SiMON FRASER UNIVERSITY

MEMORANDUM

....

From

Senate Committee on

Undergraduate Studies

Subject..

Proposed Curriculum Changes, ?

Date 1979-09-13

Department of Mathematics

Actions taken by the Senate Committee on Undergraduate Studies

at its regular meeting of 11 September,

1979

give rise to the

following motions:

y .Jrc\mTr\!.T 1

That Senate approve, and recommend approval to the Board of

Governors, the proposed new courses and discontinuance of

existing courses as specified in paper

S79- 8

6

and outlined

below:

New Course Proposals, and discontinuance of courses

MATH

251-3

Calculus III

it

MATH

253-4

MATH

252-3

Vector Calculus I

it

MATH

312-4

• ? MATH

272-3

Introduction to

Probability and

it

MATH

371-3

Statistics

MATH

313-3

Vector Calculus II

(MATH

312-4)

MATH

314-3

Boundary Value Problems

"

(MATH

413-4)

MATH

322-3

Complex Variables

"

MATH

422_4*

MATH

342-3

Elementary Number Theory

"

MATH

442-4

MATH

372-3

Mathematical Statis-

MATH

4904

tics

?

I.

MATH

375-3

Mathematical Statis-

MATH

489-4

tics 11

MATH

387-3

Introduction to Stochas-

"

MATH

486-4

tic Processes

MATH

415-3

Ordinary Differential

"

MATH

413-4

Equations

MATH

418-3

Partial Differential

"

MATH

414-4

Equations

MATH

419-3

Linear Analysis

"

MATH

4204

MATH

424-3

Applications of Complex

"

MATH 422_4*

Analysis

MATH

425-3

Introduction to Metric

"

MATH

421-4

Spaces

MATH

426-3

Introduction to I.ebesque

"

MATH

423-4

Theory

40

---

-2-

MATH 438-3 Linear Algebra

MATH 439-3 introduction to Algebraic

Systems

MATH 440-3 Galois Theory

MATH 444-3 Topology ?

'I

MATH 472-3 Linear Models in Stats.

MATH 479-3 Selected Topics: Stats.

MATH 487-3 Probability

0

S

MATH 431-4

MATH 432-4

MATH 433-4

MATH 441-4

MATH 490-4

(MATH 486-4)

NOTE The Math Department has presented a number of reasons for its

proposed curriculum revisions. Among these are the following:

1. to facilitate transfer credit to and from colleges and

other universities (by offering three rather than four

semester hour courses and by arranging lower division

sequences to consist of six semester hours in each of

the 100 and 200 divisions)

•. to strengthen slightly the lower division requirements:for

Majors and Honours

3.

to strengthen and extend the "service" functions of the

Mathematics curriculum

?

is

4.

to reduce overlap where it has developed in related courses

5.

in a few instances, to extend an "overcrowded" course to two

6.

to. improve the transition from lower division to 400 division

courses

7.

on: the basis. of experience, student interest, and current

faculty strengths to increase the coherence in several

cours,e sequences.

MOTION 2

That Senate approve, and recommend approval to Board of

Governors, the proposed changes in requirements for a Major

and for Honours in Mathematics as set forth in paper S79-86.

MOTION 3

That Senate approve, and recommend approval to the.Board of

Governors, the proposed revisions to existing courses as set

forth in paper S79-86 and specified below:

---

-3-

Re-visions to Existing

Cours'

CL..

Ige in Prcrequi3

4

tes

fc':

S ?

1.

2.

3.

4.

5.

6.

Number, vector, prerequ's 4

re,

MATH

480-3

Title and prerequisite

MCH 320-3

Description, syllabus,

ve:'or,

prerequisite

MATH

467-3

Description and prereqi!site

MATH

310-3

Vector

MATH

443-4

Change in Prerequisites or:

MATH

242-3

MATH

302-3

MATH

361-3

MATH

404-3

MATH

466-4

MATH 468-4

MATH

469-4

MATH

470-4

MATH

471-4

NOTE subject to approval of the new courses by Senate and the Board

ScUS has approved a waiver of the time la

g

to permit scheduling of

the following courses in the spring and summer semesters of 1980:

SPRING 80:

?

SUMMER 80:

MATH 251-3, Calculus III

MATH 426-3, Intro, to Lebesgue Theory

MAN 439-3, Intr. to Algebraic Systems

MATH 444-3, Topology

MATH 251-3,

MATH 252-3,

4ATh

272-3,

MATH 314-3,

MATH 342-3,

MATH 440-3,

Calculus

III

Vector Calculus I

Intro, to Prob.

?

Stats.

Boundary Value Problems

Elementary Number Theory

Galois Theory

Members of SCUS were concerned that some students might possibly

be disadvantaged by the offering of three credit courses in the spring

semester,

particularly if they had been planning to take the four

semester hour predecessor course or courses. Should this he the case

it might be particularly awkward for a student very

close

to graduation.

However it was ascertained that in providinc advance information about

course offer incs for this spring semester

?

30 the department has not

listed any of the 'redecesor courses in

?

'r-.nfhook

e

and, therefore, ?

the four courses for which a waiver has

her

granted will be offered

in

addition to those already listed and not s rerlaceirent for any

course of courses a student could have been cunting on. On this

basis

SCUS had no difficulty in granting the waiver.

'C

.2-

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.---4

=--

im

---

!D!fPrnrp

SiMON FRASER UNIVERS!

;1y ?

ri

yTjj

MEMORANDUM

SCLIS

77-2*',,,,

H.M.Evans.Secretary

........

Senate Committee for Undergraduate

Studies

Sub ject..

MATHEMATICSçURRICULUM CHA.NCES

,.

'JLJL'51g79

From ?

N. Heath

.

?

.

Administrative Assistant

to the Dean of Science

Date.

?

1979 07 18

The Faculty of Science, at the meeting of 1979 07 10 approved

the following changes to the Mathematics Curriculum. These are

now submitted to SCUS for consideration and approval.

Please note that the Fall 1979 implementation for the new

courses has been revised. It is now proposed that the new courses

will be phased-in, starting in the Spring 1980 semester. A waiver of

the two semester time lag of Senate will therefore be requested

for some courses.

t

CONTENTS

1.

Memorandum from G.A.C. Graham to C. L. Kemp dated 1979 02 14

(Revised Major & Honours requirements for Mathematics students).

2.

Rationale for changes.

3. Summary of changes.

4.

Summary Tables of courses showing prerequisites and calendar

descriptions.

5.

New course proposals (syllabus attached in each case):

MATH 251-3, 252-3, 272-3,

313-3, 314-3, 322-3, 342-3, 372-3, 375-3, 387-3,

415-3, 418-3, 419-3, 424-3, 425-3, 426-3, 438-3,

439-3, 440-3, 444-3, 472-3, 479-3, 487-3.

6.

Revisions to existing MATH courses:

riA'rH

242-3

Prerequisite

302-3 Prerequisite

310-3 Prerequisite & calendar description

320-3 Prerequisite & title

361-3 Prerequisite

404-3 Prerequisite

443-3 Vector

466-4 Prerequisite

467-3 Prerequisite, vector, syllabus & calendar description

468-4 Prerequisite

._• 469-4 Prerequisite

470-4 Prerequisite

471-4 Prerequisite

480-3 Prerequisite, number & vector.

NH/rc

?

. ?

__

?

,

?

..

4

?

N. Heath

?

. ? ..

.....

A

---

j'ii AL

,

It ?

.IL

U1I

1' £.4ItI 1. 1

MEMORANDUM

To ?

Mr.

SC[JS

Registrar's

?

Harry Evans,

OfficeSecretary

??

From G.A.C.

Mathematics

Graham,

Department

Chairman

tte

SU

b

e

ct

.

MATHEMATICS

. SCLJS METING

COURSE

-

-

-

SEPTE1c%ER

PROPOSALS/TIME

-11','-11','1979......

WAflJER

1

?

September 4, 1979

Date

This is to request a time waiver for the following courses, which the

Mathematics Department would like to offer during SPRING 80.

?

D)frr

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

......

MATH 251-3, Calculus III

MATH

426-3,

Introduction to Lebesgue Theory

'-'Li -

MATH 439-3, Introduction to Algebraic Systems

1E

Our motive in offering MATH 251-3, Calculus III in Spring 80.. (followed by

MATH 252-3, Vector Calculus I in Summer 80) is to optimize the phasing in

of the majority of the new upper division courses in Fall 80.

MATH 426-3, Introduction to Lebesgue Theory, partly replaces our present

MATH 423-4, Real Variable II, which has not been offered since 76-2.

Unless a time waiver is granted the material of MATH 426-3 will likely

not be offered this coming year which is a situation we wish to avoid.

MATH 439-3, Introduction to Algebraic Systems and MATH 444-3, Topology,

partly replace the courses MAT!-! 432-4, 441-4 that we have been offering

each Spring. However in order to conserve resources (in view of the

planned offering of MATH 426-3), we wish to offer MATH 439-3, 444-3 in

Spring 80.

L

I')

9

UA

GACG/dr

?

G.A'.C.

Graham')

cc: Dr. C.L. Kemp, Chairman

Faculty of Science Undergraduate Curriculum Committee

Dr. M. Singh, Chairman of Mathematics

MATH 444-3, Topology

S

0

I,-

---

• ?

-

?

-

• ?

SiMON FRASER UNIVERSITY

MIMORANDUM

.0

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

?

From...

Faculty of Science Undergraduate ?

Undergraduate Studies Cosmit tee

Curriculum Cittee

Mathematics Department

DateFebruary .

.

4,

At its meeting held on

February

12, 1979 the Mathematics Department

approved of the changes in our course structure that are indicated

on the

attached stmary

sheets. Detailed syllabuses and course proposal forms are

also enclosed.

Our intention is to begin offering the new courses in

Fall 1979, if

possible. To

this end it would be appropriate that the

courses are promptly

brought before

the Faculty of Science Undergraduate Curriculum Committee for

its approval.

In addition, the Mathematics Department wishes to

recamend

that,

upon approval

of the new courses, the first paragraph of item

#(i) of the

quirements

for Students Majoring or taking Honors in Mathematics

(see

page 409 of

the 78-79 calendar) be changed to

"(i) to obtain credit for Mathematics 151-3, 152-3, 232-3,

251-3, 252-3, and at least 6 additional hours in

lower

division Mathematics (Math 100-3, 190-3 and 11-3 may

not be included) or Computing Science 103-3, 105-3.

This

requirement

would normally be met by the end of the fourth

level."

This recommendation

represents a slight strengthening of our current

require-

ments and seems appropriate.

Would

you please take these proposals before the Faculty

of Science

Undergraduate Curriculum

Committee for its examination and, I hope, approval.

4

G.A.'.

Graham

GACG/dr

Enclosures: Course proposal

forms and relevant documentation

Dr. M.

Singh, Chairman

Mathematics Department

---

?

___ 0

?

2./i.

RAT', )NAIJ. ?

MATHEMATICS C)URSF PROP(.)S1'LS

• During the past year the MathemaLi

?

Department has been involved in an

?

extensive review and overhaul of cert.in elements of our course structure and

resulting revisions have now been

agreed

upon b y

the r)partment.

In general these revisions are characterised by a broadening of our

offerings at the 200 and 300 levels with a conccmitant adjustment of offerings

at the 400-level. This reflects a greater commitment, to service aspects of

our offerings; however, it was also felt that our present course structure has

not given sufficient support to mathemtics or other students in bridging the

gap between 100-level courses and the more difficult 400-level courses. The

100-level courses have not been chanqed. Many of the proposed changes bring

us more closely into line with common practice of other universities today.

In particular we have been mindful of disadvantages, relating, for example,

to over-exposure and transfer credit, involved in 4-credit courses that we

have dropped, compared to the 3-credit courses that we are adopting. We have

taken the opportunity to stretch out courses that had become materially over-

crowded, and to contract where course-overlap had crept in over the years.

A key proposal is that Math 253-4, 312-4 are to be replaced by the Second

?

?

S ?

Year Calculus sequence Math 251-3, 252-3 together with the course Math 313-3,

?

Vector Calculus II. As a result of thi, our first and second year

calculus sequence will now be similar to the corresponding sequences at most

other universities and community colleges and this should be of particular

value in streamlining transfer arrangements to and from SFtJ. The latter stream-

lining contributes, in particular, to the proposed Engineering transfer program.

The subsequent 3-credit courses in Differential Equations and Linear and

Complex Analysis are also thought to constitute a more amenable package than

the 4-credit courses they replace. In particular it is hoped that the courses

Math 314-3, Boundary Value Problems and Math 322-3, Complex Variables will

provide the students with helpful stepping stones to subsequent 400-level

courses. Further development of our Mechanics offerings awaits the approval

of the Engineering Mechanics courses Math 262-4, 263-4, which are currently

being processed at the Faculty level.

With the restructuring of the Algebra courses it is hoped that a broader

prpgram can be made available than heretofore, in the sense that it may be

found possible to offer the terminal course Math 440-3, Galois Theory, from

time to time, whereas the course it replaces has not been offered since Fall

1975. By restricting its purpose to a training in pure rational deduction

the new Number Theory course Math 342-3, which has minimal prerequisites, is

expected to be of more benefit to the general mathematics student than the

course it replaces. In Combinatorial Theory the change is minimal.

Ia ?

continued...

---

R

ationale continued ?

2.72.

One of the main reasons this course review was embarked upon was a ertaiji

lack of lustre in our Analysis sequence: with the

replacement

of Math 421-4,

423-4 by the new courses Math 425-3, 426-3 which supplement Math 242-3 and

320-3 the material has been streamlined and overlap minimized, it is hoped

that the latter four courses together with Math 444-3, Topology, will now be

an attractive package for students pursuing analysis. Students with more

applied mathematical interests or students outside mathematics may find it

useful to proceed only as far as Math 320-3, Advanced Calculus of One Variable.

In Probab.lity and Statistics the proposed courses are felt to constitute

an attractive package (though minimal compared to some universities) for

students who wish to obtain a degree that is specialized in this area of

m

athematics. The major part of Math 71-3 has been brought to the second

year level and called Math 277-3, Introduction to Probability and Statistics,

consistent with practice at most universities. The new courses Math 272-3,

372-3, 472-3 then form a natural sequence which is expected to be more

reasonably paced than the sequence 371-3, 490-4 that it replaces. The

course Math 375-3 (which partly replaces 489-4) complements Math 372-3 by

giving the Bayesian Theory of Inference and Bayesian Decision Theory, and

also raises basic issues in theories of statistical inference. The course

Math 473-3, Nonparametric Statistics, is essentially a renumbering of our

present Math 480-3. The course Math 479-3, Statistics: Selected Topics,

is being introduced so that Special Topics courses in Statistics may be

offered under the Statistics title.

Finally,

we are recommending that Math 486-4 be replaced by

an

essentially

applied probability course Math 387-3-followed by Math 487-3 which will be

devoted

more

to axicinatic and classical

p

robability theory; the latter to be

given less often than the forme-r.

Af

---

SIMON FRASER UNIVERSITY

?

MEMORANDUM

He ath

?

......

.

From

....

.

Dr...A.C,.

.3rham,.

cbairmai

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

?

Undergraduate Studies

Committee

Dean

...

f

.

Siençç

.

Office................... ?

.....

Ma

t h

e

natic

.paXtt....................

S

ub1ed

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

ICS

?

. ?

. ?

Date

................1919

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

As a result of discussions with the Chemistry and Physics

Departments the Mathematics Department has slightly altered the

prerequisite for Math 252-3, Vector Calculus I, so that students

may now take this course without having taken or concurrently

taking Math 232-3, Elementary Linear Algebra. This will have the

effect of allowing students (and in particular Chemistry students)

to include both Physics 221-3, Intermediate Electricity and Magnetism

and Math. 252-3 in their program without having also to include

Math 232-3. This seems desirable.

/--1

0

'

Dr. G.A.C. Graham, Chairman

Undergraduate Studies Committee

cc - Dr. E.J. Wells, Chairman, Chemistry

Dr. A.S. Arrott, Chairman, Physics

Dr. M. Singh, Chairman, Mathematics

CL: Revised Documentation

F

641yu

'I

I

!

-

10

?

jUR 0 18

1979

c

---

311

S

SLMMA}V OF PROPOSjD CHANGES

L alculusof Several

V

ar

j

ables

253-4 and 312-4

are

dropped and replaced by:

251-3, Ca1ulus III

?

(3-1-0)

252-3, Vector Calculus i

313-3, Vector Calculus ii

?

(3-i-U)

Differential Equations

310-3 and 467-3 are retained but with somewhat

c

-hanged syllabuses

(vectors 3-1-0 and 3-0-0

413-4 and

414-4 are

dropped and

r ep

l aced by:

314-3, Boundary

Value

Prohlpm

415-3, Ordinary Differential Equation-(j-O-0)

418-3, Partial Differ

p

nti.l Equations (3--0-0)

Linear Analysis

?

-

420-4 is dropped and

rephicprj Dy

419-3, Linear Arial'sjs

Complex Analysis

422-4-is dropped and replaced by:

322-3, Complex Variables

424-3, Applie:at luns of Comj'Iox

Analysis

( -0-0)

(3-1-n)

2/79

I

---

(3-0-0)

7

SUMMARY oFp:(Opo5-fDcANGES (cont.)

?

3/2.

A1ebra

431-4, 432-4, 433-4 are dropped

1c!

rela d by.

438-3, Linear Algebra

?

(3-1-0)

439-3, Introduction to

A1qeh,tir

Sy-.-.t.-Ms

?

(3-0-0)

4403 ' Galojs

q,

hFO ?

(3-0-0)

Number Theory

442-4 is dropped and

replacd

by:

342-3, Elementary Number Theory

?

(3-0-0)

Combinatorial Theory

The tutorial is dropped from Math 443-4 so that its vector will become (4-0-0)

Analysis

421-4, 423-4, are dropped and repLaced by:

425-3, Introduction to Metric Spaces

?

(3-0-0)

426-3, Introduction to Lebcqiie Theory

?

(3-0--0)

In addition it is proposed to slightly adapt the prerequisite and change the

title of Math 320-3,"Theory of Converq*n:e"to "Advanced Calculus of One Variable"

and a slight

modification has been proposed for the prerequisite to Math

242-3,

"Introduction to Analysis."

Topology

441-4 is dropped and replaced by:

444-3, Topology

2/79

.

---

3/3

IJMMARY OF PROPOSED

_CHANGES (t.)

0—

Probability and Statistics

371-3, ?

480-3,

486-4, ?

489-4,

490-4 are dropped and replaced by:

272-3,

Introduction

to Probability and Statistics

(3-1-0)

372-3,

Mathematical

Statistics 1

(3-1-0)

375-3,

Mathematical

Statistics II

(3-1-0)

387-3,

Introduction

to Stochastic Processes

(3-1-0)

472-3,

Linear Models

in Statistics

(3-1-0)

473-3,

Nonparametri c

Statistics

(3-0-0)

487-3,

Probability

(3-0-0)

479-3,

Statistics:

Selected Topics

(3-0-0)

In addition, certain

minor changes become necessary in the prerequisites for

Math

302-3 and 404-3.

PROPOSED PREREQUISITE

CL.S

I

.

MATH 361-3: Math 252-3 (or Math 253-4) and Math 262-4

(or

Math 161-3 or?

Phys 120-3 with permission of the Department).

M

ATH 466-4: Math 252-3 (or Math 253-4) and

Math

232-3 or permission

of

the Department. Math 313-3 is recommended.

MATH 468-4: Math 3143

or Physics 384-3 and 361-3.

Math 313-3 (or Math 312-4) should precede or

be

taken concurrently.

MATH 469-4: Math 361-3. Math

314-3

or Phys 384-3 should precede

or be

taken

concurrently.

MATH 470-4: Math 310-3 and either

Math 262-4 (or Math 161-3)

or

Phys 211-3.

Math

313-3 (or Math

312-4)

or Phys 384-3 should

precede or be

taken concurrently.

MATH 471-4: Math 313-3 (or Math 312-4) or Phys 384-3.

4?

---

APPLIED MATHEMATICS COULSE PROPOSALS

TITLE

PREREQUISITE

CALENDAR DESCRIPTION

25-3

?

(.j1c.1us ?

III

152-3 or 155-3;

1

,oar co(.)rdlnate, ?

vectors, ?

solid analytic geometry,

(3-1-0)

or 158-1 with a

grade of A or H.

I

iffrenti.al ?

calculus of several variables,

u1i,1e ?

intccjraL;,

?

line integrals. Complex numbers.

252-3 Vector Calculus I

251-3 (or

?

253-4);

?

lit t

.

rOrlt.idP, ?

Jacohians, ?

transformation of

(3-1-0)

232-3 is

lilt ?

It'

?

III

I

?

qrdl.s, ?

differentiation and integration

p.jrq.flc(y4

t,j

?

or ?

I uct ions,

?

iiteqral ?

theorems and their

II)I'I iit ioil

310-3 Introduction

to

152-3

or ?

155-3;

Lit

-order

diftereritial

equations, 2nd & higher orde

O.D.E.

or 158-3 with a

I in :ir

c'qitI

ions,

?

series solutions, ?

introduction

(3-1-0)

grade of

A

or

H.

t

rans form, systems and numerical methods,

v1i.cit:ions

?

in ?

the physical, biological and

232-3,

?

252-3

ia1.

?

sciences

I.xtrema of functions of several variables, Lagrange

313-3 Vector Calculus II

(or ?

153_4)

nultipliers, curvilinear coordinats and vector

(3-1-0)

iff.rentia1 calculus, space curves, Frenet formulae

2523

?

(

?

_4)

urfaces, curvatur", Christoffel symbols.

oto ?

or

?

r ?

and integrals. Separation of

314-3 Boundary Value

Problems

and ?

110 -

'.'ariihIer

?

tor ?

lit. ?

conduction equation, ?

the wave

(3-1-0)

i°'° ?

ii 1arLlace

t

s equation. Sturm-Liouville

rohh'ms. ?

Separation in polar coordinates.

251- ?

(o! ?

253-4).

Laplace transforms.______________________________

unctions of a

complex variable, differentiability,

Complex

Variables

,

_

,

&3

(3-1-0)

oitour

i1it'qra1s, ?

Cauchy's theorem,

?

Taylor and

310-3.

?

Mdh

.airent:

expinsior,

method of residues

i:xistence and uniqueness theorems, Green's functions

415-3 Ordinary Differ-

ential Equations

314-3

?

.'- ?

322-3

ñï ?

ccmd-order equations, plane autonomous systems,

(3-0-0)

are reoomm:nded

Lability, expansions about ordinary and singular

)ifltS

314-3 or Phys.

?

I"irst-order equations, the wave equation, charac-

384-3

418-3 Partial Differ-

ential Equations

Riemann's method , Laplace's equation,

(1-0-0)

1.4f dept.

?

313-3

i ?

;reen's and Neumann's functions, Poisson formula

is

232-3,

_xe.QiDflleflde

:.5J-3 (or

?

419-3 Linear Analysis

?

253-4) ajid 310-3.

?

(30-0)

?

1314-3 and 320-3

are recommended.

?

424-3 Applications of

?

322-3

Complex Analysis

(3-0-0)

467-3 Vihra.ions ?

232-3 and 110-3.

?

(3-0-0) ?

263-4.(or Phvs

1211-3) & 314-3

are recommended.

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

I

Convergence in Euclidean spaces, Fourier series

and their convergence, Legendre polynomials,

termite and Laguerre polynomials.

Conformal mappinq, application to boundary value

problems, Schwarz-Christoffel transformation,

integral formulas, analytic continuation, argument

principle

Vibrat j

ort; of (Ii

screte

systems with many c3egres

of freedom; matrix methods. Nonlinear vibrations;

the phase plane; singular points and limit cycles.

Perturbation methods; singular perturbation

expansions.

2/79

---

k/Z

ALGEBRA AND ANALYSIS COURSE PROPOSALS

TITLE ?

PREREQUISITE(S)

?

CALENDAR DESCRIPTION

438-3Linear Algebra

(3-1-0)

232-3

matrix

Linear

theory.

Algebra. Vector space

and

439-3 Introduction to

Algebraic Systems

232-3

Algebraic

systems including, for example,

(3-0-0)

groups, rings.

?

Polynomial theory.

440-3 ?

Galois

Theory

434-3 ?

(or 431-4)

?

.tnd

An

i

ntroduction to the theory of

(3-0-0)

-------------

---------------------

435-3

?

(or 432-4)

fields, with emphasis on Galois Theory.

Divisibility,

342-3 Elentary Ntmther

Any 200 level mathe-

Theory

matics course,

primes, congruences,

arithmetic functions

and

related topics.

(3-0-0)

443-4 Combinatorial

(4-0-0)

Theory

Same

Unchanged.

Vector change only.

445-3 Introduction to

320-3.

Metric Spaces

Metric

spaces,

convergence

?

nmetric

(3-0-0)

spaces, continuity, compactness,

connectedness and completeness,

contraction

m

apping principle, and

other useful theorems.

An introduction

to the Lebesgue integral.

426-3 Introduction to

Lebesgue Theory

320-3

(3-0-0)

-

and some of

itsapplicatjons,

TOpoiogy ?

425-3 (or 421-4) or

(3-0-0) ?

permission of the

department,

320-3 Advanced Calculus of 242-3 (or 241-2) and

One Variable (3-1-0) 251-3 (or 253-4)

Title & prerequisite

change only.

242-3 Introduction to

?

152-3 or 155-3.

Analysis

(3-1-0) ? -

Prerequisite change

only.

Development of elementary theory of

topological spaces.

Unchanged,

Unchanged,

2/79

?

S

/0

---

PROBABILITY AND STATISTICS COURSE

-PROPOSALS

TITLE ?

PREREQUISITE (S)

?

CALENDAR DESCRIPTION

272-3 I.ntro. to Prob.

152-3 or 155-3 or

Ba.ic

?

l aws

of

probability, sample distributions.

and Stats

158-3

Tnroduct-ion to statistical applications.

(3-1-0)

372-3 Mathematical

251-3 ?

(or 253-4)

Techniques of estimation

?

and testing

Statistics I

and

272-3 (or 371-3)

hypotheses, one-sample and two-sample tests.

(3-1-0)

Tntrodut:ion to analysis of variance,

re g

ression and correlation.

Samplinq theory and Bayesian approaches to

375-3

Mathematical

251-3 ?

(or

253-4)

Statistics II

and 272-3 (or 371_3)

inference. ?

Types of probability distributions.

(3-1-0)

Bayesian decision theory.

?

Method of maximum

likelihood. ?

Tllüstrations of the different

methods.

387-3 Introduction

to

272-3 ?

(or ?

371-3) ?

or

Markov chains. Random walks. Continuous time

Stochastic Processes

permission of the

processes. ?

The Poisson process. Markov processes

(3-1-0)

department

Gaussian processes.

472-3 Linear Models

in

232-3 and 372-3

Linear models, analysis of variance and

Statistics

(or 371-3)

covariance, multiple regression, introduction

(3-1-0)

to the design of experiments.

Nonparametric

372-3 (or 371-3)

?

or

Same as for Math 480-3.

?

This is a number

Statistics

permission of the

change and vector change only.

(3-0-0)

department

487-3 Probability

387-3 (or 486-3)

Probability spaces, prob. distributions, laws of

(3-0-0)

large numbers, characteristic functions,

central limit theorems, infinitely divisible

distributions. ?

Conditional distributions

and expectations.

479-3 Statistics:

Will be specified

Variable topics.

Selected Topics

according to topics

(3-0-0)

offered under this

number.

302-3 Statistical Methods

101-3 or 272-3

Unchanged

(3-0-1)

(or 371-3),

or Arc

?

376-5

or Econ 332-3

404-3

Statistical Design

272-3 (or 371-3) ,

Unchanged

& Analysis of

or

302-3

Experiments (4-1-0)

'

0179

*

1/

---

SENATE COMMITTEE ON UNDERGRADUATE STUDIES

CQURi l PHOPO.SAL FORM

CIflrInformation

?

Department:MATHEMATICS

- Abbreviation

Code:

MATH Course Number: 251

?

Credit Hours:3

?

Vector:3-1-0

Title of Course:

?

CALCULUS III

Calendar Description of Course:

Polar coordinates, vectors, solid analytic geometry, differential calculus of

several variables, multiple integrals, line integrals. Complex numbers.

Nature of Course - Lecture/tutorial

Prerequisites (or special instructions): MATH 152-3 or 155-3; or MATH 158-3 with a

What

approved:

grade

Students

course

of

?

A

who

or

(courses),

MATH

have

B.

?

253-4

obtained

if

any,

credit

is being

for MATH

dropped

253-4

from

cannot

the calendar

receiv eA

1

if

credit

this

/

for

coUrse

MATH

is

251-3.

2.

ScIl

.

eduli

ng

How

frequently will the course

be

offered? Every semester

Semester in which thu course will first

he

nffered?

Which of your present faculty would be available to make the proposed offering

possible: ?

All faculty

Objectives of the Course

Third course in mainstream calculus sequence. Would be taken by

all majors in mathematics, physics and chemistry.

4.

Budgetary and Space Requirements (for information only)

What additional resources

will he

required in the following areas:

Faculty

Staff

Library

Audio Visualf

?

NONE

Space

Equipment

5. Appro

al

Date:

?

'91')

CtJS 71-34h:- (When completinq this

form,

for Lnstructjons see Memorandum scus 73-34a.

At t,icli

('()UrSC

outline)

9

SEPii

Department Chairman

?

-

?

Dea

?

Chairman

CL1Q

---

MATHEMATICS 251-3

r

?

CALCULUS III

Chapter 12 - Polar Cc

Section 12.1

?

Section 12.2

?

12.3 ?

12.4

?

12.5

ordinates ?

(2 weeks)

Polar Coordinates

Graphs of Polar Equations

Relations between Polar and Rectangular Coordinates

Area in Polar Coordinates

Arc Length in Polar Coordinates

Complex Numbers

?

(1 week)

The complex plane, algebra of complex numbers, quadratic

equations, the Euler formulae.

lu

Chapter 15 - Differential Calculus of Functions of Several Variables

Chapter 14 - Vectors

Section 14.1

14.2

14.3

14.4

14.5

14.6

14.7

14.8

and 3-Space

The 3-Dimensional Coordinate System

Distance

Sketching Graphs

Vectors

Dot and Cross Products

Equations of Lines and Planes

Functions from R

n

to Rm

Limits and Continuity

(3-4 weeks)

(3. weeks)

Section 15.1 Partial Derivatives

15.2 Chain Rules

15.3 The Gradient

15.4 Directional Derivati ies

15.5 Local Extrema of Functions of Two Variables

15.6 Absolute Maxima and Minima

Chapter 16 - Multi

p

le InteQratjon

?

(2 weeks)

Section 16.1 Double Integration

16.2 Iterated Integrals; The Fundamental Theorem

for Double Integrals

16.5 Transformation of Multiple Integrals

16.6 Double Integrals in Polar Coordinates

Chapter 17 - Vector Calculus

Section 17.1 Work and Line Integrals

17.2 Computation of Line Integrals

Though not part of the syllabus, you may also wish to study the material in

Chapter 13 - Differential Equations. (This

'

material is covered more thoroughly

in Math 310-3.)

PREREQUISITES: MATH 152-3 or 155-3; or MATH 158-3 with a grade of A or B.

+..4

. .hi

4IS ?

ob4 (,

?

. *

44

J4

441W4 ?

ct4.

S

TEXTBOOK: CALCULUS WITH ANALYTIC GEOMETRY, Second Edition

?

fAT ?

by Howard E. Campbell and Paul F. Dierker

( ?

Published by Prindle, Weber and Schmidt, Inc. (Wadsworth)

I?

---

S$ ?

c l

*

ON UI

DECMD(JJ SUDI$

CCJRIf PiPosj FORM

Cnd,z

ntOtOn ?

Department kh?MMTXCB

in

Abbreviation Code:MATH Course Number: 252

?

Credit Hour.*j

?

vectors 3-1-0

Title of Course:

?

VC'1OR CALCUUJS I

Calendar Description of Court':

and

Differentials,

integration

Jacobier.8,

of vector

f

unctions,

trnormajon

i

nteqrai

of

multiple

theorems

integrals

and th

j

differ"tiation

r

appliøatj.

Nature of Course Lecture/tutorial

Prerequisites

MATH

312-4

232-3

cannot

precede

(or

receive

special

or

credit

be taken-'instructions):

for

Co

?

MATh

ncurrently.

students

252-3.

MATH

who

251-3

have

(or

obtained

253-4).

credit

It

is

for

rec.nd.d

NUH

?

that

What

app

roved:

course

MATH

(courses),

253-4 and

if any,

312-4

is

are

being

being

dropped

replaced

from the

by MATH

calendar if this course is

251-3 252-3 and 313-3.

.

Schedulinq

flow frequently

will the

course

he

Offered?

Every

semester

Possible:

Which

Somcst(r

of your

in

All

which

pre

faculty

g

the

ent

course

faculty

will

would

first

be

available

he

offered?

to make

Fatt-9q.9

the

proposed

?

offering

'4'

Objectives of the Course

Fourth

cduree in mainstream calculus sequence. Would be taken

by all

majors in mathematics and physics.

4. Budgetary and Space Requirements (for information only)

What

Faculty

additional resources will be required in the following

•r.s,

Staff

Library ?

JNONE

Audio Visual

Space

Bquipment

S. Awroval

- ?

(

(

?

Department Cha raan

?

Dean

-f

?

Chatasn, $CUS

?

Attach

SCUS

7 3-34b:--

course outline).

(When

co

mpleting this form, for

ins

tructions see Nsmor.sd

?

73-34a. ?

- ?

/fr'

---

V--

V

?

V ?

V

-S

Mathematics 252-3

r

Vector Calculus I

1.

Multiple integration

?

0 weeks)

Review of double integrals, iterated integrals. SuraCe ar-es.

Triple integrals. Transformation

of

multiple integrals. Integrals

in cylindrical and spherical coordinates.

2.

Vector integral calculus - introduction

?

- ?

(3

wee

k

s)

Review of line integrals. Green's theorem • Path independence.

Line and surface integrals in three d-mensiona. The divergence

theorem. Stokes' theorem.

3.

Differential calculus of several variables

?

(2k, weeks)

Differentials and theorems on differentials (Note: differentials

are not discussed in Math 251-3). Implicit functions. Jacobiane.

Partial derivatives and chain rule using Jtoobians. Theorems

On

Jacthians. ?

V ?

-V

4.

Vector differential calculus

?

V

?

(2 mesk.)

Vector differentiation. Space curves. Applications in mechanics.

Gradient, divergence and curl. Identities involving differential

( ?

operators..

S. Further integral calculus

?

Mj weeks)

Green's theorem for multiply-connected regions. Divergence and

Stokes' theorem in terms of grad, div and curl. Path independence

and exact differentials in three dimensions.

PREREQUISITE: MATH 251-3 (or 253-4). It is recownd•d that *I

precede or be taken concurrently.

Studnts who

have

obtained credit for MATH 312-4 cannot

receive

credit

for

MATH

252-3.

TEXTBOOK: Calculus with Analytic Geometry, 2nd Editiar b

y

Can5s!? &

Dierker. (Chapters 16 and 17 should he used R

.

07

ctir I

and 2 of the course.) For secin - 5,

tr' e

chosen by the instructer.

References for syllabus outline:

Sections 1-2: Advanced Calculus,

?

serbs,

?

tc ?

c.

Section.. 3-5: Vector Analysis, Scham sarLee tht

?

36.

---

SENATE COiiJTTT ?

ON i)

GRADA';'E STUD.1S

?

COURSE PG?CsAL FO

C.

'ri1,jr inforrn.tion

Department:

?

MATHEMATICS

?

40

-

?

ALti i i t I )rI (r,dt.: MATH Cour :e Nijmlx r:

?

272

?

Credit

Hour;: ?

j ?

Vector: 31-0

I- j

t

IC

(f

?

je: ?

TNTP)DUCijO To I'1)BAjLl

?

AND SThTISTTCS

Cu

IcrvLr I

?

crptin

?

f (or-,:

Basic laws of probability, sample distrik)utions

?

T-

fl

applications.

?

- ?

cc Statistical

Nature of Course

Pr

erequisites (or special instructions):

?

MATH 152-3

on.

155-3 on. 158-3

S-tw1ent who have obtained c&edJ.t son. MATH

371-3

cannot n.ecevQ ctedi.t son.

272-3.

approved:

What course (courses), if any, is being dropped from the calendar if this course is

MATH

371-3

2.

Fk,w

frequently

will the Course he offered?

T wice

pe-4

1ewL

Semester in which the celirs(' will first be offered?

possible:

?

V1r.4.

Eave4, Stephens,

V4Uga4,

&JeLdon

Which of your present faculty would be available to make the proposed offering

Objectives

to

To provide

mathematically

of the

a basic

Courseoriented

introduction

?

students.

to

pr

obability,

This is the

applied

foundation

Probability

course

and

for

statistics

.

students

wishing to pursue a sequence in Probability and mathematical statistics.

4.

Budgetary and Space Reguireents (for information only)

What additional resources will be required in the following areas:

Faculty

Staff

Library

?

NONE

Audio Visual

Space ?

-

Equipment

5. proval

Date: ?

fi&.

/)i/91

Department Chaian

_______

SEP 79

Ian ?

Chairman,

Sctjs

Attach

SCUS

73-34h:-

course outline).(When

completing this form, for

in

structions see Memorandum SCTJS

73-34a.

/6

---

MATHEMATIC:

;

27.-

Introduction to r'rc.brihility & Statistics

(

1.

Elements of probability (A Venn Diagram Approach)

Sets and operations on sets, Permutations, Combinations, Postulates of

Probability, Frequency Definition of Probability. Additive and

Multiplicative theorems, Conditional Probability, Independent and

Mutually Exclusive Events. Bayes Theorem.

2.

Probability Distributions

Random Variables, Distribution FunctionS, Binomial, HypergeOlfletriC,

Poisson, Multivariate-Discrete distributions with a discussion of

- - conditional and marginal distributions.

3.

Mathematical Expectation - Discrete Random Variables

Expectation, Moments, Chehycheff's Theorem, Law of Large Number, Moments

of Distributions in Part 2, Moment Generating Function and its properties.

Moment Generating Functions of Binomial and Poisson.

• 4. Probability Densities

Properties of Probability Densities and their Distribution Functions.

( ?

The Uniform, Exponential, Gamma and Normal Densities. Change of Variable.

5. Mathematical Expectation. Continuous Random Variables

Expectation, Moments, Moments of Distributions in Part 4. Moment

Generating Functions of Distributions in Part 4.

6 Sums of Random Variables

Sums of discrete random variables and their moment generating functions.

Sums of continuous random variables and their moment generating functions.

The distribution of the mean. Statement of Central Limit Theorem, Normal

approximation of Binomial.

7. Sampling from Normal Populations

The distribution of x, and the t-distribution.

PREREQUISITES: Either MATH 152-3 or 155-3 or j8-3. Students who have obtained

credit for Math 371-3 cannot receive credit for Math 272-3.

. TEXTBOOK. Mathematical Statistics by Freund

or

As noted on Mathematics Textbook List.

1/78

?

/7

---

SENATE COMMITTEE ON UNDERGRADUATE STUDIES

COURSE PROPOSAL FORM

Calendar Information

Department: MATHEMATICS

Abbreviation

Code:

MATH Course Number: 313

?

Credit Hours:3

?

Vector:3-1-0

Title iF

i

ourse: ?

VECTOR CALCULUS II

Calendar Description of Course;

Extrema of functions of several variables, Lagrange

m

ultipliers, curvilinear

coordinates and vector differential calculus, space curves, Frenet formulae;

surfaces, curvature, Christoffel symbols.

Nature of Course Lecture/tutorial

Prerequisites (or special instructions) :

?

MATH 232-3 and 252-3 (or 25-4)

Students who have obtained credit for MATH 312-4 cannot récieve

credit for Math 313-3.

What course (courses), if any, is being dropped from the calendar if this course is

approved: ?

MATH 312-4

2 .

Srhedujjny

How frequently will the nurse he offered? Twice per year

Semester in which the cnrse will first 'c offered?

?

Fall

Which of

y

our present faculty would be arai1able to make the proposed offering

possible- ?

All faculty

Objectives of the Course

The course covers a range of techniques of wide use in applications of mathematics,

mainly concentrating on functions of several variables and vector calculus. it is

a continuation of second year calculus courses.

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

(.17é!j7cS

Ii ?

SEP117

DaI /

?

Chairman,

scus

SCUS 73-34h:- (When completing this form, for instructions see Memorandum SCtJS 73-34a.

Attach course outline) .

5. Approval

Date:

?

J.

j7C)

Department Chairman

S

/4;,

---

- - 0

?

MATHEMATICS 113-3

VECTOR

CALCULUS I I

IE

1.

Review ?

(1 week)

Quick

review

of vector calculus.

2.

Applications

of Partial Derivatives, Extrema

? (2

weeks)

Applications

of partial derivatives to geometry. Envelopes.

Extreina of functions of several variables. Extrema under

constraints. Applications.

3.

Curvilinear

Coordinates in Two and

.

Three Dimensions ?

(3 weeks)

Curvilinear

coordinates. Coordinate curves and surfaces.

Orthogonal systems. Gradient curl, divergence, Laplacian etc.

in orthogonal curvilinear systems.

4. Space curves

?

(2-3 weeks)

Parametric representation.

Arc length. Tangent vector.

Nomal and binormal. Curvature and torsion. Frenet formulae.

5.

Surfaces ?

(4-5 weeks)

ParatriC representation. Tangent plane, normal. First

fundamental form. Second fundamental form and normal curvature.

Principal

curvatures and directions. Gauss-Weingarten

formulae.

Christoffel symbols.

PREREQUISITES:

MATH 232-3

and 252-3 (or

253-4)

?

54At

4L.

mm

3I.-+

f-C..WIl. ?

r

.i..&jt

4e.

TEXTBOOK: ?

To

be chosen by

the Instructor

to cover the

above syllabus.

References for syllabus outline:

1.

Advanced

Calculus, Schaum Series, Chapter 8

2.

Vector Analysis,

Schaum Series, Chapter 7

3.

Differential

Geometry, Schauin Series, Chapters 3-5, 8-10.

03/79

­­

0

U

ii

---

SENATE COMMITTEE ON NDiGRADÜPTE STUi3iES

?

COURSE PROPOSAL FORM

I eriidr Information

?

Department: MATHEMATICS

?

S

Abbreviation Code: MATH Course Number: 314

?

Credit Hours: 3

?

Vector: 3-1-0

Title of Course:

?

BOUNDARY VALUE PROBLEMS

Calendar Description of Course: Fourier series and inteqrais. Separation of variables

for the conduction equation, the wave equations and L-place's equation. Sturm-

Liouville problems. Separation in polar coordinates. Laplace transforms.

Nature of Course: Lecture/tutorial

Prerequisites (or special instructions): MATH 252-3 (or

253-4)

and 310-3

m

f

I7

I

/'7//

- 4L

- ?

at7Zh

4._

?

e

/'lt.

iZe ?

r.ct

ftp.

tjrj'f'

/

"'

-

1 ?

tA

/i3i'-j

What course (courses), if any, is being dropped from the calndar if this course is

approved:

MATH 413-4 and 414-4 are being replaced by MATH 314-3, 415-3 and 418-3.

2.

Scheduling

How frequently will the course be ofi'rcd? Twice per year

Semester in which the course will first be offered?

Which of your present faculty would be available to make the proposed offering

possible: All applied mathematics faculty.

Objectives of the Course

Introductory course in partial differential equations covering separation

of variables and transform methods.

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:

1/7) ?

$p

117i

Department Chairman

?

Chairman, SCUS

SCUS 73-34h:- (When completing this form, for instructions see Memorandum SCUS 73-34a.

Attach course outline)

2

---

MATHEMATICS

414-3

eBOUNDARY VALUE PROBLEMS

1.

Fourier Series and Integrals ?

(2 weeks)

Periodic functions and Fourier series. Even and odd

functions-Statement

of

convergence

properties. Fourier integral.

Applications.

2.

Separation of Variables ?

(5 weeks)

The heat equation

in one dimension with various boundary

conditions.

Sturm-Liouvi]].e

problems and eigenfunction expansions.

Semi-infinite

and infinite regions.

The wave equation in one

dimension, bounded and

unbounded regions.

The potential equation in rectangle,

slot and disk.

3.

Higher Dimensions

?

(4 weeks)

Two dimensional heat

equation in rectangular and polar

coordinates;

Bessel functions.

Other applications

of

Besse] functions.

Separation

in spherical coordinates.

4. Laplace Transform ?

(2 weeks)

Review of

Laplace

transform and its eLementary

properties. Partial

fractions and

convolutions. Application to partial

differential

equations

(If time permits, other integral transforms

should be

discussed.)

PREREQUISITES: MATH

252-3

(or

253-4)

and 310-3

TEXTBOOK: ?

BOUNDARY VALUE PROBLEMS

by D. L. Powers

OR As

noted in the Mathematics Department

t.ztbook list.

11/78

,--

10

-

I

---

SEp ii

SENATE COMMITTEE ON

UNDERGRADUATE

STUDIES

COURSE PROPOSAL FORM

Department:MATHEMATICS

Course Number:322

?

Credit Hours:3

?

Vector:

Calendar Information

Abbreviation Code: MATH

__.

Title of Course:

?

COMPLEX VARIABLES

Calendar

residues.

Contour

Description

integrals, Cauchy's

of Course:

theorem,

Functions

Taylor

of a

and

complex

Laurent

variable,

e

xpansions,

differentiability,

method of

Nature of Course Lecture/tutorial

Prerequisites (or special instructions): MATH 251-3 (or 253-4)

Students who have obtained credit for MATH 422-4 cannot receive

credit for MATH 322-3.

What

approved:course

?

(courses)

MATH 422-4

, if any, is being dropped from the calendar if this course is

S

c

hcdu liny

How frequently will the course be offered?

?

Once per year

Semester in which the course will first be offered? Fall

?

a

Which of your present faculty would be available to make the proposed offering

possible:

All faculty

Objectives of the Course

Introductory course on functions of a complex variable.

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: cJ%

f,

'V27

Department Chairman

IJean, ?

Chairman, SCUS

CIJS 71-341,:- (When completiriq this iorrn, for instructions see Memorandum SCUS 73-34a.

At t

id

I

oIIrse outline) .

2.

---

SENATE

COMMITTEE ON

UNDERGRADUATE STUDIES

COURSE PROPOSAL FORM

- Alendar Information

?

Department:

?

Mathematics

Abbreviation Code: MATH Course Number: 342

?

Credit Hours:3 ?

Vector:3-0-0

Title of Course:

?

ELEMENTARY NUMBER THEORY

Calendar Description of Course:

Divisibility, primes, congruences, arithmetic functions and related topics.

(Same as present Math 442-4)

Nature of Course Lecture

Prerequisites (or special instructions):

Any 200 level mathematics course. Students who have obtained credit for Math

442-4 cannot receive credit for Math 342-3.

What course (courses), if any, is being dropped from the calendar if this course is

approved:

MATH 442-4

2. Scheduling

How frequently will the course be offered? Once per year

Semester in which the course will first be offered? Summer 1980

Which of your present faculty would be available to make the proposed offering

possible:

?

Drs. Freedman, Sember and others

•

ectives of the Course The subject of elementary number theory has considerable value

as a medium through which students can get training and experience in pure rational

deduction. Changing this course to 3 lectures and no tutorial and allowing the minimal

prerequisites proposed above should benefit the students in the following ways: They

may take the course'ear].y in their upper levels mathematics work so that it may serve

as a transition course from the more elementary lower level work to the more sophisticated

upper level work; also the pressure of a 4 hour lecture plus tutorial course has been

4. Budgetary and Space Requirements (for information only) reduced so that the student may

find it a less strenuous transition.

What additional resources will be required in the following areas:

Faculty

Staff

Library

NONE

Audio Visual

Space

?

3

Equoer.t

5. Approval

Date: ?

•)I

Department Chairman

/ •?

?

3EP

1 79

D an /

?

Chairman, SCUS

S-

?

- -34b:- (When completing this form, for instructions see Memorandum SCUS 73-34a.

A.

?

course outline).

-' ,

---

MATH 322-3

C

CDMPLEX VARIABLES

1.

Complex Numbers

Arithmetic

representations

operations,

of complex

complex

numbers,

conjugate,

powers and

absolute

roots.

value,

g

eometric

2.

Complex Functions

Limits, continuity, derivatives,

Cauchy

-Riemann conditions, analytic functions.

3.

Elementary Functions

The

f

unctions,

exp

onential,

branch

t

points

r

i

gonometric

and

branch

and hyperbolic

lines, inverse

functions,

trig

onometric

the logarithmic

functions.

4.

Introduction to Conformal Mapp4

Elementary properties of conformal mapping, linear fractional

transformations,

mapping by elementary functions.

( ?

5. Complex Integration

Line integrals in complex plane, Cauchy's theorem for simply and multiply

connected regions. Cauchy's integral formula, higher derivatives of

theorem.

analytic functions. Morera's theorem, maximum modulus theorem, Llouvjj.les

6.

Power Series

Properties of power series; Taylor and Laurent

series; differentiation

and

i

ntegration of power series; uniform convergence.

7.

Calculus of Residues

Residues and poles; residue theorem, evaluation of residues; contour

integration, evaluation of definite integrals; integration around a

branch point.

PREREQUISITE

:

MATH 251-3 (or 253-4).

?

Students who

MATH

have

322-3.

obtained credit for MATH 422-4 cannot receive credit for

TEXTBOOK: Complex Variables and

Applications

by R.V. Churchill, J.W. Brown,

and R.F. Verhey (Chapters 1 - 7)

(

?

1979-02-27 ?

.

---

SENATE COMMITTEE ON UNDERGRADUATE STUDIES

COURSE PROPOSAL

FORM

Aftendar

wbreviation

information

?

: ?

Department:

_

MATHEMATICS

Code:MATH

Course Number

?

372 ?

Credit Hours:

3

?

Vector:

3-1-0

Title of Course:

?

MATHEMATICAL

STATISTICS I

Calendar Description of Course:

Techniquu 06 etniation56 and te.6t,4fng hjpothe2sei,,

One-4ampLe andtwo-6aJnpee .teots. ln-t'wdacJon to anti 06 vaAiiznce,

negMA4A.on and con1LQJJiton.

Nature of Course

LectwLe/tJJjo4ii1

Prerequisites (or special instructions):

MATH

251-3

(0 /

1

253-4)

and

272-3 (o

i

L

371-3)

Stadejto who have obtained cdLt 6oA

MATH 490-4

cannot 'eceve c/tedLt o't

312-3.

What course (courses), if any, is being dropped from the calendar if this course is

approved:

Maii't 371-3, 490-4

Scheduling

How frequently will the course be offered?

?

Twice pe,

,

L

yea.

Semester in which the course will first be offered?

FaL ?

&c-3

Which of your present faculty would be available o make the proposed offering

Possible:

Vi. Eave, Stephen4, V4€2ea4, We2don

Obectives of the Course

'

?

?

ontinuatjon of Math 272 in Classical Statistical methods.

p

rovides introduction to

basic techniques used in applied statistics.

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

Approval

/f7

J

1') ?

ii

Department Chairman

?

an? /

I ?

Chairman, SCUS

4h:- (When completing this form, for instructions see Memorandum

SCUS 73-34a.

urse outline).

---

MATHEMATICS

142-3 ?

ELEMENTARY NUMBER THEORY

I. Basic Material (order only approximate):

A.

The integers (brief)

B.

Divisibility,

Euclidean algortihm qcd; 1cm

C.

Primes, unique factorization

D.

Congruences, residue classes, systems of linear

congruences

E.

Euler-Fermat

Theorem (need t = Euler 0-function)

F.

Arithmetic functions,

0,

T, 0,

etc.

Mcbius inversion formula

G.

Distribution

of prime numbers, sieve of Eratosthenea

H. Quadratic

reciprocity, Legendre symbol, quadratic

reciprocity law

II. Additional material may

be presented at

the discretion of the instructor.

PREREQUISITE: Any 200 level

mathematics course.

(

?

Students

who have obtained credit for Math

442-4 cannot

receive

credit for Math

342-3

TEXTBOOK: ?

The textbook will b (;hosfr) from the following

list:

1.

Topics

from the Theory of Numbers by

Grosswald

2.

An Introduction

to the Theory of Numbers by

Niven and Zuckerman

3.

Elementary

Number Theory by Dudley

4.

Nuuer

Theory by G. Andrews

PLEASE CHECK THE

MATHEMATICS DEPARTMENT TEXTBOOK

LIST FOR

CURRENT TEXT IN USE.

7/78.

.

(

:1?

---

--

?

MATHEMATICS

372-3

MATHEMATICAL STATISTICS I

Sampling distribution

theory. The X and F distributions, and their

applications.

Methods of estimation. Maximum 1ik2Iihood, Bayes estimators. Introduction

to Decision Theory.

Confidence intervals.

Tests of hypotheses. ?

The bivariate normal distribution.

Introduction to regression and correlation.

Introduction to analysis of variance.

TEXTBOOK: John E. Freund, MATHEMATICAL STATISTICS

PUBLISHER: Prentice-Hall

P

REREQUISITES: MATH 251-3 (or 253-4) and 272-3 (or 371-3)

Students who have obtained credit for MATH 490.-*

cannot receive credit for MATH 372-3

­ _

0

---

SENATE;

C

O

MMITTEE

ON UNDERGRADUATE STUDIES

?

COURSE

PROPOSAL

FORM

?

- ?

Infoi--mation

Department: ?

MATHEMATICS

Abbreviation Code:

MATH

Course Number:

375 ?

Credit Hours:

3

?

Vector:

3-1-0

Title of Course:

?

MATHEMATICAL STATISTICS ii

Calendar

£1zLhood.

Typez

06

Description

pkobabuJJq

TU

?

of

aton2,

Course:

dibtJ0.

09 the

3ae.oian

ScnpLiq

di44eAent

theoty

deciLon

methods.

and

-thewty.

Bayuian

Method

a

ppuaches

06

to

maxmwn

£nvLene.

Nature of Course

Le.ctwe./t,j,

S-tuderitó

Pr

erequisites

who have

(or special

obtained

instructions)

c,'Le.dLt

60A

MATH

:

?

MATH

489-4

251-3

cannot

(oi.

teceive

253-4)

cAedit

and 272-3

60A

(wt

375-3.

371-3)

What

approved:course

?

(courses)

-

, if any, is being uroppeci from the calendar if this course is

MATH 489-4

?

2. ?

hedul ing

Flew frequently will the course be offered?

Once pvt yeoA

Semester in which the course will first

be

offered?

FaU ?

°3

Possible:

Which of your

Vn,.

present

Eave.,

faculty

Ste.phe.no

would

, ViJJe.ga,

be available

OJeLdovi

to make the proposed offering

Obj

ectiv of the Course

To

i

ntAoduce ztudents to c

/

cet

p/wb1'eJ?6 in &tati,6ticat in4eAence with

pateu1aJL

em

P

ha

-6is

on the

B

ayesian appfwach to i

n

KeAence and de.cJon theoky.

4. Budgetary and Space Requirements (for information only)

What additional resources

will

be required in the following areas:

S

S

Faculty

Staff ? -

Library

?

NONE

Audio Visual

Space ?

-

Equipment

5. Approval

Date:[.

Department Chai rmafi

L

lan

/ 2j ?

SEP

(

?

Chairman, SCUS

CUS 73-341):- (When completing this form, for instructions see Memorandum SCUS 73-34a.

Attach course outline).

?

-

2.-

ci-

---

- 0

MAT!IEMATI''S 375-3

( ?

MATHEMATICAL STATISTICS IT

1.

Joint probability distributions. Marginal and conditional

distributions. Transformations.

2.

Bayesian inference. Prior, postrior and predictive distributions.

Bernoulli, Poisson, exponential and normal models. Location and

scale parameter models.

3.

Bayesian decision theory. Utility Linear and quadratic losses.

Bayes estimates. The value of irformation.

4.

Likelihood methods. Maximum likelihood estimation. Posterior

likelihood intervals. Bayesian testing of models.

. ?

5. Two sample problems. The Behrens-Fisher problem. The ratio

of normal means.

TEXTBOOK: INTRODUCTION TO PROBABILITY AND STATISTiCS FROM A BAYESIAN

VIEWPOINT by Dennis V. Lindley.

Vol. II: Inference.

PUBLISHER: Cambridge University Press (1970)

PREREQUISITES: MATH 251-3 (or 253-4) and 272-3 (or 371-3)

Students who have obtained credit for MATH 489-4

cannot receive credit for MATH 375-3.

(

- r.

---

SENATE COMMITTEE ON UNDERGRADUATE STUDIES

COURSE PROPOSAL FORM

- (

ordr !ufOrmatj(,n

Department:

Abbreviation Code

MATH

Course Number:

?

387

Credit Hours:

Title

of ''ourse:

?

INTRODUCTION TO STOCHASTIC PROCESSES

MATHEMATICS

?

.

3 ?

Vector:

3-1-0

Calendar Description of Course:

Ma.'thot,

Chaim.

Random

waJIz6. Contnaou time pitocee2. The

Po.ioon

p'wceos.

Ma'thov pn0ee6se4. Gauzzian

plLoce.44e4s.

Nature of Course

Prerequisites (or special instructions)

MATH

272-3 (Ok 371-3) Ok pe. n'.ó-410n oK the de.pwttme.nt.

Student,6 who have obtained

cAedLt JOA

MATH 486-4 cannot

4eceive c/LedLt 6

0A 387-3.

What course (courses), if any, is being dropped from the calendar if this course is

approved: Math 486-4 iz being 4e.p!ace.d by

Math

387-3 and 487-3

2.

Scheduling

110W

frequently

will the course he offered?

Once

pelt

qea.-'t

Semester in which the course

Will first he offered?

FaU t4

't3

Which of your present faculty would

he

available to

make the proposed offering

possible: ?

Vi. Kim, Eave4, Thomson, Weldon, S-tephen4

Objectives of the Course

An introduction to stochastic processes.

this is an important course for students interested in applications of probability.

Techniques like Markov chains, the Poisson Process, queuing theory, renewal theory

are needed in many branches of science.

?

-

4. Budgetary and Space Requirements (for inlormation only)

What additional resources will be required in the following areas:

Faculty

Staff

Library ?

NONE

Audio Visual

7

Space

Equ

i pmerit

5.

Approval

Date: ?

/977

(//

?

Department Chai an

?

Den

SCUS 73-34h:- (When completing this form, for instructions see Memorandum SCUS 73-34a.

)\ttacli course outline).

-'I I

?

fj

Chairman,

scus

e_-^

S

-

2o

---

-0

MATHEMATICS 37-3

(

?

I

NTRODUCTION TO STOCHASTIC PROCESSES

Random variables. Probability and

q

n,rdti

tit

.

, F(iR:t

ions expectation.

Markov chains. The Chapman-Ko1mogo

)

v equations.

Branching processes.

The Poisson Process.

Continuous time Markov chains. Queuing systems.

Introduction to renewal theory and reliability theory.

TEXTBOOK; INTRODUCTION TO PROBABILIt'

y

MODELS by Sheldon

M. Ross

SPUBLISHER: Academic Press

( ?

PREREQUISITE: MATH 272-3

(or

371-3) or

permission of the department.

Students who have obtained credit for MATH 486-4

cannot receive credit for MATH

387-3.

---

SENATE COMMITTEE ON UNDERGRADUATE STUDIES

COURSE PROPOSAL FORM

Cdendur information

-

?

Department:

Abbreviation Code:MATH Course Number: 415

?

Credit Hours:

MATHEMATICS

?

S

3 ?

Vector:3-0-0

Title of Course: ?

ORDINARY DIFFERENTIAL EQUATIONS

Calendar Description of Course:

?

Existence and uniqueness theorems, Green's functions

for second-order equations, plane autonomous systems, stability, expansions about

ordinary and singular points.

Nature of Course Lecture

Prerequisites (or special instructions) :

?

MATH

310-3;

MATH 314-3 and 322-3

are recommended.

Students who have obtained credit for MATH 413-4 cannot receive credit for MATH 415-3.

What course (courses), if any, is being dropped from the calendar if this course is

approved: ?

MATH 413-4

Sctcduliny

How frequently will the course he offered?

?

Once every two years

Semester in which the course will first he offered? Fall -

fo-3

Which of your present faculty would be available to make the proposed offering

possible: Drs. Bojadziev, Graham, Lardner, Sharma or others.

Objectives of the Course

Advanced course on ordinary differential equations. Would be taken only

by majors in mathematics or perhaps physics.

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

t1iL

Department Chairman

?

D an

SEP ii

Chairman, SCUS

.1

---'

.-

SCUS 73-34h:- (When completing this form, for instructions see Memorandum SCUS 73-34a.

Attach course outline)

31

---

I ?

I

SENATE COMMITTEE ON UNDERGRADUATE STUDIES

?

COURSE PROPOSAL FORM

lftndar

MW

?

Information

Department: MATHEMATICS

Abbreviation Code: MATH Course Number:418

?

Credit

Hours: 3

?

Vector:

Title of Course: PARTIAL DIFFERENTIAL EQUATIONS

Calendar Description of Course: First-order equations, the wave equations,

characteristics, Riemann's method, Laplace's equation, Green's and Neumann's

functions, Poisson formula.

Nature of Course Lecture

Prerequisites (or special instructions):

?

MATH 314-3 (or Phys 384-3)or permission of the Dept.

MATH 313-3 is recommended

Students who have obtained credit for MATH 414-4 cannot receive credit for MATH 418-3.

What course (courses), if any, is being dropped from the calendar if this course is

approved: MATH 414-4

Scheduling

How frequently will the course he offered? Once per year

Semester in which the course will first

be

offered? Fall

Which of your present faculty would he available to make the proposed offering

possible:

All applied mathematics faculty

QiMiCctives

of the Course

Advanced course in partial differential equations. Would be taken only by

majors in applied mathematics or physics, but would be an important course

for such students.

Budgetary and Space Requirements (for information only)

What additional resources will be required in the following areas:

Faculty

Staff

NONE

Library

Audio Visual

Space

Equipment ..-

Approval

Date: ?

)'.,L.

/, f97

Department Chairman

9H\/L2

14 ?

0

'-&

SEP

fl

A)

4ap ?

Chairman, SCUS

(When completing this form, for instructions see Memorandum SCUS 71-34a.

*41):-

urse outline)

---

MATH

415-

(

ORDINARY DIFFERENTIAL EQUATIONS

I. First-order Equations

Review of solution methods; initial value problems;

comparison theorem.

2.

Second-order Linear j9ati.uus

Initial value

problem; J.)rOptrtles of the Wrouskiari;

separation and comparison

theorems; adjoint operator arul Laqrame

identity;

Green's functions.

3.

Linear Equations with ColisLa

nt

Characteristic polynomial;

Solution ha,es;

Stability;

inhomogeneous equations;

the transfer function; (;rttns function.

4.

Power Series Solutions

Method of undetermined coefficients;

lstssel

t':nct ior.s;

analytic functions;

method of majorants; fir st-rder equat

I()iS.

5.

Plane Autonomous

Systt.ms

cycles.

The

classification

phase plane;

of

linear

critical

ailt

pints;

ISifltui1 ?

f.iapnhloV

cuts;

method

Ii iar

and

e

quivalence;

applications;

stability

limit

and

6.

Existence and Uniqueness theorems

Well-posed problems;

Pit;ard

iteration process; linear

systems.

7.

Regular Singular Points (brief treatment. if time is short)

Continuation principle;

ILYo

order equations; regular

singular points for

second order equations; Bessel equation; hyperqeometrjc

function.

PREREQUISITES: MATH

obtained

310-3;

credit

MATH

for

314-3

MATH

and

413-4

322-3

cannot

are

recommended.

receive credit

Students

for MATH

who

415-3.

have

TEXTBOOK: Ordinary

by G. Birkhoff

D

ifferential-Equations

&

(;

.

t'. -

Rota

(3rd Edition), chapter

1 -

6 & 9

S

(p..

?

11/78 ?

.

3.'t

---

MATH 4i-

PARTIAL DTFFERENTiAL EQJAT IONS

I.

First

Order Equations

Linear first order equations, .hi

tact ?

i ;t. i

r Vati

ables ; quasi-i i near

equations, method of Lagrange.

II.

The Wave Equation

(one

space-dimension)

Vibrating string. U'AIembrt's formula, boundary-value problems,

integral form of the wave equation,

characteristics,

well-posed

problems, discontinuities of the olut.iori, separation of variables*,

Riemann's method.

III. Laplace's Equation

Physical examples, harmonic functions, separation of variables*,

fundamental solution, Green's formula, Green's and Neumann's functions,

maximum principle and uniqueness, method of images, Poisson's formulae

for circle, sphere and half-space.

(

* "Separation of variables" method

is to

he done Very briefly or not at all.

This method is discussed in Mathematic!. 314-3.

PREREQUISITES: MATH 314-3 or permission of the department.

MATH 313-3 is recommended. Students who have obtained credit for

MATH 414-4 cannot receive credit for MATH 418-3.

TEXTBOOK: Partial Differential Equations of Mathematical Physics

by Tychonov & Samarski

?

(out of print as of October 1977)

Partial D

i

fferential Equations of Mathematical Physics

by Tyn Myint-u

I'artial. D.if1ereri ?

.iI

I(1Ilit

T!, ?

An

?

tit r(ittict

O)t

by E. C. Young ?

(C)I ?

of rPrillt ?

r. n t

?

y 797

Please check the Mat:hcmjti

?

ledhook

1,

i' For 'urrent text in use.

11/78

.

C

---

Information

Abi r v j

t I

on Code : MATE!

Department: MATHEMATICS

Course Number: ?

419

?

Credit Hours: 3

?

Vector:

3-0-0

.

SENATE COMMITTEE ON

UNDERGRADUATE

STUDIES

COURSE PROPOSAL

FORM

Title ?

Course: ?

LINEARANALYSIS

Calendar Description of Course: Convergence in Euclidean spaces, Fourier series and

their convergence, Legendre polynomials, Hermite and Laguerre polynomials.

Nature of

Course

Lecture

P

r'requisjtes (or special instructions): MATH 232-3, 251-3 (or 253-4) and 310-3.

MATH 314-3 and 320-3 are recommended.

Students who have obtained credit for MATH 420-4 cannot receive credit for MATH 419-3.

What

approved:

course

MATH

(courses),

420-4

if

.

'

fl

y,

is being dropped from the calendar if this course is

Flow frequently will the course he offered?

?

Once per year or less

Semest('r in which the course will first be offered? Fall

Which of your present faculty would be available to make the proposed offering

possible: ?

Most faculty in the department

2JectivesoftheCourse

This course, bridging pure and applied

mathematics,

gives an introduction

to applied functional analysis.

4. Budgetary and Space Requirements (for information only)

What additional resources will be required in the following areas:

Ficul ty

Staff

Library ?

NONE

Audio Visual

Space

Equi

pment.

-

?

w

ii

Department Chairman

Y

?

Den ?

Chairman, SCtJs

:CUS

73-34h:- (When compietjnq this form, for instructions see Memorandum SCUS 73-34a.

?

Attjc!i course outline) .

?

-0

(iiL

---

MATH 419-3

C

LINEA} ANALYSIS

The following syllabus refer.

,.;

to th!- urnended t(Xtlx)ok.

1. Vector Spaces

Quick review of real vector spaces and linear transformations and

?

(5 lectures)

matrices (Chapters 1 & 2).

2. Euclidean Spaces

Euclidean vector spaces; convergence in Eociidan spaces..

?

(7-8 lectures)

(Chapters 7 & 3 - omit 7.6 & 7.7)

3. Fourier Series

• ?

Fourier series; convergence properties of Fourier

:-eYe.

?

10 lectures)

(Chapters 9 & 10; Chapter 10 probably cannot be covered

thoroughly in the time allowed).

4. Orthogonal Systems

Legendre, Hermite & Laguerre polynomials.

?

(12 lectures)

(Chapters 11 & 12 - omit 12.9 - 11).

PREREQUISITES: MATH 232-3. (or PHYS 384-3) or permission of the Department.

MAT!! 314-1 and 320-3 are recomendtd.

Students who have obtained credit tor MATH 420-4

cannot receive credit for MATH 4-

19-3.

TEXTBOOK: ?

An Introduction to Linear Analysis

by Kreider, Kiler, Ostbr; and Per¼ins

OP As noted

in

the Matinem;itics Depa!tment textbook list.

•l979_02_27

7.7

---

SENATE COMMITTEE ON UNDERGRADUATE STUDIES

?

COURSE PROPOSAL FORM

.1 niar roformation

?

Department: MATHEMATICS

fl"

at ion Code: MATH Course Number: 424

?

Credit Hours: 3

?

Vector: 3-0-0

of course: ?

APPLICATIONSOFCOMPLEXANALYSIS

'ndr Description of Cur:;e: Conformal mapping, application to boundary value

problems, Schwarz-Chi-

j

st-offel transformation, integral formulas, analytic

continuation, argument principle.

Nature of Course

?

Lecture

Prerequisites (or special instructions) : MATH 322-3.

Students who have obtained credit for MATH 422-4 cannot received credit for MATH 424-3.

What course (courses) , if any, is being dropped from the calendar if this course is

approved: ?

MATH 422-4

S.-hcdulinq

How frequently will the course he of tcrcd

?

Approximately every second year

çQ\\

Semest'r in which t.lic rour;O will first h offered?

?

Spring

Which of your present faculty would he av i lable to make the proposed offering

possible: ?

All applied mathematics faculty

ObjectivesoftheCourse

To give an introduction to the use of complex variable methods in the

solution of boundary value problems in the physical sciences and

engineering.

4. Bud

getaryandSpaceRequirements (for information only)

What additional resources will be required in the following areas:

Faculty

Staff

Library ?

NONE

Audio Visual

Space

E(JtI i }

flflerI

I ?

-

5. Approval ?

/ /' ?

) ?

\

Date:

4

SEP

Department Chairman

?

ean/ ?

Chairman, SCUS

CUS 73-34h:- (When completinq this form, for instructions see Memorandum SCUS 73-34a.

Attach course outline)

---

— 0

MATH 424-3

(

?

APPLICATIONS OF COMPLEX ANALYSIS

I..

Mapping by Elementary

Functions (Review)

Mapping

z

fl&3

, z , exp

by

linear

z , sin

functions;

z

linear frtion.l

iiaiisformations; the functions

2. Conformal

Mapping

Properties of conformal mapping; conjugate harmonic functions;

boundary value

problems; transformation of boundary conditions.

3. Applications of ConformalMpi

Boundary value problems for steady temperature

distributions, electrostatic

potentials and fluid

flow; introduction to aerofoil

theory.

. 4. Schwarz-thristoffel

Transformation

Mapping of real

axis

onto general polygon; triangles and

rectangles;

( ?

infinite strip; channels with slit or offset -

5. Integral Formulas

Dirichiet and Neumann problems for (ii!-,k

and

halt-plane; Poisson integral

formula and related formulas.

6.

Further Topics

(a)

Analytic continuation, reflection principle;

(b)

Poles and zeros, essential singularities, the argument

principle;

(c)

Riemann surfaces.

PREREQUISITE:

MATH

322-3. Students who have obtained credit for MATH 422-4

cannot receive credit for MATH 424-3.

TEXTBOOK:

?

Complex Variables and Applications

by R.V. Churchill, J.W. Brown and R.F. Verhey (Chapters 4, 8- 12)

111/78.

---

SENATE COMMITTEE

ON (IN F:Rr,RArMJATE STTJDIES

Calendar Information

?

COURSE PROPOSAL FORMDepartment:

?

MATHEMATICS

S

Abbreviation Code:

MATH

Course Number:

4P6

?

Credit Hours:

3

?

Vector:-

3-0-0

Title of Course:

?

INTJ?ODU(TJON TO METFUC SPACE'S

Calendar Description of Course:

Metric spaces, convergence in metric spaces, continuity, compactness,

connectedness and completeness, contraction mapping principle, and

other useful theorems.

Nature of Course

Lecture

Prerequisites

credit for

(or

MATH

special

422-4

instructions):

cannot receive

MATH

credit

320-3.

for

Students

MATH

425-3.

who have obtained

What

approved:

course

MATH

(courses),

421-4

if any, is being dropped from the calendar if this course is

2. Schedul4

How frequently will the course be offered?

Once per year

Semester in which the course will first be offered?

Pall

19 ?

6-3

i-

Objectives of the Course

possible:

Which of your present faculty would be available to make the proposed offering

our

oer

all

.

offerings in Ana7ysis.

of

the oi'erZap existing bctwc?n Math

242-3, 320-3

and

421-4.

Together with

This course is a revision of Math 421-4. It is designed to eliminate some

th other two new

n Proposed courses (Math 426-3 and

444-3) it will

streamline

Drs. Eaves, Kim, Ryeburn, -'ember, Shen, Thomson and others

?

S

4. Budgetary and Space Requirements (for information only)

What additional resources will be required in the following areas:

Faculty

Staff

Library ?

NONE

Audio Visual p

Space

Equipment

. Approval ?

( /.

1 \ I

L

Date: ?

/', /

?

/- 1

I ILL/ c

Department Chairman

?

a

SEP 11 79

Chairman, SCUS

SCUS 73-34b:- (When completing this form, for instructions see Memorandum scus 73-34a.

Attach course outline).

?

V

17 4

C'

---

MATH 42-

INTDUCTION ) METRIC SPACES

(

1.

Metric Spaces

2.

Convergence in Metric Spaces

3.

Open Sets, Closed Sets and Bundei -ets

4.

Continuous Functions on Metric Spaces

5., Uniform Continuity

6. Compactness, Connectedness and Conipi eteness

7.

Weierstrass Approximation Theorem,

Arzei(1

Theorem tnd

Fixed-point Theorem••

PREREQUISITES: MATH 320-3

. ?

Students who have obtained credit for Math 421-4 cannot,

receive credit

for Math 425-3.

(

?

SUGGESTED TEXTBOOK: Methods of Real Analysis by R. Goldberg

(Chapters 4, 5, 6, 10 and possibly parts of 9)

PLEASE CHECK MATHEMATICS TEXTBOOK FOR CURRENT PEXT IN USE.

0 ?

Draft Jan. 22/79

---

SENATE COMMITTEE ON UNDERGRADUATE STUDIES

COURSE PROPOSAL FORM

Calendar Information

?

Department:

MATHEMATICS

Abbreviation Code:

MATH

Course Number:

426 ?

Credit Hours: ?

3 ?

Vector:

3-0-0

Title of Course:

?

INTRODUCTION TO [,EBESGUE THEORY

Calendar Description of Course:

An introduction to the Lebesque integral and some of its applications.

Nature of Course

Lecture

Prerequisites (or special instructions):

?

MA?'!?

320-3. Students who have obtained

?

credit for

MATH

423-4 cannot receive credit for MATH 426-3.

What course (courses), if any, is being dropped from the calendar if this course is

approved:

MATH

423-4

2. scheduling

How frequently will the course be offered?

Once per year

Semester in which the course will first be offered?

Spring 1980

Which of your present faculty would be available to make the proposed offering

possible: Dr's. Eaves, Freedman, Kim, Sember, Shen, Thomson and others

s- Objectives

This

of

course

the Course

is a slight

.

?

revision

of

Math

423-4.

This course constitutes

0

an introduction to Lehesque integration. It is an integral part

of

the

package designed to strenZin our Analjoi: offerings.

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:

?

j '/ 7

SEP 11 79

Department Chai'rman

?

Ddan

I ?

Chairman, SCUS

SCUS 73-34b:- (When completing this form, for instructions see Memorandum SCUS 73-34a.

Attach course outline).

---

S

4

?

MATH

426-3

I

?

INTRODUCTION TO LEBISGUE ?

!t!IOY

1.

Measurable Sets

2.

Measurable Functions

3.

Definition of the Lebesgue Integral

4.

Convergence Theorems of the Lebesgue Integral

5.

Applications (e.g. The

L 2

Theory of Fourier Series).

PREREQUISITES:

MATH 320-3.

?

Students who have

obtained credit for Math 423-4 cannot receive credit for Math 426-3.

SUGGESTED

TEXTBOOK: Methods of

Real Analysis

by R. Goldberg ?

(Chapters 11 and 12)

PLEASE CHECK MATHEMATICS TEXTBOOK FOR CURRENT TEXT

IN USE.

(

.

?

Jan. 22/79

---

SENATE COMMITTEE ON UNDERGRADUATE STUDIES

?

COURSE PRUPOSAL FORM

Calendar Information

Department: Mathematics

Abbreviation Code: MATH Course Number: 438

?

Credit HOurs:3

?

Vector:— 3-1-0

Title of Course:

?

LINEAR ALGEBRA

Calendar Description of Course:

Linear Algebra. Vector space and matrix theory

Nature of Course

?

Lecture /Tutorial

Prerequisites (or special instructions): Math 232-3

Students who have obtained credit for Math 431-4 cannot

receive credit for Math

What course (courses), if any, is being dropped from the calendar if this course is

approved:

Math 431-4

2. Scheduling

How frequently will the course be offered: Twice per year

Semester in which the course will first

be

offered? Fall

Which of your present faculty would be available to make the proposed offering

possible:

Drs. Berggren, Brown, Gerber, Reilly, and others.

Objectives of the Course

The course is the present Math 431-4 less the theory of annihilators,

the functional characterization of determinants, and the spectral theorem

- replacing the latter by diagonalizable operators.

4.

Budgetary and Space Requirements (for information only)

What additional resources will be required in the following areas:

Faculty

Staff

Library

Audio Visual ?

NONE

Space

Equ ome r t

5. Approval

Date: ?

/ ?

/

779

?

.

I

SEP

1179

Department Chairman

?

Chairman, SCUS

SCtJS 73-34b:- (When completing this form, fox instructions see Memorandum SCUS 73-34a.

Attach course outline)

---

MATHEMATICS 438-3

LIEARAL.;EBR1

I.

Brief review

of matrices and systems of linear equations.

A.

Matrices over a field.

B.

Operations on matrices.

C. Invertible matrices.

D.

Complete solution of a system of linear equations.

II. Vector Spaces.

A. Subspaces.

B. Bases and

dimension.

C.

Coordinates and computations involving subspaces.

III. Linear transformations.

A.

The space L(V,W).

B.

Representation by matrices.

C. Linear

functionals & dual space.

D.

Transpose of a transformation.

IV.

A

brief

review

of polynomials, factorization.

V.

Properties of Determinants.

VI. Direct-sum decompositions.

—

*I. Inner Product Spaces.

A.

Inner product spaces.

B.

Linear functionals and adjoints.

C.

Positive, unitary and normal operators.

VIII. Diagonalizable operators.

If time permits additional topics may be chosen from IX, X, XI or XII.

IX.

A.

The Spectral Theorem.

B.

Simultaneous diagonalization of normal operators.

C.

The primary decomposition theorems.

OR

,,

is.

?

a.........

OR

XI. Jordan forms.

OR

-

?

XII.

Numerical methods in linear algebra.

PLEASE CHECK MATHEMATICS TEXTBOOK LIST FOR CURRENT TEST

IN

USE.

S ?

PREREQUISITE: Math 232-3

Students who have obtained credit for Math 431-4

cannot receive credit for Math 431-.

July 1978

1/:

---

SENATE COMMITTEE ON

UNDE

RGRADUATE STUDIES

COURSE PROPOSAL FORM

Calendar Information

?

Department:

?

Mathematics

Abbreviation Code: MATH Course Number:

?

439 Credit Hours:

?

3 Vector: 3-0-0

Title of Course:

?

INTRODUCTION TO ALGEBRAIC

SYSTEMS

Calendar Description of Course:

Algebraic systems including, for example, groups, rings. Polynomial theory.

Nature of Course: Lecture

Pr

erequisites (or special instructions):

?

MATH 232-3

Students who have obtained credit for Math 432-4

cannot receive credit for Math 435-3.

What

approved:

course

?

(courses),

Math

if

432-4any,

is being dropped from the calendar if this course is

2.

?

Scheduling

How frequently will the course be offered?

?

Once per year

Semester in which the course will first be offered?

?

Spring 1980

Possible:Which

of

?

your

Drs.

present

Berggren,

faculty

Brown,

would

Gerber,

be available

Reilly and

to make

others.

the proposed offering

Objectives of the Course

categories,

This course

semigroups,

is the present

and

Math

tensor

432-4

products

with the

of abelian

elimination

groups.

of material

on

4. ?

BudgetaryandSp

aceRequirements (for information only)

What additional resources will be required in the following

areas:

Faculty

Staff

Library ?

NONE

Audio Visual

Space

5.

?

Approval

Date:

SEP

1179

/ /

Department Chairman

?

D ?

-

an

?

Chairman, SCTS

AttachSCJS

73-34b:-course ?

outline).(When

completing this form,

?

for

?

i n r

t;ruct

j

on ?

see Memorandum SCUS 73-34a.

4"

---

4

MATHEMATICS '13--3

INTRODUCTION TO ALGEBRAIC SYSTEMS

I. Brief review of sets, functions and relations.

II. Groups.

A. Subgroups.

S. Homomorphisms.

C.

Quotient groups.

D. Finite groups - Lagrange's Theorem, Cayley's Theorem, permutation

groups, Sylow subgroups.

E. Direct products.

III. Abelian Groups.

A. Free

abelian groups.

B.

Decomposition of cyclic groups.

C. Finitely generated Abelian groups.

IV.

Rings

and Integral Domains.

A.

Subrings and ideals.

B.

Homomorphisms.

C.

Polynomial rings, unique factorization.

V.

Introduction

to Fields.

A.

characteristic of a field.

B. Finite fields.

C. Algebraic extensions.

As time

permits

topics chosen from the following will be introudced.

Free Groups,

Semigroups, Categories and Functors.

PREREQUISITE: Math 232-3

Students who have obtained credit for Math 432-4

cannot receive credit for Math 43J-3.

PLEASE CHECK MATHEMATICS DEPARTMENT TEXTBOOK LIST FOR CURRENT TEXT IN USE.

July 1978

0

---

S

SENATE COMMITTEE ON UNDERGRADUATE STUDIES

COURSE PROPOSAL FORM

Abbreviation

Calendar Information

Code:MATH

?

Course Number: 440-3 Credit

Department:

Hours:3

Mathematics

?

Vector:3-0-0--

?

S

Title of Course:

?

GALOIS THEORY

Calendar Description of Course: An introduction to the theory of fields, with

emphasis on Galois theory.

Nature of Course

?

Lecture

Prerequisites (or special instructions) : MATH 438-3 (or 431-4) and 439-3 (or 432-4)

Students who have obtained credit for Math 433-4

cannot receive credit for Math 46-4.

4f0-9.

What course (courses), if any, is being dropped from the calendar if this course is

approved:

Math 433-4

- Scheduling

How fre

q

uently will the course be offered?

?

Once every two years.

Semester in which the course will first be offered? FE[I919

Which of your present faculty would be available to make the proposed offering

possible: ?

Drs. Berggren, Brown, Gerber, Reilly and others.

Objectives of the Course

This is the present Math 433-4 course with the elimination of topics from

valuations, ordered fields, and algebraic number theory. It is expected

that the elimination of one hour will make the course more accessible to

a larger number of students.

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

5. Approval

SEP it

?

Department ChairmanJ

?

- Ean' ?

Chairman, SCUS

SCUS 73-34b:- (When completing this form, foi instruction:; see Memorandum SCUS 73-34a.

Attach course outline) .

?

S

---

4

MATHEMATICS 44- 3

C,AJ)j;

THEORY

I.

Field Theory.

(1)

Finite

and algebraic extensions: Conjugate elements.

(2)

Characteristic, prime subfields, separable and inseparable

extensions,

perfect fields.

(3) Separability of extensions.

(4) Normal extensions, splitting fields.

(5)

Finite fields, GF(p'), multiplicative group of a finite

field is cyclic.

(6)

Primitive

elements.

(7) Algebraically closed fields.

(8)

Galois extensions.

(9) Fundamental Theory of Galois Theory.

(10)

Cyclotomic

fields.

(11) Solutions of polynomial equations by radicals.

PREREQUISITE: MATH 438-3 (or 431-4) and 439-3 (or 432-4). Students who have

obtained credit for MATH 433-4 cannot receive credit for MATH 496-3.

++0-3.

Recommended Text

?

Algebraic Extensions of Fields

by P. McCarthy

or

As noted on the Mathematics Department Textbook list.

DRAFT: July 1978

4

0

ri

---

Calendar Information

COURSE PROPOSAL FORM

Department:

MATHEMATICS

S

SENATE COMMITTEE ON UNDERGRADUATE STUDIES

Abbreviation Code:

MATH

Course Number: 444

?

Credit Hours: _3

?

vector:

3-0-0

Title of ourse:

TOPOLOGY

Calendar Description of Course:

Development

of

elementary theory

of

topological spaces.

Nature of Course

Lecture

Prerequisites (or special instructions):

MATH 425-3 (or 421-4), or

permission of the

?

Students who have obtained credit for M11T11 4'11-4 cannot reeeivc credit

?

Department.

for

MATH

444-3.

What course (courses), if any, is being dropped from the calendar if this course is

approved: ?

MATH

441-4

2. Scheduling

How frequently will the course be offered?

Once per year

Semester in which the course will first be offered?

Spring 1980

Which of your present faculty would be available to make the proposed offering

possible: Drs. Gerber, Ryeburn, Sember, Thomason, Thomson and others

i-- Objectives of the Course

?

This course will be a natural follow-up for the proposed MATH 425-3

? -

in which metric --paces are examined. The metric space material now

present in Math 441-4 has been eliminated; it is covered in the new

course Math 425-3.

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:

?

JAL /', /7j

Department Chairman

/

,/J 1>

/

?

1 ?

oC—/

/

Chairman, SCUS

SEP 11 79

SCtJS 73-34b:- (When completing this form, for instructions

see

Memorandum SCUS 73-34a.

Attach course outline).

---

.

(I

?

MATHEMATICS 444-3

TOPOt.A)(;Y

I. Core topics. (The order is subject t) variation, depending upon

the text used

and

the wishes of the instructor.)

A.

Topological spaces and methods ut definition

B.

Continuity, subspaces, product spaces, quotient spaces

C.

Special properties

1.

Separation properties

2. Connectedness properties

3.

Compactness properties

4. Countability properties

II. Additional topics, to be chosen by the instructor, which may include

( ?

some of the following.

A. Convergence

B. Metrizability

C.

Covering properties

D.

Ho1Ttopy theory; the fundamental group

E.

Function Spaces

F. Unifirm Spaces

PREREQUISITE: MATH 425-3 (or 421-4), or permission of the department. Students

who have obtained credit for MATH 441-4 cannot receive credit for

MATH 444-3.

TEXTBOOK: ?

As

noted in

the textbook list of the Mathematics Department

Possible Textbooks:

Elementary Topology by Gemignani

Introduction to

General

Pcpoogy by flu

Undergraduate Topology by Kasriel

Foundations of General Tonology by 'er"i

0

a.

---

SENATE COMMITTEE ON

UND

ERGRADUATE STUDIES

?

COURSE PROPOSAL FORM

Information

Department:

MATHEMATICS

?

S

Abor r

:vjatjjn Code:

MATH

Course Number:

472 ?

Credit Hours:

?

3 ?

Vector:

?

3-1-0

Title of

Course:

?

LINEAR MODELS IN STATISTICS

Caienddr Description of Course:

Lnea-t

vtiwducon

modeLs,

to

anatysiz

the degn

o4

o6

va'znee

epement.

and covaiArtce, mutp!e

?

eon,

Nature of Course

Lec-twe/twto,,jj

Prerequisites (or special instructions):

?

MATH

232-3

and

372-3

(oiL

371-3)

S-tudents who have obtained cedLt

6olt

MATH

490-4

cannot kece,cive c'LedLt eon.

472-3.

What

approved:course ?

(courses)

MATH

490-4

, if any, is being dropped from the calendar if this course is

•

?

Sj

How frequently will the course

he

offered?

Once pelt qea_k

Sernestor

in

which

the curu4- will

fi rst

In-

offered?

Sp-'iinq ?

-.

Which

of your present faculty would be aviiab1e to make the proposed offering

possible:

?

DU -

S-tepheno, Wet-don, Eave.6

Objectives of the Course

To teach students some of the most widely used methods of statistical analysis,

and to aive a good mathematical formulation and understanding.

4.

Budgetary and Space Requirements (for information only)

What additicnal resources will be required in the following areas:

Faculty

Staff

Library

?

- ?

NONE

Audio Visual (

Space

Equipment

5. Approval

/ ?

/1 ?

SEP 11 79

Department Chairman

?

De n

?

Chairman, SCUS

Att(:ji

scij.s

73-34h:-

course

(When

outline).

completing this form,

-

for instructions see Memorandum

scus

73-34a.

---

.

MATHEMATICS 472-3

LINEAR MODELS IN STATISTICS

1.

The general

linear model: ?

m.jLrix ?

t)rmuatmrI.

2.

Application

of the

?

linear mode t. ?

to ?

ana Lys i - ?

of

variance,

With distribution

theory of

?

the AN(VA

tible.

?

Te;tis

of appropriate

hypotheses.

Effects

of ?

fail urt: ?

in mode ?

isurnpt ions.

3.

Applications

of the ?

tnuar model. ?

tu

?

(a) ?

multiple regression

(b)

?

curvilinear models

including use

of orthogonal polynomials

(c) ?

analysis of covariance

4.

Introduction

to design

of

experiments.

(

TEXTBOOK: THEORY AND APPL[CAPION 01 'i'It'

],IN[.:Ap MODE!. by Franklin A. Graybill

PUBLISHER: Duxbury

PREREQUISITES: MATH 232-3 and 372-3 (or 371-3)

Students who have obtained credit for MATH 490-4

cannot receive credit for MATH 472-3.

--

k

0

---

SENATE COMMITTEE ON UNDERGRADUATE STUDIES

?

COURSE PROPOSAL FORM

CiIndir

Information

Department:

MATHEMATICS

Abbreviation Code:

MATH

Course Number:

479

?

Credit Hours:

3

?

Vector:

3-0-0

Title of Course

?

STATISTICS: SELECTEV TOPICS?

Calendar Description of Course:

Nature of Course

LectuAe/tuto&iat

Prerequisites (or special instructions):

?

Wifi be .6peci6ied accoAding to topics

?

oejtd wide't these riwnbex,,

What

approved:course

(courses) ,

if

any, is being dropped from the calendar if this course is

NONE

Scheduling

110W frequently will the course be

offered?

Onee. eve.&q 2 ot 3 yeao

Semester in which the course will first be offered?

?

Fcfl 1980 on. Sptng 1981

Which of your present faculty would be available to make the proposed offering

possible: ?

Vn4. Eave4, V-Ltea, Wedon, S-tepheLn

Objectives of the Course

Statistics is developing rapidly and a selected topics course will provide

the opportunity to introduce additional subjects, (e.g. multivariate analysis)

to students. Useful to have the selected topics labelled Statistics for

student transcripts.

4.

Budgetary and Space Requirements (for information only)

What additional resources will be required in the following areas:

Faculty

\

Staff

NONE

Library

Audio Visual

1

Space

Equipment

5.

Approval

iJ ?

A ?

L ?

SEP

11 179

Department Chairman

?

an (

?

Chairman, SCUS

CUS 71-34h:- (When completinq this form, for instructions see Memorandum SCUS 73-34a

ALt ich (urse outline).

L]

r

2.

---

I

?

I

SENATE COMMITTEE ON IJNDERIRADUATE STUDIES

COURSE PROPOSAL FORM

Clendar Information

?

Department:

MATHEMATICS

Abbreviation Code:

MATH

Course Number:

487 ?

Credit Ueurs:

?

3

?

Vector:

3-0-0

2.

Ii

Title of Course:

?

VKUAILJIY

Calendar

ha&acu4-t

Description

?

UflcOvL6,

of Course:

eentjwi

P'tobabeLt,

?

it thcDnenU,

paec, d.tibutiovt,

inuitef.t di

taws

sLbe

odLtnbwtLoni.

?

aqe twibv,

Condtorta2 di t&ba-tions and epctat IOU .

Nature of Course

Lecta&e

Prerequisites (or special instructions) : ?

MATH 387-3 (on

486-4)

What course (courses) , if any, is being dropped from the edlendar if this course is

approved: ?

MATH 486-4 -I6 being nepeacd by Math 387-3 and 487-3

Scheclul in

Flow frequently will the course be offered?

Ovice, e)Jvu( two qeaA.6

Semester in which the course will first

he

offered?

Fat! 499

04

Spivig 1-8U

Which of your present faculty would be iv.i ii thie to mike the proposed offering

possible:

DU.

Kim, Eave4, Thomoovi

Objectives of the Course

To provide the axiomatic treatment of probability theory. A much deeper

treatment than can be given in Math 272 is given here.

4.

Budgetary and Space Requirements (for information only)

What additional resources will be required in the following areas:

Faculty

Staff

?

Library ?

NONE

Audio Visl

Space

Equipment

5. Approval

?

(/

7

?

____

79

Department Chairman

?

D6ant

?

Chairman, SCUS

SCUS 3-341-):- (When completinq this form,

for

instructions see Memo

r

andum SCUS 73-34a.

Attice course outline)

33 -

---

S

MATHEMATICS 487-3

PROBABILITY

?

S

Classical probability. Axiomatic probability.

Conditional probability and

Inde

pendence. Limit Theorems.

Random walks.

Martingales.

PRER

TEXTBOOK:

EQUISITE:

PROB

MATH

ABILITY

387-3

WITH

(or

APP

486_4)

LICATIONS by Michael Woodroofe

f

j_ -'

---

SiMON FRASER UNIVERSITY

?

75"

29

MEMORANDUM

0 .. . .... . H.....

M. ...Evans

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

scus ................ ......

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

Subject....

Appendix ... to ... memorandum

Mathematics Curriculum Changes

From. ?

N. Heath ?

.. ?

.. .

Assistant to the Dean. .of Science

Date

?

1979 07 23 ?

..

Item 6. Mathematics Curriculum Changes - Revisions to existing

Mathematics courses.

(see

pp.

416-423 of 1979-80 Calendar for current listings

of prerequisites etc.)

MATH 242-3 Introduction to Analysis.

New prerequisite statement to read:

"MATH 152-3 or 155-3. Students who have obtained credit for

MATH 241-2 cannot take MATH 242-3 for further credit."

The revision deletes MATH 158-3 as an alternative prerequisite.

0 ?

MATH 302-3 Statistical Methods

New prerequisite statement to read:

"MATH 1013 or 272-3 (or 371-3) or ARC 376-5 or ECON 332-3

(Mathematics major and honors students may not use this course to

satisfy the required number of semester hours of upper division

Mathematics courses. However, they may include the course to satisfy

the total number of required hours of upper division credit)."

The revision reflects the replacement of MATH 371-3 by MATH 272-3.

MATH 310-3 Introduction to Ordinary Differential Equations

New calendar description to read:

"First-order differential equations, second and higher order

linear equations, series solutions, introduction to Laplace transform,

systems and numerical methods, applications in the physical,

biological and social sciences."

Now

pt , ?

I I ( ,' ?

t • ( emont t

"MATH

?

I 5- 3; or MATH 158-3 with a grade of A or B.

i

?

I I

?

!:rom tho dolotion of the MC- 23-4

---

-2-

Appendix to Mathematics

Curriculum Changes

MATH 320-3 Theory of Convergence.

New title to read, "Advanced Calculus of One Variable."

New prerequisite statement to read:

"MATH 242-3 (or 241-2) and 251-3 (or 253-4).

The new title is one traditionally given to courses with a

similar content to MATH 320. The prerequisite revision arises

from the deletion of MATH 253-4.

MATH 361-3 Mechanics of Deformable Media.

?

New prerequisite statement to read:

"MATH 252-3 (or MATH 253-4) and MATH 262-4 (or MATH 161-3

or PHYS 120-3 with permission of the Department)."

The revision follows from the deletion of MATH 161-3 and MATH 253-4.

MATH 443-4 Combinatorial Theory

Vector changed from (4-1-0) to (4-0-0). The nature of the

subject matter makes tutorials unnecessary.

MATH 466-4 Tensor Calculus

New Prerequisite statement to read:

"MATH 252-3 (or MATH 253-4) and MATH 232-3 or permission of the

Department. MATH 313-3 is recommended."

The revision follows from the deletion of MATH 253-4 and

MATH 312-4.

MATH 467-3 Vibrations

Vector changed from (3-1-0) to (3-0-0). Tutorials have been

found to be unnecessary in this course.

New Calendar description to read:

"Vibrations of discrete systems with many degrees of freedom;

matrix methods. Nonlinear vibrations; the phase plane; singular

points

expansions."and

limit cycles. Perturbation methods; singular perturbation

?

40

.3-f

---

Appendix to Mathematics ?

-3-

.

?

Curriculum Changes

MATH 4A7-1 VihrM-innc r'nnt

Revised Syllabus - See appendix attached.

New prerequisite statement to read:

"MATH 232-3 and 310-3. MATH 263-4(or PHYS 211-3)and MATH 314-3

are recommended."

The revision in prerequisites follows from the deletion of

MATH 161-3 and from the syllabus change.

MATH 468-4 Continuum Mechanics

New prerequisite statement to read:

"MATH 314-3 and 361-3. MATH 313-3 (or MATH 312-4) should

precede or be taken concurrently."

The revision follows from the deletion of MATH 312-4.

MATH 469-4 Fluid Dynamics

New prerequisite statement to read:

"MATH 361-3. MATH 314-3 or PHYS 384-3 should precede or be

taken concurrently."

The revision follows from the deletion of MATH 312-4 and PHYS 382-4.

MATH 470-4 Variational Calculus

New prerequisite statement to read:

"MATH 310-3 and either MATH 262-4 (or MATH 161-3) or PHYS 211-3.

MATH 313-3 (or MATH 312-4) or PHYS 384-3 should precede or be taken

concurrently."

The revision follows from the deletion of MATH 161-3, PHYS 382-4

and MATH 312-4.

MATH 471-4 Special Relativity

New prerequisite statement to read:

"MATH 313-3 (or MATH 312-4) or PHYS 384-3."

The revision follows from the deletion of MATH 312-4 and PHYS 382-4.

0

---

-4-

Appendix to Mathematics

Curriculum Changes

MATH 480-3 Non-Parametric Statistics

New course number to read:

"MATH 473-3."

New prerequisite statement to read:

"MATH 372-3 (or 371-3) or permission of the Department.

Students who have obtained credit for MATH 480-3 cannot receive

credit for MATH 473-3."

The prerequisite revision follows from the upgrading of the

statistics stream of courses, including the introduction of MATH 272-3

and the replacement of MATH 371-3 by MATH 372-3.

New vector, (3-0-0).

Tutorials are not considered to be necessary in this course.

.

NH/rcw

)

N. Heath

0

---

I

n

(

?

Revised Syllabus for:

?

14ATH4ATICS 467-3

p

VIBRATIONS

1.

Discrete Systems

Linear systems of differential equations; examples of mechanical or

electrical vibrations. Matrix methods. Complex eigenvaluea: repeated

eigenvalues. Fundamental matrices. Inhomogeneous linear systems.

2.

Nonlinear Vibrations

The phase plane; classification of singular points; solutions close to

singular points. Isoclines. Periodic solutions; limit cycles. Poincar-

Bendixeon theorem. Applications to nonlinear mechanical and electrical

vibrations.

3. Perturbation Methods

Regular perturbation expansions and their non-uniformities. Linstedt-

Poincar method. K-B-M method. Method of averaging. Two-timing.

Matched asymptotic expansions and boundary layers. Many-variable

expansions.

---

rjbArIt U!1Vt1(fj'

S

-

MEMORANDUM

H.M. Evans, Secretary

Senate Committee' on

Undergraduate Studies

MATHEMATICS

...........

TICS

.

CURRICULUM CHANGES

From

?

N. Heath

Adm

inistrative Assistant

to the Dean of Science

Date..,,,,,,,,,, 1979 09 05

The following minor change to the Mathematics curriculum Should have

been included in my earlier memo of 1979 07 23.

MATH 404-3 Statistical Design and Analysis of Experiments

New

p

rerequisite statement to read:

MATH 272-3 (or 371-3) or 302-3. Permission will be given to

students from other departments with suitable backgrounds."

The revision reflects the replacement of MATH 371-3 by MATH 272-3.

.

NH/mgj

?

N. Heath

.

---

SiMON FRASER UNIVERSITY

5- ?

72,'C

MEMORANDUM

?

Mx...

.Iixy. .&as

?

From ...

....

.

S.ingh,..Chg.irrnan...........................

Registrar

.b. l 4 cs .

Pp.rtmeri.t

Sub1ect

...

MAT....çp.lUM

....

?

Date. ?

Septembe.....919 ... .......................

I thank you very much for your care and interest in the proposed math

curriculum changes to be broughtbefore the SCUS meeting next Tuesday.

Regarding your first enquiry during our telephone conversation today:

The material in the existing MA'fl-I 414-4 (Partial Differential Equations)

has been supplemented and rearranged to bring forth the new proposed

courses MATH 314-3 (Boundary Value Problems) and MATH 418-3 (Partial

Differential Equations). The contents of the existing MATH 413-4

(Ordinary Differential Equations) has been modified to bring about the

proposed MATH 415-3 (Ordinary Differential Equations). Thus, the sylla-

bus for MATH 314-3 should contain the following additional statement

under prerequisites:

'Students who have obtained credit for MATH 414-4 cannot

receive credit for MATH 314-3. However, students who

have obtained credit for MATH 413-4 can receive credit

for MATH 314-3.'

Mr. N. Heath has informed me that your concern about MATH 404-3

i115

been

taken care of.

None of the new proposed courses are scheduled for Fall 79. However, we?

have already scheduledthe following proposed courses for Spring 80 and Summer 80:

?

SPRING 80:

?

SUMMER 80:

MATH

251-3,

Calculus III

';.TE

251-3, Calculus ?

III

MATH 426-3,

Intro. to Lebesgue Theory

ik ?

TL 252-3,

Vector Calculus I

MATH

439-3,

Intr. to Algebraic Systems

MATH

272-3, Intro, ?

to Prob. ?

Stats.

MATH

444-3,

Topology

MATH

314-3,

Boundary Value Problems

MATH

342-3,

Elementary Number Theory

MATH

440-3,

Galois Theory

It shall be a real hardship for us to undo this scheduling at this late stage.

If, however, SCUS does not have enough time to approve the entire rnth package,

)en I would appreciate t if at least

the

above listed courses are apPT:ved.

Thank you.

S

---

4

?

.

311"ifl1'

r1tA5rJLt UINIVLI(SflY

MEMORANDUM

To .

?

Mr.

Registr

gista

?

.

i's

:

......

ai

•

?

Secretary

..

to SCUS

?

?

. ?

Undergraduate

athematics Department

Studies

Chaian

Committee

................... a

Sub1ect.. ?

.çps...

..9.P.9SLS ?

I

Date.....

?

30,

?

979

COURSE O'ERLAP AND LIBRARY RESOURCES

Enclosed are copies of memos sent to other faculties, in corliance

with course overlap regulations, informing them of those of our course

i3PO

.

i1s

that are soon to go before SCUS. There were no responses from

the other facu ies indicating any course overlap.

Alsc closed is a copy of a letter to Mr. Larry Thomas, Library,

requesting confirmation that the Library resources are adequate in the

araas covered by the new courses. Mr. Thomas provided a written state-

ment that the Library collection is indeed adequate and this statement

was passed along to the Dean of Science Office.

I hope the provision of these memo copies will satisfy the needs of

SCUS.

(yai

rE1EL1Ji

U 63 11

?

A. C.

AR

PL

I

S

OFICF

G.A.C. Graham

cc: Mr. Nick Heath

?

. ?

DESK

Dean of Science Office

.

.