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- .--- -
V
SiMON FRASER UNIVERSITY
?
S1
74-50
MEMORANDUM
From
SENATE COMMITTEE ON UNDERGRADUATE
STUDIES
I
I
?
SENATE
Date
?
APRIL
18, 1974
Subject
NEW COURSE PROPOSALS -
MATH
154-3, 155-3, 194-3, 196-3
MOTION 1:
?
"That Senate
the new cour
MATH
154-3 -
MATH
155-3 -
MATH 194-3 -
MATH
196-3 -
approve, as set forth in
S.74-.50,
se proposals for:
Calculus I for the Biological Sciences
Calculus II for the Biological Sciences
Euclidean Geometry
Modern Geometry."
MOTION 2:
?
"That Senate waive the normal two semester time
lag requirement in order that
MATH
154-3
may be
first offered in the Fall semester
74-3."
(Note:
MATH 195-3 -
Introductory Geometry will be discontinued
?
on the introduction of
MATH
194-3
and
MATH
196-3.)
0
 
SJIItDI iJ I'1
?
S74°
1j1tt]'1I'1
b• ?
New Course Proposals - F.ci.lty of
Subject
From .........
Senate ... Comnitt,ee. on
..tndergraduate. Studies
Date
........April
19,
S
To
The Senate Carrmittee on Undergraduate Studies has examined
the following course proposals - Mathematics
15143:
Calculus I :or the
Biological Sciences; Mathematics
155-3:
Calculus II for the Biological
Sciences; Mathematics
19
1
4-3:
Euclidean
Geometry; and Mathematics
196-3:
Modern Geometry. It is recommended that these courses be approved.
It is further recommended that, should these proposals be accep;ed by
Senate, the normal two semester time lag be waived in the case of
Mathematics
1514_3
so that it may be offered in the Fall semester,
1974.
97 -
I .rkgridg
.
?
:arns
att.
0
 
SiMON FRASER UNIVERSITY
MEMORANDUM
........Sena..eComm
?
on
?
............
From
....
....................
.
.
n4ga4ua.te
Ss
.................................
S
u
bj ect
...... .....
NEW
MA'1'I
c S
.........
.............................................
.
.
Date .....
COURSE PROPOSALS
At its meeting of March 19, 1974 the Faculty of Science approved
four new Mathematics courses as follows:
MATH 154-3 Calculus I for the Biological Sciences
MATH 155-3 Calculus II for the Biological Sciences
MATH 194-3 Euclidean Geometry
MATH 196-3 Modern Geometry
Attached is a rationale for the initiation of the calculus courses
for the biological sciences, course proposal forms for 154 and
155 and a statement on the effect these courses have on the
prerequisite structure of Mathematics courses. Additionally,
• ?
there is a rationale for the replacement of MATH 195-3 with
194-3 and 196-3, and course proposal forms for these new courses
as required.
It is to be noted that the intended initial offering cf 154-3
is 74-3 which will require the approval of SCUS and such
recommendation ?
Senate.
1w
cc: A.H. Lachlan, Chairman
Department of Mathematics
Jr
. ?
.., '
 
SiMON FRASER UNIVERSITY
MEMORANDUM
?
.
From
?
Dr. A. H. Lachlan,
Mathematics Department
Date. .
?
December 3, 1973
Following discusSiOnS with the Department of Biological Sciences,
this Department agreed to split the first year calculus courses into two
sections. One section was for students in Biology, and the other for
those in Chemistry, Mathematics and Physics. This has been done on an
experimental basis for the past two years and is considered to be worthwhile.
One positive result-is the reduction of class size, in the case of
Math 151-3 from 250-300 students to lectures with 100-150 students
in each section. For the past year, a textbook different from the one
used in the regular section of Math 151-3 has been adopted and as a
result, there have been syllabus changes. This is one of the reasons
we are making formal proposals for new course numbers. The other reasons
are to ease administrative procedures with respect to pre-registration
in these courses. Without separate course numbers, it is difficult for
. ?
the Registrar's Office to ensure that students register in the appropriate
lecture and tutorial sections. During the experimental period this has
resulted in tutorial assignments for the split calculus courses being
done departmentally
.
The new course numbers will mean that these courses
can be treated like the others in the pre-registration procedure.
 
Appendix B3
SENA'[1' cO>Y.i:TTLE 0 1:;fl1;R(;Ar)UAT
?
;Tu:):!:S
.
COUiSE I0)L FOIL",
Calendar Ifor.ion
?
Department: Mathematics
Abbreviaien Code:
?
Course umbcr;154-3
?
Credit Hours:3
?
Vector: 3-1-0 -
Title of Course:
?
Calculus I for the Biological Sciences
Calendar Description of Course:
The logarithmic, trigonometric and exponential functions. Limits and continuity.
The derivative and.techniques of differentiation. Maxima, minima, the mean value
theorem. Applications for the Biological Sciences.
Nature of Course Lecture/tutorial.
Prerequisites (or special instructions): Math 12 '(B.C. Schools) or Mathematics 100-3.
Students with other qualifications must consult an advisor in the Mathematics Department
before they can be admitted to the course. Students who have received credit for either
Mathematics 150-3 or-151-3 cannot receive credit for Mathematics 154-3.
What course (courses), if any, is being dropped from the calendar if this course is
approved:
None.
2.
Schedu1iij
How frequently will th& course be offered? Twice per year, in the fall and spring semester
Semester in which the course will first be offered? Fall 1974
Which of your present faculty would be available, to make the proposed offering
. possible?
All faculty members.
3.
Objtcttv
'
.s of the Course
The objective of the course is to make the study of calculus more relevant to students
in Biological Sciences. The difference between the topics discussed in Math 154-3 and
those discussed in Math 151-3 is very small. The emphasis in Math 154-3 is placed on
the application of techniques learned in calculus to problems in the Bi.oligical Sciences,
wherever it is possible.
4.
Budgetary and Space Requirements (for information only)
What additional resources will be required in the following areas:
Faculty There will be no net increase in faculty teaching time required for this course.
For the past two years, the Department has offered separate sections of Math 151-3
Staff
?
in the Fall semester. One section has been for Biology students; and the other?
Library for Chemistry, Mathematics and Physics students. This experiment has proved to
be successful and as a result, the Department has rearranged its upper level course
Audio Visual offerings so that it can afford to' offer this course in Spring semesters.
Space
None.
Equipment
5.
Approvnl
Date:_____________
• ?
(L 64.
?
c.
?
______
__
I)epnrtncnt Chairman
?
'
?
Dean ?
Chairman, ;ce:;
SCUS 73-341):- (When
completing
thin
form, for 111jtruct1c'nu
iwe Memorandum SCUS 73-34.t.
Attach cotirtw out: line)
 
C
MATHEMATICS 154-3
Calculus for Biology Students
I.
Real Number, Sets, Functions and Limits
Section 1.0 Real Numbers, Order, Absolute Value
1.1 Sets, Set Notation, Operations with sets
1.2 Functions (Polynomial Functions, Rational Functions)
1.3 Addition, Multiplication, Division and Composition
of functions
1.4 Limits
1.5 Increments and Rate of Change
1.6 Review of Trigonometry (3 lectures)
1.7 Limits of Trigonometric Functions
1.8 Limit as x tends to Infinity
II.
The Derivatives
Section 2.1 Slope and Equation of Straight Lines
2.2 Continuous Functions
2.3 The Derivative of a Function (Geometric and Physical
. ?
Interpretation, Rate of Growth)
2.4 The Derivative of Polynomials
2.5 The Derivative of Products and Quotients
2.6 The Derivative of Composite Functions
2.7 The Derivative of sin u and cos u
2.8 Derivatives of tan u, cot u, sec u and csc u
2.9 Higher order Derivatives
2.10 Exponential and Logarithmic Functions (See Seeley's
Approach)
III.
More About Derivatives and Their Applications
Section 3.1 Curve Analysis
3.2 Maxima - Minima
3.3 Applications of Maximum - Minimum
3.4 The Differential
3.5 Implicit Differentiation and Applications
3.6 Inverse Functions
3.7 Derivatives of the
Inverse
Trigonometric Functions
3.8 Geometric Interpretation of Rolle's Theorem and the
Mean Value Theorem
TEXT: Calculus for Business, Biology and the Social Sciences
by Crowdis, Shelley and Wheeler
November 1973
 
SENATE COMMITTEE ON UNDERGRADUATE STUDIES
?
NEW
COURSE PROPOSAL FORM
.1. Calendar
Information ?
Departmen
_---"
t:
Abbreviation Code:
?
Course
Numbe
r:155_3 ?
Credit Hours:3 - Vector:
Title of Course: Calculus II for the Biological Sciences
Calendar Description of Course:
The integral......Techniques ..of: .ntegration: Series. Differential equations, partial
differentiation. Applications to the Biological Sciences.
Nature of Course
?
Lecture/tutorial.
Prerequisites (or special instructions): Mathematics 150-3 (with a grade of A or B)
or Mathematics 151-3 or 154-,.3:. Students who-
,
have received.credjtfo]- Mathematics
152-3 cannot receive credit for this course.
What course (courses), if any, is being dropped from the calendar if thiw course is
approved:
None.
2. Scheduling
How frequently will the course be offered? Oiceperyear in 'the Spring.
Semester in
which the course will first be offered?
?
Spring 1975.
Which of your present faculty would be available to make the proposed offering
possible? ?
All faculty members.
3.' Objectives of the Course
The ob.ject±ve'ef the,'. course is to'make"t'he study- ofcalcuiius.more,re:1evant to students
in. ?
has'-be'en pepared:,On the asszmption'that those
students .wh'o take the coursewil"l probably. hot take further coursesLn mathematics.
For this reason. a greater variety--of topics-are discussed in Math 155-3.
4.
Budgetary and Space Requirements (for information only)
What additional resources will be required in the following areas:
Faculty
?
There will. he. no net increa'se,'.-in
,
faculty teaching. time required' for'.this course.
For 'the past,. two
-
years" the. fleparmet
'
:has'offered separate sections of Math
Staff
?
152-3:'in theSpringsemes:ers; with-one section 'b
'
eing:primarily for students in
Library ?
Biological Sciences.
Audio Visual7
Space ?
None.
Equipment
5. Approval
Date':
4. ?
/ ?
/ 4
Department Chairman
?
Dean ?
Chairman, SCUS
SCUS 73-34b:- (When completing this form, for instructions see Memorandum SCUS 73-34a.
Attach course outline).
 
MATHEMATICS 155-3
Calculus for Biology Students
IV.
Introduction to the Integral
Section 4.1 Area Bounded by a Curve
?
4.2 Sigma Notation
4.3 Properties of the Integral
4.4 The Indefinite Integral
4.5 Indefinite Integrals - Trigonometric Functions
V.
Integration
Section. 5.1 The Fundamental Theorem of Calculus
5.2 The Natural Logarithm
5.3 The Exponential Function
5.4 Integration by Parts
5.5 Trigonometric Substitutions
5.7 Improper Integrals
5.8* Use of semi-log and log-log graph papers,
VI.
Applications of Integration
Section 6.1 Areas
6.2 Probability
6.3 Families of Curves, Parameters, Moments
6.4 Normal Curve Areas, Areas with Tables
6.8t Natural Growth and Decay
VII.
Functions of Several Variables
Section 7.1 Functions of Several Variables
7.2 Three-Dimensional Coordinate Geometry
7.3 Partial Derivatives
7.4 Extrema for Functions of Two Variables -
Maximum and Minimum
75* Curve Fitting - Least Square Method
VIII.* Introduction to Ordinary Differential Equations
.
curve fitting
Section 8.1 Differential Equations
8.2 First Order Differential Equations
8.3t Natural Growth and Decay
8.4 Systems of First Order Linear Differential Equations -
Species Competition
C
 
-2-
IX. Matrices and Vectors
Section 9.1 Matrix Notations
9.2 Matrix Algebra
9.3 Applications
* Materials which have to be supplemented by the instructor from
sources other than the current textbook.
t This topic is covered twice.
TEXT: Calculus for Business, Biology and the Social Sciences
by Crowdis, Shelley and Wheeler
.
ell
S
 
SiMON FRASER UNIVERSITY ?
MEMORANDUM
......................Faculty
?
of
?
Science
?
.From...........
.
.P..ayebUr.n..........................................................
11
Dept. of Mathematics
Subject............
Calculus
land II Courses ?
Date............
March 20,
and Prerequisites
Here is the prerequisite structure for Calculus courses, and
.courses dependent upon them.
Course
?
Prereauisites
.
.
142-2: Pure Mathematics II
150-3: Calculus for Social
Sciences
151-3: Calculus I
152-3: Calculus II
154-3: Calculus Ifor the
Biological Sciences
155-3: Calculus II for the
Biological Sciences
161-3: Statics
232-3: Elementary Linear
Algebra
241-2: Pure Mathematics III
253-4: Calculus III
371-3: Introduction to
Probability
141-2 (Pure Mathematics I), or
150-3, or 151-3, or 154-3
Math 12 (B.C. High Schools), or
100-3 (Survey of College
Mathematics)
Math 12 (B.C. High Schools), or
100-3
150-3 (with a grade of A or B), or
151-3, or 154-3
Math 12 (B.C. High Schools), or
100-3
150-3 (with a grade of A or B),
or 151-3, or 154-3
150-3, or 151-3, or 154-3 must
precede or be taken concurrently
150-3, or 151-3, or 154-3
142-2, and either 152-•3 or 155-3
Physics students may substitute
253-4 for 142-2
152-3, or 155-3 with a grade of
AorB
152-3
'V
 
Faculty of Science ?
Page 2 ?
March 20,. 1974
NOTE: Students may not receive credit for more than one of
the three courses 150-3, 151-3, 154-3, nor may they receive
credit for more than one of the two courses 152-3 or 155-3.
Students are not normally permitted to enroll in courses un-
or
less
higher.
prerequisite courses have been passed with a grade of C
—
L: s ez.-Oz - - -
David eburn
.
0
 
SiMON FRASER UNIVERSITY
?
MEMORANDUM
Dr.
,
S. Aronoff
?
From. .
?
Dr. A. H.,:.. Lachlan, chairman
Dean of Science
?
Mathematics Deparl:ment
Subject.....'. NEW COURSE PROPOSALS , - Math 194,- 3,,,,,,,
?
Date ...... ..... ?
.December... 3.,. 1973
?
.
and Math 196-3
Math 195-3 has been a fairly successful course and we have received
numerous requests from both our faculty and our students for another
Geometry course. Our proposal to replace Math 195-3 by two new courses
Math 194-3 and Math 196-3 would satisfy this request and at the same
time handle a problem with the old course. Math 195-3 tried to cover
two separate areas of Geometry - classical Euclidean Geometry and
Modern Geometry. Neither one of these interesting subjects could be
. ?
done in sufficient depth to satisfy either the students or the faculty.
We have in effect split Math 195-3 into two courses each covering one
of these areas. The need for a course in Euclidean Geometry is all the
more important now since the standard High School course (Grade 10) in
Geometry has been all but scrapped.
A!. / r (
.• ?
.t. .... ...'
...P . \
?
..
4.. - .
 
1-.
SENATE COMMITTEE ON UNDERGRADUATE STUDIES
NEW COURSE PROPOSAL FORM
Al. Calendar Information
?
Department: Mathematics
Abbreviation Code:
?
Number:
.
194-3 ?
Credit Hours:3
Title of
Course:
Euclidean Geometry.
Calendar Description of Course:
Plane Euclidean geometry, congruence and similarity.
Theory of parallels. Polygonal areas, Pythagorean
-
Theorem. Geometrical constructions.
Nature of. Course
?
Lecture/tutorial...,''
Prerequisites (or special instructions): Math 11 (B.C. Schools) or permission of the
Department. Students who "have. obtained- credit' for Mathematics 195-3 cannot receive
credit for Mathematics 194-3.
What course (courses), if any, is being dropped from the calendar if thlsr course is
approved:
Mathematics 195-3.
2. Scheduling
How frequently will the course be offered? Once every two years.
Semester in
which the course will first be offered? Spring 75.
Which of your present faculty would be available to make the proposed offering
' possible? ?
.
?
.
J.L. Berggren, H.. Gerber
3.
Objectives of the Course
Geometry is the basis..of o'st'of.the mathematics. done today. Courses 'in'geometry are
essential for a:student's overall view of mathnatics. T}e'o,b'ec'tive of this course
is to teach 'the student the.basic geometry of the Euclideap plane.
4.
Budgetary and Space Requirements (for information only)
What additional resources
will be required in the following areas:
Faculty- There will be no net :increase in faculty teaching tiire require for this course,
Staff
since it is--areplacement for-Math-195, and will be offered in alternate years.
0 ? '
Library
Audio
Space
Visual(.
f
?
None.
Equipment
5.
Approval
Date:
• ?
-
O ?
Department
Chairman ?
Dean ?
-
?
Chairman, SCUS
SCUS 73-34b:- (When completing this form, for instructions see Memorandum SCUS 73-34a.
Attach course outline).
Vector: 3-1-0
 
MATHEMATICS 194-3
Euclidean Geometry
The object of this course is to teach the student the basic geometry
of the Euclidean plane. It will include both theory and the constructions
so that, by the end of the course, the student should have mastered enough
theory to allow him to do fairly difficult constructions on a systematic
basis.. Some attention will also be paid to non-Euclidean and projective
geometry and how these differ from Euclidean.
The topics covered, in order, and the approximate number of hours
devoted to each are as follows:
Axioms of Plane Geometry
(1)
Congruence of Triangles
(2)
Theory of Parallels
()
Polygonal Areas
(3)
The Pythagorean Theorem
and Some Generalizations
(J)
A Geometric Approach to Algebraic
Identities and Quadratic Equations
(2)
The Geometry of the
.
Circle
(4)
The Power of a Point with
Respect to a Circle
(1)
The Construction of a Sine Table
(2)
The Construction of the Regular Pentagon,
Inscribing Polygons in a Circle
?
(3)
A Theory of Proportion
?
(1)
Applications of this Theory to
Similar Figures
?
(5)
• General Form of the Pythagorean Theorem
?
:1)
• Methodical Approach to Geometrical Constructions
?
'6)
f
•
?
PREREQUISITE: Math 11 (B.C. High School) or permission of the Department.
TEXT: Euclid's Elements, vols. I and II.
 
SENATE COMMITTEE ON UNDERGRADUATE STUDIES
NEW COURSE PROPOSAL FORM
1.
Calendar Information ?
Department:Mathematics ?
-
Abbreviation Code:
?
Number: 196-3 Credit Hours: 3- Vector:-3-1-0
Title of Course: Modern Geometry
Calendar Description of Course:
Points and lines at infinity. The theorems of Menelaus and Ceva. Cross ratio.
Harmonic division. Transformation theory of the plane.
Nature of Course Lecture/tutorial.
Prerequisites (or special instructions): Mathematics 11 (B.C. High Schools) or
permission of the Department. Students who .have obtained credit for Mathematics
195-3-cannot receive credit for Mathematics 196-3.
What course (courses), if any, is being dropped from the calendar if this course is
approved: Mathematics 195-3.
2. Scheduling
How frequently will the course be offered? Once every two years.
Semester in which the course will first be offered? Spring 76.
Which of your present faculty would, be available to make the proposed offering
possible? J.L. Berggren, H. Gerber, B.R. Alspach.
3. Objectives of the Course
The object of this course is first to discuss the use of modern techniques, especially
transformations, to obtain results in classical plane geometry. The second goal of
this course is to introduce new geometries to the student. Much time is spent at
the beginning of the course on elementary projective geometry.
4.
Budgetary and Space Requirements (for information only)
What additional resources will be required in the following areas:
Faculty
There will be no net increase in faculty teaching time required for this course
since it
,
is a replacement for Math 195, and will be offered in alternate years.
Staff
Library
Audio Visual ?
None, ?
Space
Equipment
5.Approval ?
.
Date: ?
.
1
01
Department Chairman
?
Dead'
?
Chairman, SCUS
SCUS 73-34b:-
(When
completing this form, for instructions see Memorandum SCUS 73-34a.
Attach course outline).
 
MATHEMATICS 196-3
Modern Geometry
1.
Sensed magnitudes
2.
Infinite points and lines
3.
The theorems of Menelaus and Ceva
4. Cross ratio
5.
Harmonic division
6.
Modern Elementary Geometry of the circle
7. Transformation theory of the plane
8. Applications of homothety
9.
Isometrics and similarities
10.
.Inversionand applications of inversion
PREREQUISITE:
Math 11 (B.C. High School) or permission of the Department.
TEXT: A Survey of Geometry (Revised Edition) ,Howard Eves, Allyn and Bacon

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