface integrals; Stokes' theorem and divergence theorem;
curvilinear coordinates; applications.
Nature of Course : Lecture/Tutorial
Prerequisites (or special instructions): MATH 253-4. Students who have obtained
credit for MATH 311-4 cannot subsequently
obtain credit for MATH 312-4.
What course (courses), if any, is being dropped from the calendar if this course is
approved:
MATH 311-4
2. Scheduling
How frequently will the course be offered? Twice a year
Semester in which the course will first be offered? Fall 1975
Which of your present faculty would be available to make the proposed offering
possible: ?
All faculty members.
ObjectivesoftheCourse
The object of this course is to provide a standard treatment of calculus of
several variables.
4.
BudgetaryandSpaceRequirements (for information only)
What additional resources will be required in the following areas:
Faculty
Staff
Library ?
NONE
Audio Visual
Space
Equipment
5.
Approval
Date:
?
17/10/74
Department Chairman
?
Dean
?
Chairman, SCUS
SCUS 73-34b:- (When completing this form, for instructions see Memorandum SCUS 73-34a.
Attach course outline).
MATHEMATIC 312-4
. ?
MULTIDIMENSIONA4 CALCULUS
1. Quick review of functions of several variables. (1 - 1 1/2 weeks)
:. Di
r
ferential operator V ; gradient, divergence and curl of vector
valued
functions;
directional derivatives; geometrical applications
(2 weeks).
3. Extrria of functions of several variables; extrema under constraints
(Lagrange multipliers method); application of Lagrange multipliers
method (1 1/2 weeks).
:.
.tiple integrals, iterated integrals; change of variables in
.nultiple integrals. (2 weeks)
j.:.
3fld
surface integrals; simply or multiply connected regions;
irendence of the path; Green's Theorem; the divergence theorem,
3r':,s
theorem, physical applications. (3 weeks)
. ?
6. ?
iear coordinates; coordinate curves and coordinate surfaces;
vectors; orthogonal curvilinear coordinates; gradient, cur',
iaa, etc. in orthogonal
curvilinear coordinates.
(2 weeks)
(N:s ro be prepared for students)
'EX[': 1. Advanced Calculus by Watson Fulks
Advanced Calculus by D.V. Widder
Advanced Calculus by A. Taylor and R. Mann
The Instructor should choose any one of the above textbooks)
0
SENATE COMMITTEE ON UNDERGRADUATE STUDIES
COURSE PROPOSAL FORM
Calendar Information ?
Department: ?
Mathematics
Abbreviation Code:
?
Number:320
?
Credit Hours:3
?
Vector:3-1-0
Title of Course: THEORY OF CONVERGENCE
Calendar Description of Course:
Sequences and series of functions; uniform convergence; consequences of uniform
convergence; improper integrals; additional applications of convergence.
Nature of Course: Lecture/Tutorial
Prerequisites (or special instructions): MATH 253-4. Students who have obtained
credit for MATH 311-4 cannot subsequently
obtain credit for MATH 320-3.
What course (courses), if any, is being dropped from the calendar if this course is
approved:
MATH 311-4
2. Scheduling
How frequently will the course be offered? Initially each semester.
Semester in which the course will first be offered?
?
Fall 1975
Which of your present faculty would be available to make the proposed offering
possible: All faculty members.
Objectives of the Course: This course is designed to acquaint the students with the
important notion of uniform convergence. By discussing this concept in connection
with sequencesand series of functions and improper integrals one demonstrates its
usefulness in various applications. At the same time, this treatment of uniform
convergence will improve the students' ability in pursuing abstract mathematical
thinking.
4. Budgetary and Space Requirements (for information only)
What additional resources will be required in the following areas:
Faculty
Staff
Library ?
NONE?
Audio Visual
Space
Equipment
5. Approval
Date: ?
17/10/74
. ?
Department
C/( v&
Chairman
-7
/
I ILA,
Dean
?
Chairman, SCUS
SCUS 73-34b:- (When completing this form, for instructions see Memorandum SCUS 73-34a.
Attach course outline).
2;;--
THEORY OF CONVERGENCE
-iee Series ?
2 weeks
1.
Convergence, absolute and conditional.
2.
Series with non-negative terms. Comparison tests.
3.
Series with non-negative terms. Ratio and root tests. Remainders.
4.
Series with variable signs.
5.
More delicate tests.
II. Scuence and Series of Functions. Uniform Convergence.
?
2 1/2 weeks
1.
Uniform convergence.
2.
?c.nsequences of uniform convergence
(Integration
and differentiation).
l's and Dirichlet's tests.
III. The Taylor Series
?
2 weeks
1.
Power series. Interval of convergence.
2.
Properties of power series.
3.
The Taylor and Maclaurin series.,
4.
The arithmetic of power series.
IV. Improper Integrals ?
3 1/2 weeks
1.
Improper integrals. Conditional and absolute convergence.
2.
Improper integrals with non-negative integrands.
3.
The Cauchy principal value.
4.
.;iform convergence and some consequences.
?
V.
T': ' ?
e
chosen from:
?
2 weeks to any
?
W ?
I: ?
Integral Representations of Functions
?
one topic
(a)
Generalities
(b) Gamma and Beta functions
II.
Asymptotic series and integrals (Notes to be supplied to students')
III.
Fourier Series (Notes may be supplied to students from
'Advanced Calculus' by
I.S.
Sokolnikoff)
(a)
Criterion of Approximations
(b)
Fourier coefficients
?
Cc)
?
Dirichlet conditions
(d) Orthogonal functions
(e) Expansion of functions
(f) Change of intervl (if time permits)
?
TEXTS: ?
1. Advanced Calculus by Watson Fulks
2. Advanced Calculus by D.V. Widder
3. Advanced Calculus by A.E. Taylor and R. Mann
(The Instructor should choose any one of the above texts)
0
4cc4s
7yr64'
SENATE COMMITTEE ON UNDERGRADUATE STUDIES?
COURSE PROPOSAL FORM
0
Calendar Information
?
Department:
Abbreviation Code:
?
Course Number:420
?
Credit Hours:
Title of Course:
?
LINEAR ANALYSIS
Calendar Description of Course:
APPENDIX B
Mathematics
4 ?
Vector: 4-1-fl
Fourier Series, harmonic analysis, eigenvalue problems in differential equations.
Some special functions.
Nature of Course: Lecture/Tutorial
Prerequisites (or special instructions): MATH 232-3 and 253-4 and 310-3 (or 352-2).
MATH 320-3 (or 311-4) is highly recommended. Students who have obtained credit
for MATH 412-4 cannot subsequently obtain credit for MATH 420-4.
What course (courses), if any, is being dropped from the calendar if this course is
approved:
MATH 412-4. See attached for details.
2. Scheduling
How frequently will the course be offered? Once a year.
Semester in which the course will first be offered? Spring 1976
Which of your present faculty would be available to make the proposed offering
possible: All faculty members.
*objectives of the Course: The objective of this course is to utilize the tools of
Euclidean vector spaces and linearity with development of the theory of Fourier
series, Sturm-Liouvj].le theory and other aspects of differential equations. Special
functions and the separation of variables technique are developed as a byproduct.
4. Budgetary and Space Requirements (for information only)
What additional resources will be required in the following areas:
Faculty
Staff
Library
?
NONE
Audio Visual
Space
Equipment
5. Approval
Date:
?
7/10/74
?
7/I lJ7
ItA
Department Chairman
?
Dean
Chairman, SCUS
SCUS 73-34b:- (When completing this form, for instructions see Memorandum SCUS 73-34a.
Attach course outline).
S
'I
1. C:1.cndar Information
What course (courses), if any, is being dropped from the calendar if this
course is approved:
MATH 412-4. NOTE: MATH 420-4 is in every respect except name and number
identical with MATH 412-4, Methods II. The disappearance of MATH 311-4,
>cthods I, makes the continued existence of a course called Methods II
unreasonable. The new number, 420, is reasonable since the course will
then have a number appropriate to its location among our other analysis
courses (320-3,
421-4, 422-4, and 423-4);
the new name, unlike Methods II,
is informative.
S
0
MATHZXAT:CS 420-4
LINEAR ANALYSIS
S
Ts ccrse serves two main purposes: First, it introduces the student
t .i
?
t1oris of linear algebra and second, it develops the concept and
t:, tcr..iqs associated with the method of separation of variables in
3fferential Equations. Theprimary tool is Fourier series and the
curse .evlops the underlying theory.
The following syllabus refers to the recommended text.
Chapter 1 - ?
Real Vector Spaces
Chapttr
2
- ?
Linear Transformation and Matrices
(Give a quick review here - about 5 hours)
Cha-tr
;' - ?
Euclidean Spaces - 3 hours
?
(Omit 7-6, 7-7)
C'n.Dter
3
-
?
Convergence in Euclidean Spaces - 3 hours
(Omit 8-5 for later consideration in Chapter 10)
t •
- Fourier Series - ?
2 -
3
hours
13 ?
- Convergence of Fourier Series - 12 hours
• ?
..
- ?
(Lhocral Series of Polynomials -
?
6-9 ho,:-,
i3
(On treat Hermite, Laguerre polynomia. 1ess
interhive1y
than Legendre.)
2
boundary Value Problems for Ordinary Differential
Equations
?
-
?
6 - 7
hours
'Omit 12-9,
?
12-10, ?
12-11)
• ?
:.tc
13 ?
- Boundary Value Problems for
Partial
Differential
Equations
?
- ?
2 - 5 hours
Sections 13-4 and 13-6 plus some other material if
time allows.
(hapt
14
?
-
Boundary Value Problems for Laplace Equations
?
-
?
4
hcur
(Omit 14-7)
Chapter 15
?
- Boundary Value Problems Involving Bessel Fur.tiors
Can be omitted or given some converage as time allows.
Difficult to cover without knowledge of 413.)
TEXT: AN INTRODUCTION TO
LINEAR ANALYSIS - •Kreider,
Kuller, Ostberg & rki's
S
?
H
RATIONALE:
The Department of Mathematics wishes to change the number and name of
Mathematics 412-4 (Methods II) to Mathematics 420-4 (Linear Analysis),
since with the disappearance of Mathematics 311-4 there will be no Methods
I course. The numbering also makes it clear that it belongs to the
analysis subset (320-3, 420-4, 421-4, 422-4, and 423-4) and the name is
informative. The course is identical with the old Mathematics 412-4.
.
.
0
rc: 7
Y -J-ir
C,
APPENDIX C
- ?
.thenatics 310-3 replaces 352-2, 312-4 and 320-3 replace
.;: 420-4 replaces 412-4, the following calendar changes will be
requirement:
in the case of honors students - to obtain credit in the following
2ivision Mathematics courses:
:i14, 352-2, 421-4, 422-4 and at least one of 431-4 or 432-4."
- ?
at the existing requirement specifies 18 of the required 50
f upper division Mathematics work.)
.:ujrment:
the case of honors students - to obtain credit in the foli'owirc.
r division Mathematics courses:
310-3, 312-4, 320-3, 421-4, 422-4, and at least one of 431-4 or
32-4.
:rat now 22 of the 50 hours would be specified.)
C. ?
prrquisites should be changed.
.,o
?
. ?
- ?
Old prerequisites:
?
MATH 352-2. MATH 311-4 is highly reomnccd.
?
New prerequisite:
?
MATH 310-3 (or MATH 352-2) , and 30-3
?
(or
MATH
311-4).
?
44-4: Old prerequisite:
?
MATH 352-2 and 311-4.
?
New prerequisite: ?
MATH 310-3 (or
MATH 352-2) ad MATH 31.-4
(or MATH 311-4).. MATH
32C-3 is
hih- rcrtnded.
?
41-3: Old prerecuite:
?
MATH 316-3 (or
MATH
406-3), and MAT:i 3-2.
?
New rerequxsi
.
te:
?
MATH 310-3 (or MATH 332-21, and MATH
?
(or
MATH
MATH
406-3).
?
421-4: Old prerequisite: ?
MATH 241-2.
MATH
311-4 is highly
?
cmenr''.
?
New prerequisite: ?
MATH 241-2.
MATH
320-3 i highly ri
?
iic:aed.
?
422-4: Old prerequisite: ?
Either
MATH
311-4, or both of M.T:
53-4 and
241-2.
?
New prerequisite: ?
MATH
253-4. MATH 320-3 is highly recommended.
P3cc
279
?
466-4: Old prerequisite: ?
MATH 2534.
MATH
232-3 is highly recommendeo.
?
• ?
New prerequisite:
?
MATH 253-4, and
MATH
232-3 or permission of the
Mathematics Department. MATH 312-4 (or
MATH
311-4)
is highly recommended.
e 279 (Continued)
47-3: Old prerequisite: MATH 161-3 and 352-2. MATH 311-4 and 361-3 are
?
highly recommended.
New prerequisite: MAT!! 161-3, MATH 310-3 (or MATH 352-2) and
PHYS 203-2.
MATH
361-3 is highly recommended.
4L8-4: Old prerequisite: MATH 311-4 and 361-3.
New prerequisite: MATH 312-4 (or Math 311-4) and MATH 361-3.
470-4 Old prerequisite: MATH 161-3 or PHYS 203-2. MATH 311-4 or PHYS 382-4
should precede or be taken concurrently.
New prerequisite: MATH 161-3 or PHYS. 203-2. MATH 310-3. Both
MATH 312-4 (or MATH 311-4) and MATH 320-3 (or MATH 311-4),
or else PHYS 382-4, should precede or be taken
concurrently.
471-4: Old prerequisite: MATH 311-4 or PHYS 382-4.
New prerequisite: MATH 312-4 (or MATH 311-4), or PHYS 382-4.
.
0
PPRQt$ITE PATICNALE
0
MATH 42-4: Has been
MATH
311-4, or else MATH 253-4 and MATH 241-2.
To be
MATH
253-4, with MATH 320-3 highly recommended.
Th, 'AT!1 241-2 prerequisite was more of a mathematical maturity requirement
thu. 'or.
ub':,1ute need for knowledge gained while studying the material of
i-. The MATH 253-4 course, as currently taught, will provide the
r.x:urience needed to allow MATH 422-4 to be takenwith profit. There
is no question that MATH 320-3 would provide material making the theoretical
part of MATH 422-4 easier to understand, but Physics honours students, who
will
take
MATH
422-4, should not be kept from doing so through lack of
MATH
320-3. Physics honours students will have had
MATH
241-2 anyway (and we hope
this will be changed to MATH 320-3).
Has been MATH 161-3 and MATH 352-2
1
with MATH 311-4 and
MATH 361-3 highly recommended.
To be MATH 161-3, MATH 310-3,
and PHYSICS 203-2, with
MATH
.
361-3
highly
recommended.
r.t
?
?
h'sics 203-2 prerequisite will provide students with two mechanics
?
Thysics201-2 and Physics 203-2) which will help motivate the mathe-
r.t
?
this course. Neither MATH 312-4 nor MATH 320-3 is absolutely
•i. ?
rcr this course, so the
MATH
311-4 recommendation should be dropped.
Has
been MATH 361-3, and MATH 311-4 or PHYS 382-4 as corequisites.
To be MATH 422-4.
.s ?
'r'.sents a slight shift in viewpoint. Fluid dynamics can be looked
Ci
:i;'plied complex analysis, and indeed one MATH 422-4 text we have used
& Redheffer's Conülex Variables) shows how to interpret analytic
c:s in terms of fluid flow in a way attractive even to pure mathematicians
:v
;rid
mathematicians feel that if the approach to the same material in
4'
.
-4 is changed in this way, MATH 422-4 will give more appropriate
on for the course.
M;T 470-4: Has been MATH 161-3 or PHYS 203-2, and MATH 311-4 or PHYS 382-4
as corequisites.
To be MATH 161-3 or PHYS 203-2, and MATH 310-3, with MATH 312-4
and MATH 320-3
(or else
PHYS 382-4) as corequisites.
The introduction
of the differential equations prerequisite
(MATH 310-3) will
insure that students will have had some experience with ordinary differential
equations
before looking at the Euler-Lagrange equations.
xc,44J
74:;
APPENDIX D
.
CHEMICAL PHYSICS
Major Program - Current Mathematics requirements:
MATH 151-3, 152-3, 232-3, 253-4, 352-2
Proposed Change: Delete MATH 352-2 and add MATH 310-3.
Honors Program - Current Mathematics requirements:
MATH 151-3, 152-3, 232-3, 253-4, 311-4 (or 431-4), 352-2,
412-4 (of PHYS 382-4)
Proposed Change: MATH 151-3, 152-3, 232-3, 253-4, 310-3
312-4 (or 431-4), 420-4 (or PHYS 382-4).
CHEMISTRY
Chemistry Core Program (Major and Honors Programs)
Current Mathematics requirements: MATH 151-3, 152-3,
253-4, 352-2
Proposed Change: Delete MATH 352-2 and add MATH 310-3.
Chemistry Minor Programs (General Chemistry and Physical
and Nuclear Chemistry)
Current Mathematics requirements: MATH 151-3, 152-3,
253-4, 352-2 recommended
Proposed Change: Replace MATH 352-2 with 310-3.
PHYSICS
Major Degree
- Levels 3 and 4 - Present Mathematics requirements:
MATH 253-4, 352-2
Proposed Change: Delete MATH 352-2 and add MATH 310-3.
Levels 5, 6, 7, and 8 - Present Mathematics requirements:
MATH 311-4
• ?
Proposed Change: Delete MATH 311-4 and add MATH 312-4.
.....
- ?
I
- ?
Appendix
Page 2
Honors Degree
Levels 3 and 4 - Present Mathematics requirements:
MATH 241-2, 253-4, 352-2
Proposed Change: Delete MATH 241-2, 352-2 and add MATH 310-3.
Levels 5, 6, 7, and 8 - Present Mathematics requirements:
MATH 311-4, 414-4, 422-4, one of 431-4, 432-4
Proposed Change: Delete present requirements and replace
with: MATH 312-4, 320-3, 422-4 and one other MATH course
numbered 412 or greater.
0
J -
?
JC'4f7dW
_J
APPENDIX E
Subject: MATH 241-2 Prerequisite
Because the Physics Department has proposed that MATH 241-2 be
dropped from the core program in Physics, the Department of
Mathematics has proposed the following change in the prerequisite
for that course:
Current prerequisite: MATH 142-2 and 152-3. For Physics students,
MATH 253-4 may be substituted.
Proposed change: Delete, "For Physics students, MAT!-! 253-4 may
be substituted."
S
.
0
