C
I
O
N
M
P U T E R S
T E A C H I N G
Computing
1979Stateof the Art Reportof Instructional
Mathematics and Statistics
HerbertL. Dershem,HopeCollege
CONDUITSeriesEditorfor Statistics
DavidA. Smith,DukeUniversity
CONDUITSeriesEditorfor Mathematics
l}coNDUrT
Contents
l . Introduction
Backgroundand Cunent Pattems
3. Exarnplesof the Use of Computing in
Mathematics
4. Summaryof Survey Results
c. Prospectsfor the Future
6. Infonnation Sources
Materials of lnterest
I
I
3
6
l1
22
25
29
l. Introduction
This report
is prinarily
concerned rvith the nontraditional
use of computers in undergraduate
courses in mathematics anal statlstics.
For reasons explaineil befo$r, vre make only passing mention of Lraditional
compuLer use in courses in numerical anafysis, computer science, progiamming, operations research, and
other areas for which computing is essentially
mandatory.
Except for statistics
courses, the alominant computer activities in the courses under consideration
are probl em-so1ving,
sim(A great deal of progranuning
ulation,
and learning to progtam.
goes on in loiver-division
instruction
mathematics courses not
explicilly
labefed as programming courses.)
Tn statistics
courses, the dominant activities
are data analysis and problem(much of the latter
presumably dependent on the former).
solving
Most of this computing is being alone on largeto mealilrm-size
machines in an interactive,
time-sharing
mode with programs lvritten in BASIC oT FORTRAN.
In the recent past, the number of computer users among mathematics faculties
has increased significantly.
Receptiveness to
the use of computers in traditionally
computerless cou!ses has
increased even more, but a number of barriers
have prevented
translating
this heightened interest
into actual use:
obsolete
or awkvrard hardware and softwaret
a budgetary crunch tha! prevents keeping up with new developments,
even when costs are declining;
lack of time for developing new materials and lack of
reward for those who take the limer and perceived lack of class
(Subtrac!ing anytime for adding anything to existing
courses.
thing is seldom considered. ) Then there are barriers
that are
never mentioned on survey forms, such as ego damage suffered by
an instructor
\rho finds that his or her own training
is inadequate or outmoded and fears (correctly)
that stualents will pick
up computing faster
than he or she.
In contrasl to the situation
only a few years ago, there are
no!r' effective,
transferable
m a t e r i a l s t o s u p p o r t c o m-D
a nu dt e r u s e i n
a wide range of mathematics anal statistics
courses,
the process of produclng such materials has become more ralionaf
and
sophisticated.
Hov/ever, av/areness of these matelials
on the part
of the faculty
using computers remains very fow, as evidenced by
the fact that, most of them continue to prepare their
own materials.
Given t'he fact that the 1evel of use is not anvlvhere near
(of potential
saluration
use, not of existing
facit-ities),
one
can confialently ptedict
continueal lnctease of use, subjecL to the
same constraint.s that, have operated in the recent past, especially budgetary constraints.
Awareness of materials wilt continue
to grow, due lo moalest marketing
efforts,
conferences,
and
reporte
in journals
that are not specifically
computer-or i enteal .
Microcomputers
where alepartments
will
have an effect,
especially
can find a vray to acquire t.hem as office
equipment or woral
processors, but relalively
few mathematicians are presently
aware of ttreir potentia1
The more innovative
anal soptristicateal
developments in technology anal courseware have had little
impacl on the vasl najority
of campuses, and ttrat will
conlinue to be the case, especially
where computing facilities
are orienteal towaral aalministralive
or
Bu1:there are many
research neeils, or worse yet, nonexistent.
br.ight spots on the ?rorizon suggesting an inuninent dawning and a
emergence of inexpensive,
sunny tomorroiv, !r'ith the simultaneous
and effective
haralware and transferable
sbftware,
easy-to-use,
and of heighteneal interest
on Lhe part of the mathematics
faculty.
2
'
2. Background and Current Patterns
The decade of the sixties
was a time of revolution
in the
mathematics curriculum
of primary and seconalary schooLs.
Concurrent with these changes was a quieter
reorganization
of the cur-
yi^'rl"m ir .dl ladac ah,i _'iversities.
The most eftective
voice
for change jr the colIege mathe-atics
curricu.Lur in the past 15
years l^as been the Corunittee on the Undergraduate
Program in
(CUPM) of the Mathematical
Mathematlcs
Association
of America,
This committee
was charged with
the responsibility
for making
recommenalat ions for the improvement
of college
and university
mathematics
curricula
at all
leveIs
and in all
educational
areas.
This group issued periodic
reporls
on various
areas of concern,
including
a 1965 report
entitled
A Generaf Curriculum
in Mathematics for colleges.
Tnis report. whichhadwidespreadandex
;T;6-f;ElnE;aE-Gn-
the mathematics programs in the u.s.
colieses
curriculum,
and universities,
undertook to identify
a centlal
beginning with calculus,
that would serve the basic needs of
those desiring an undergraduate ealucation in mathematics.
Many
col leges revised their course ofIerings in directions suggesLed
by this report.
Although the presence of computers was being
EelL in Lhe curricula o.[ other disciplines,
t h i s I 9 6 5 C U P Mr e p o r L
did not address itself
to the relationship
of the computer to
education in mathematics.
Apparently
it ldas the view of experienced teachers and researchers in 1965 that the computer. had ]itt]e
to
to contribute
lhe classroom.
Nevertheless. scores of individuals
were experimenting with the conpuler to augment instruction
in mathematics,
prinarity
During this period, the
in statistics
and calculus,
National science Foundation, through its office of Computing
played a major role in promoting the development and
Activieies,
use of computer-based instructional
materials
in mathematics by
projects,
funding computer-ori ented curricular
summer institutes in computing and mathematics for college teachers, and a
number of farge curricufum development projects of which mathematics was a part.
The number of apparenLly successfuf trials
of compuLer-based
instructional
materials is now fairly
l a r g e , a n d C U P Mh a s s i n c e
published
and
t\4to reports
dealing \,tith mathematics instruction
T
b
e
f
i
r
s
t
f
o
r
computing.
of these reports,
Recommendations
an
Undergraaluate Program in Computational Mathematics (CUPM, 197f),
ciences that
combines courses in mathematics,
computer science,
and comprltational mathematics.
This suggestion grew out of the committee's
basic recommenalation that "mathematics alepartments should experiment \rith innovative
undergraduate mathematics programs which
elphasize the construcLive and algoriLhmic aspects of nathenatics,
anal which acquaint
studenls with computers and with the
uses of mathematics in computer applications."
The seconal
repott,
Reconnnendations on Unalergraduate Mathematics Courses
Involvinq
computinq (CUPM, 1972), tecognized 1:he potential
influence of l.he computer on the basic undergraduate
courses in mathematics, and proposed changes in certain traditional
courses, as
well as the introduction
of some new couases alesiqned to take
advantaqe of the computer,
Perhaps the first
subsLantial siqn of growing acceptance of
these ideas was the symposium on "The Influence
of Computing on
jointly
Mathematical
Research and Ealucation,,
sponsored by the
American Mathematical
Society and the Mathematical
Association
of
America in connection \rith theii
annual summer neetings
in 1976
in Missoula, Montana. Subsequent national and regional meetings
of both AMS anal MAA have includeal a variety
of speakers, panels,
and speciaf sessions on computer-related
topics,
including
the
use of computers in unalergraduate courses.
A more recent stimulus to qrowlh in this type of computer
use is the report of a National
Research Council conunitlee
( A M T R A C )o n t h e r o f e o f a p p l i c a t i o n s
in Lhe underqraduate mathematics curricufum.
This report may stimulate
the CUPM-type
6fF^r+c ^f
5r+Lough it is considerablv less detailed
than any of the CUPMdocuments.
Among its many recommendations
i c
+ha
f^l
I ^L'i
nd
-
[We recoinmend] "that every mathematics major acquire early
in his or her colleqe career a basic competence in computer
programming so that he or she can desrgn algorithms
and write
programs of some complexrty.
This competence may often besC
be garned bv requiring
a course in computer sctencet \rhere
Lhis option is used, Lhe requrred course should be designed
so that many of the examples anal exercises
relate
to the
material of the studentrs mathematics courses,
Further,
[we
recommendl that, to t.he extent possible,
the student's computing kno\,rledge be utilized
in appropriate
mathematics
courses.
An additional
factor
beating on the trenal in curriculum
c h a n g e ( n o t n e g l e c t e d i n l h e A M T R A Cr e p o r t )
is rhe changing
employment piclure
for mathematicians.
There is nov/ a cleal
recognition
that a mathematician
ivhose training
is exclusively
theoretical
and abstract
is not as enployable
as he or she was in
formel years.
As a consequencer college teachers are now more
receptive
to changes in the curriculum
that \doulal provide for
different
avenues of ealucation within
the mathematical
sciences,
programs that ealucate in the applications
especially
of mathematics to other disciplines,
ot programs that offer a computer science emphasis.
Thus, there is now a favorable
climate
for the
introduction
of computer-oriented
instruction
into t,he curriculum
on a broad scale.
Some of the earfy experiments with computer materials
for
the mathematics classroom have matured into publications
\no!
necessarily
of lhe traditional
textbook l]ype) and are listed
in
our bibliography
below.
Others have run their
course and died,
including
some very ambitious and briefly
successfuf ones, such
as CRICISAM. It is sti1l
l:he case that most of the supplementary
materials
for tradilional
courses never leave the sile of origin.
but it is nov/ possible
t.o find good materials
in some lransfer(This
able form across a broaal range of the standard courses.
was not the case only a few years ago,)
Nevertheless, a majority
of the mathematics instructors
willing
or eager to use computers
are stil1 writing
their own materials,
in some cases due to their
ignorance of available material s.
There are several reasons for this gap of information
about
(1) The farge-scale,
materials,
grant-supported prononprofit.
jects have usually not been funded for massive advertising
and
(2) Commercial publishers have been ambivamarketing efforts,
Ient about investing
in computer-related materials.
On the one
hand, they would ]ike to be one jump ahead of the competilion
profitable
\,/ith ne\rly emerging and potentially
materiafs;
on the
practices
olher hand, their
conservative
cause thenr not to pubIish in new areas unfess they get rave reviews and to stop adver(Rave
tising
anything thal doesn't show a profit
very quickly.
reviews and quick profits
are almost incompatibte with published
materiafs in newly emerging areas due to the conservative practices of educators when it comes to curricufum change.)
(3) FlnalIy,
the widely read journals are just no\d catching up
with computer- induced changes in the curriculum,
Computer-wise innovators
are now developing
naterials
that
depend on and benefit
from new technologica]
developments: microcomputers, graphics alevices, voice synthesizers,
and so on,
At
the same time, large numbers of mathematics teachers are just
beginning to fe.arn about their First computer, wqich is Iikely Lo
be small, shared with many users, and capable of communicating
on-Ly via punched cards or teletypes.
As we predicted in our previous report, many schools are focked in to obsolete computing
sysle-rs by a budget crunch thaL does nol even permit soending a
few thousanal dollars
for a modest microcomputet
system (although
some instructors
are buying their
own and sharing with their
students).
There are probably nany fewer campuses no\i/ \^rith no computer system at all,
but the technological
and development'al gap
between the "haves" and lhe "have-nots"
of the computer world is
actuallv widenino.
3. Examples of the Use of Computer in Mathematics
We 1ist. here some of the ways computing is being used in
mathematics and sLatistics
courses.
This list
is not exhaustive
anal the examples are not necessarily
the besi of their type,
Some are represented
by published materials
anal/or tr.ansferable
software, and others exisL only at the site of orLgLn at Lhe present time.
l/here materials are available,
these are listed
in
the bibl iooraDhv.
Problem-Solving
Problem-solving
is the dominant mode of computing in mathemalics courses, and examples may be found throughout
the materials ]isted in the bibliography.
We will
cite only one example
of a use that \,/as rare a few years ago and is becoming standard
in an otherwise conventional course.
There is a growing consensus that the standard undergraduate
course in orclinary differential
equations should introduce the student to numerical as weff
as analytic methods of solution.
While most instructors
do not
spend a great deal oF time on rh-is (many sti]l
view the whole
idea with a great deal of suspicion),
new differential
equations
texts (for example, Hagin) contain some materiaf on numerical
methods that may range from a simple discussion of Euler's method
up to fourth-order
Runge-Kutta and predictor-corrector
melhods.
For those using texLs lacking chis materjaf or noc going far
enough wilh il,
there are now gooal supplementary materials
available (for example, Van lwaaralen).
Illustration of Concepts
It is now routine
to actually
evafuate Riemann sums when the
integral
is first
introduced in the calculus course.
This is a
muctr more usefuf way to i1luslrate
the concept than the traditional,
but clumsy, digression to cover formulas for sums of
polters, \dhich leads to the worst possible
integer
way to find the
area of a triangle.
Simple Riemann sums can be evaluated using a
calcufator,
but more complicated ones become tedious because of
the function evaluations.
Thus, access to even a sma1.I computer
is verv helpful -in keeDing the calcuLatioFs €rom getting in the
way of unde.stardind the integral
as a number,
AnothFr
pramnlF
nF
.nn.Fb-
rFihTdr.a--nt
in.ir.llus
is
the
observation
that the location
of roots by interval -ha] v i ng is
proof of the Intermediate Value fheorem (see
also a constructive
Statistical Packages
Tkto approaches to the implementation
packages
of statistical
are illustrated
L'y the Tanis package and by Minitab.
The Tanis
package consisls
of a set of FORTRANsubroutines
and an accompanying laboratory
manual containing
exer.cises the stualent can
carry out on the computer through the use of t.he subroutines.
The exercises
are intended for use in a mathematical
probability
.
l
h
^ computer
and statistics
course at the junior-senior
levFL.
is used in these exercises as a l]ool to simulate random experiments anal to produce computational
graphical
analyses of the
results.
fhe subroutines are written
to be used in either a
proorams
batch or an interactive
environment with student-lvritterr
that cal l them.
In contrast,
the Minitatt, approach is to provide the stualent
with a separate language to generate, anafyze. and display statistical
data.
An accompanying hanalbook is provided that introduces the features of the language and contains exercises making
plots,
use of simufation,
and techniques to illustrate
statistical concepts and data exploration
methoClology.
Like the Tanis
package, Minitab
is written
in FORTRANand is available
in both
batch and interaclive
modes. Minitab, however, requires no prior
programming knowledge or computer experience on the part of the
student.
Data Analysis
The three most conmonly used data analysis packages are
SPSS, SAS, and BMDP. Each of these packages consists of a set of
rouLines for daLa enLry. data manage-e1L,and statistical
analysis.
Each also provides its own language and a user's manual.
The manuals present Lhe syntax of the Ianguages and alescriptions
of the procedures that are irplemenLed.
Computer-Assisted Instruction
In proportion
to the time and effort
expended in rnirnicking
techniques
successful
in other fields,
computer-a s s i sl:eal in(CAI) in college-level
struction
math has not become common.
one reason has been the limitations
of physical facilities:
teletype-Iike
devices lvith low transmisii6n
speeals and limited
character sets are noL well suited Lo communilating nachenatics.
Another reason is that the concepts encountered 1n
courses beginning lvith calculus
aie not easily
taught or
learned by rote alrill
techniques,
although these may be ver:y
effective
for acquiting necessary computational skills.
A
good example of useful CAI materials
at. the precalculus
1evel
is the package developed recently
at' the University
of
Tennessee
at
f^r,lrill
:h.l
Chattanooga
6r^.+i-a
by
in
Richard
w^ri^rlc
Detmer
+^6i-c
in
and Clinton
AldaL.'
Smullen
ih^lrrdind
word problems,
An example of materials
being
aleveloped
at lhe
calculus
level is the package (not yet avai.Lable) by Frank Anger
(Their proand Rita Rodriguez o' the University
of Puerto Rrco.
grams are in BASIC for an HP 2000/Access
presystem with
text
p
r
o
g
r
a
m
'
s
sented to the student
in Spanish.
The
REMark statements are in English,
however. )
A number of systers
have bee.1 desiqned
For tl^e developnent
in mathematics.
of CAI materials
In this
appfoach,
the focus is
than the finished
materon moving the development
system rather
D
e
s
c
r
i
p
t
i
o
n
s
t
h
e
f
o
l
l
o
r
v
i
n
g
e
x
a
m
p
l
e
s
m
a
y
b
e
f
o
u
n
d
in the
ials.
of
p
r
o
c
e
e
d
i
n
g
s
:
(
M
a
r
k
I
a
T
H
D
O
C
c
h
r
i
s
t
e
n
s
e
n
,
c
e
o
r
g
i
a
T
e
c
h
)
, and
CCUC/9
(
D
o
u
g
A
i
m
s
,
A
I
t
o
D
i
s
t
r
i
c
t
,
C
a
l
i
f
o
r
n
i
a
)
.
Palo
School
OuATE
CAVCATC
Detmer and Smullen have
CMI system for their
algebra
-s ) ^s L e- m
.. ,
pdue\r.
afso developeal a simple but usefuf
course in which students
are seff-
Ll n- l- - -w
tha
i neF
n,^F^r
^r
'l:t\
---
r. n a n a g e r
uses Lhe computer.
I4ast-ery LesLs are generaLed by the
actually
SLudents requesL tesLs or re-Lests
computer and kepL on fiIe.
whenever
they are ready,
and the tests
are graded inunediately
by
a lab assistant
using a computer-prepareal
answer key.
Alt
progress
record-keeping
and pacing of the students'
is handted by
on-Iine
data files.
A similar
system has been described
by W.J. Smolinski
of the
Llniversity
of Nev/ Brunswick in ERM 10 (19?8, pp. 56-63),
This
systen was alesigned for an efectrical
engineering
course,
but
would be adapcable to any quantitative
course.
The pr-LncipaI
package and the Detmer-Smullen
difference
between this
system is
thaL Lhe Eests are generated on-l ine when tl^e sLudent -equests
parameone at the terminaf.
The instructor
identifies
certain
F-.-
i-
Fh-
Fh^r
ara
aYnina.l
hlr
thus individualizing
the test.
The test is printeal for the student at a hard-copy Lerminal.
Numerical anslvers are identified
the student reby parameters, anal rvhen the test is finished,
program
the
computer
and
enters
his
numerical
anslvers at
enlers
the terminal.
Grading and record-keeping are r\en done by the
computer.
Corrputer-assisLed LesL construcEion (CATC) can be very useful even if the course is not self-paced
and not computermanageal. For example, Mark HaIe (University
of Florida)
has
developed a problem generator for differential
equations.
Graphics
While graphics
equipment is not yei: available
on most co1fege campuses, many experiments are under way lo exploit
this
medium for the obviously
visual
aspects of many mathematics
courses.
These projects are much too diverse and systemdepenalent 1:o categorize
neatly or summarize briefly,
but most
involve a "super blackboaral" approach, some afso incorporaling
motion.
For examples. see the papers by Gerry Porter (University
of Pennsylvania) and Elliot
tanis (nope College) in t.he NECC/79
Proceedings,
Another approach that has oeen tried
is Lo Lse corrpuLer
graphics
(for example,
to design and produce static
materials
customized
overhead transparencies
or handouts).
See the paper
by K. Joy, J,R. Warner, and R. Yuskaitis
in the CCUC/8 Proceedings for an example,
Finally,
lvhile v/aiting
foj: the graphics
equipment Lo arrive,
character graphics (fine-printer
or low-speed terminal)
is
a feeble but useful substitute.
Every computer system has programs available
for character plots of simple functions,
For an
example of three-dimensional
character graphing, see Smith's
Surface package.
Networking
The primary net$/orking service supporting college-level
education is EDUNET. A node of this network provides access by
Ioca] phone call lo many large, sophisticated
computer systems
and a lot of packaged software.
For example, Shapiro's TSCT
materials
are available
from the Llniversity of Minnesota via
packages such as SAS and SPSSare avaifable
EDUNET. Statistlcs
from a number of suppliers.
The network also provides a way to
examine materiafs,
such as those from CONDUTTb
, efore decidinq to
purchase them.
There are some risks and frustrations
associated with using
a remote system, although EDUNET is doing everything
possible
to
assure that help is available.
One of its early offerings
was
the MACSYMAsymbolic manipulation
systen from MIT, a very po!,rerfuf tool fol advanced mathematics and applications.
Unfortunate1y, the version MIT offered was problematic and not maintained.
EDUNEThas since withahaq/n this service,
br.tt there is some prospect that a supported version of I4ACSYMAv7i11 become available
(A good version of MACSYMA
o n E D L I N E Ti n 1 9 8 0 .
is available via
ARPANET for those institutions
that qualify,
or by long distance
phone call to MIT, piohibitively
expensive for mosL potential
users, )
Wond Processing
The plimary obstacle
in mathto compuler-based text editing
deematics has been the linited
capability
of typewriter-like
formulas anil sl/mbols.
vices for proalucing acceptable mathematical
'rith dot natri)a alevices anal programNow it is becoming possible,
Barry MacKichan and
mable keys, to overcome this difficulty.
are using Pascal on a
Roger Hunter (New Mexlco State University)
processor that $ti1t
Terak computer to develop. a nathematical
telt
notes, ancl so
make it possible
to wriLe and edit papers, leclure
proper
sTilh
mathematical
spacing
anCI
characters.
forth,
t'he
lo
4. Summary of Survey Results
As was the case wi1-h the 1978-79 CoNDUIT surveys in other
survey was in three
disciplines,
the mathematics/statistics
parts:
The survey forms vrere
department,
faculty,
and course.
that they fifl
out anal resent l:o department heads requesting
forms anil pass on to appropriate
faculty
turn the departmental
forms.
The latter
forms vr'ere
membels lhe combined facufty/course
afso sent alirectly
to approximately
10O faculty
members known to
using computers in instruction.
In all,
8O0 departbe actively
mental forms and 961 faculty
forms reporting on 2,050 individual
courses were returned,
Delmrtmental Profiles
Most of our returns
are from departments with Mathematics or
The few from alepartments
Mathematical Sciences in thei! titles.
and/or computer science are all from large schools.
of statistics
of these departments are shown
some demographic characteristics
in table 1.
percent of the tlepartment heads responaling reportetl
Fifty-four
alepartments over the past
increaseil use of lhe computer in their
two years, 43 percent reported no change, and only three percenL
Three out of four expect to see increased
reported a decline.
use over the next two years, and less than one percent foresee a
decrease.
lfhere there has been an increase in use, the alominant leaand changes in lhe
sons have been demand by students and faculty,
use (and growth of use)
computer system.
The factors ]imitinq
These facare seen to be lack of funds and ]ack of equipment.
in smaller schools anal in schoofs where
tors are most important
(But most of the schoofs where
there is litt]e
or no use now.
all or nearfy a]l of the faculty use the computer are also
Lack of funds is also the major reason cited by those
small.)
gro\,rth, lrhi1e equipment changes anal increaseal
who see no future
ihrFrFe,
FrF
Fv^a.+F,i
t^
hp
l-ha
nrivird
.ny.as
hw
fhose
\^rho dO
see gro\r"Lh.
colPast increases
tend to be concenlrateal
in the four-year
leges and universities,
and stagnation
is concentrateal in the
Future growth
schools that do not offer a bachelor's degree.
appears to be most likely
in depaltments that offer a bachelor's
or master's as their highesl: alegree, much less 1ike1y in the departments granting Ph,D.'s anal in the junior colleges'
11
Less tl.an tlro percent of alepartment heads identifieal
micros
ag a source for future
change, but' to a perGon these tesponalents
_ expec€eil increased computer use.
TABLE 1
Departmental
Demographic
Category
Highest
gchool
Profile
Respon se
degree
enrolln6nt
Department
enrollment
Percent
None
Associate
Bachelor's
Master' s
Doctorate
39
13
1t
1-1,000
I ,001-5,00q
5,001-15,000
> r5,000
4L
20
L3
1 1 - 1 00
1 0 1 -5 0 0
50 1 - 90 0
> 900
9
18
> 2 0
27
20
16
FfE faculty
Number of faculty
usrng comPuters
Extent
of
use
o
I
2
3
4 or rnofe
None
Infrequent
Moilerate
Exlensive
25
L9
18
25
23
39
7
Faculty Profiles
of our 961 facull:y responalents are shown in
Characteristics
about
members ans\^/ering questions
Of those faculty
table 2.
yeafs,
pasl
trvo
in
the
increaseal use
change, 66 percent reported
p
e
r
c
e
n
t
r
e
D
o
r
ted
f
o
u
r
lO percenl reported no change, and only
p
e
r
c
e
n
t
r
e
s
p
o
n
d
e
n
t
s
see
o
f
l
h
e
s
e
Seventy-three
decreased use.
years,
percent
see
no
l:wo
26
increased use in the next
further
t
h
e
r
e
has
w
h
e
r
e
p
r
e
d
i
c
t
d
e
c
r
e
a
s
e
.
p
e
r
c
e
n
t
a
change, and only one
o
f
l
v
e
r
e
l
a
c
k
f
a
c
t
o
r
s
t
h
e
l
i
m
i
t
i
n
g
been a decrease ol no change,
change
no
a
decrease
or
lfhere
money and lack of support staff.
the reasons most often cited were satis expected in the future,
The primary reasons for
and/or interest.
uration of facilities
past
course
changes, hard\,/are,
v/ere:
increaseal use in the recent
gro!r'th
field,
in that or.der.
in
the
student demand. and
software,
!o
be
hardware,
forces
appear
the driving
increases,
Fo]. future
number of
anal
the
growth
t]he
field,
in
student demand,
software,
order
different
(These
in
a
somev/hal
are
rated
factors
stualents.
i
s
s
een
w
h
e
r
e
h
a
r
d
l
t
a
r
e
s
t
a
t
i
s
t
i
c
s
,
in alepartments of
by faculty
important'
as
more
and
soft$rare
)
matter
ai a much less important
are
gro\,rth
use
in
compuler
factors
timiting
The most important
TABLE
Faculty
of
Schoof
Demographic
Profile
Response
CaLegory
fype
2
school
enrol lment
Acaalemic rank
University
I9
4T
4A
r-1,000
1 ,001-5, 000
5, 00I-15 , 000
> 15,000
No response
16
39
30
13
3
Instructor
Asst. Professor
Assoc. Professor
12
27
32
D-^+-.-^-//.r""i-
)L
Two-year
other
Numbet of courses
with computing
P e r cen t
0
I
2
3
4 or more
5
'1
29
25
2A
18
seen to be: lack of time, equipment (not so important to statisticians),
funds, software, support, training
of students (more
important to statisticians),
and acaalemic rewalds, in that order,
Over half the responilents mentioneal lack of time, and jusl under
one-fourth
mentioned lack of reward.
riafs,
We will
see in lhe next section that use of published mateexceDl in the categories ot progrdnning, nrrerical a-laIy-
cic
rh,n
c^iah^a
i<
a+i
ll
:r
pa-rr
r
l^!.'
l6!/el
.
I4rhen
asked what materials
needed to be developed,
the order of responprogramming exercises,
ses was: problem-solving,
sinulation,
dril1
and practice,
tutorial,
and data analysis,
Foi those in
statistics
departments,
the order was quite
different.
Over
Lhree-fourths
cited
data analysis,
while
simulation
anal problemsolving
were a distant
second and third,
and none of the other
categories
received
substantial
support.
It is worth noting
(a fifth
here Lhat only a lhird
of the respondents
in the case of
statisticians)
were aware of the existence
of CONDUIT, and only
six Dercent had used anv CONDUIT materials.
It \,/il] be clear
from the bibliography
that
rnany of the materials
"neealeil" alreaaly
(CONDUIT's and others).
exist
Ho\^rever, it is not clear \,vhether
perceptions
our respondents
v/ere really
expressing
of need or
of their
own patterns
iust
of use.
Course Profiles
A breakdown of the 2.O50 individual
courses reported
shown in table
3,
Mathemalics here means evervthinq
not
in the other
caleqories.
is
included
TABLE 3
course
Category
Number
'7
20
293
Mathematics
Stati stics
q^i
a^mn,r+ar
Numerical
Other
Breakalov/n
an-6
Analysls
( unidenti
fied
)
401
151
't4
Percent
35
I4
13
t1
20
7
Publ i shed
Material s
77
156
104
411
3
Several observations
dvef
40
ncr^F.t
n-
l-\F
about table
.^rlrqFc
3 are in
rahdrta,i
^ra
order.
-ha
in
First,
afaas
oT
.om-
puter science, computer programming, and numerical analysis.
\vhere computer use is no1: only manalatory but essentially
wellestablished,
well-understooal,
and ivell-supporleal
by text materiafs.
In schoofs that are large enough to have a separate computer science department, these subjects are nornalfy among its
(placement of numerical analysis is subject to 1oca1
listings
politics),
but in most schools they are still
taught in the mathematics alepartment, if al all.
CONDUIThas never assumed any
for distribution
ln these areas,
responsibility
of materials
because none seemed to be needeal, our emphasls has been, anal
continues to be, on traditional
mathematics and statistics
ne\^7
courses in vrhich use of a compuler is still
a refalively
idea.
Thus, except for a brief
cofiunent about the ma]-erials in
tlvo
use in computer science courses, we will
focus on the first
in table 3.
A further
breakalown of the maLhematics
categories
courses into traditional
cateqories is shown in table 4,
TABLE 4
Mathematics
uourse
trt
Courses Using
Number
Le
CalcuIus ( singl e-vari abl e )
Linear Algebra
Liberal
Arts Mathematic s
Precalcuf us
Finite
Mathematics
Cafculus (mul tivariable )
nnar^+
i ^nc
Mi+hamat
T i ha:r
Dacar
i -rl
'^}l
M^Aal
DY^dr:hmi
i nd
Ahc+r>-+
A I dahr:
r!r
Aalvanced
Sl.mbol ic
Totals
/n^^^r
69
69
6A
46
32
30
29
h^
Teacher Education
Engineering
Mathematics
Number Theory
Business Mathematic s
Probability
.6^n6+
L94
'7'7
^^r,
CaI cul us
Logic
20
13
11
7
6
4
3
2
12A
Computer s
Perc ent
ll
l0
10
9
6
4
4
4
3
3
2
2
2
1
1
Publ i shed
Mater ia I s
l1
9
4
4
4
r2
2
3
2
I
1
1
r00
7'7
The following
patterns
of computer use and materials
emerged
from the course survey.
As noted already,
for mosl courses ttte
only computer-rel ated text used (if any at all) was a book on
programming.
About 50 percent of the respondents reporteil
using
prepared
their
olvn
notes, another six percent somebody else's
notes.
The prevailing
types of student activities
were problem(these
solving,
then simulation
anal learning
to program
two about
even), then drill
and alat.a analysis (a1so about even).
The primar.y activity
for instructors,
if they useal the computer at all,
was alemonstrations.
Most computinq in Lhis field
is being done on large mainframes and on minicomputers,
vith
the mainframes holding
a stight
edge (not as large an ealge as for all disciplines
surveyed).
Of
course, the mainframes serve more users and tend to be locateal at
the larger
schools,
so many more students are using large compulers than small ones.
The use of both microcomputers
and programmabfe calculators
is still
very sma]I in mathematics courses.
The dominant mode of use for both maxis and minis is interactive,
with 65 percent reporting use of hard-copy terminals and 58 perontv .q nar.Fnr rFn^r+ use of
(
p
u
n
c
h
e
d
p
r
o
c
e
s
s
i
n
g
batch
cards and line printers)
and 17 percen!
report using graphics display terminals.
Of course, the batch
processing is being done largely on mainframes ancl with Iarger
numbers of students per course.
The ]anguage used most often i€
BAS]C, by almost a two to one margin over !'ORTRAN, lvith a]l other
Ianguages far behinal.
The most populai. of the other languages is
APL, and it is used by less than l0 percent,
APL and Pascal are
in.use primarily
at schools with less than 10,000 students, anal
PL/I is found primarily
at schools with more than 10,0O0. As
with large computers and batch processing,
the use of FORTRANis
understated
in terms of number of students,
because it too is
associated vlith Iarger numbers per course.
The level of comput-inq acLiviLy by studenLs is greatest for
freshmen (nearly half of the courses reported
are al: the freshman
Ieve1) and decfines rapidly with the upper-Ievel classes.
The
use of plob]em-solving
also declines lvith student advancement,
and simulation
lakes over as the alominant mode in the junior
and
y
e
a
r
s
.
senior
Tutorials,
drills,
and learning to program are
activities
that are heavily concentrated in the freshman yea!r as
one \roulal expect.
These patterns
of student use are the same
regardless of the size of the school, but class size has a alefinite bearing:
simulations
are somewhat more likely
with smaller
classes,
and tutorials
and drills
some\dhat more likely
with larger classes.
DeronsLration, tl^e toprarking Lype of instructor activity,
cuts across differences
of school type and size, 1eve1 of course,
computer type, and language used.
However, alemonstralions
are
l a c a
l i k a l l ,
w i + 1- i
-1r cc
ci zac
^!'6r
-,
-JVIoUS
rea-
(The technology exists for large-sca1e alemonstration s , but
sons.
it ntould be expensive to equip every classroom.)
Other instruc-
management, test generasuch as inslructional
tor activities,
are concentrateal at the freshman feve1,
tion,
and test scoring.
and on mainframes with FORTRANas l:he
with large class sizes,
u|Jer
d urrr9
fdrrguo\jc.
courses showeal about one-fourth
class sizes for the reported
in each of the ranges 6-15, 16-25, and 26-50, and half the remainder with five or less, anal half over 50. Almost 70 percent
and most of
of these courses v/ere one semester or one quarlef,
For 80 percent of the colrrses, the
the resl not over one year.
conputer supported noL rore than 20 percent of Lhe studenL's
computer use
Lo optional
of required
time.
However, the ratio
was almost two to one.
Computer Use in Statistics
courses is quile conunon. The
Computer use in statistics
predominant application
is the use of the compuier as a computational. tool to allow the stualent to avoial tealious, time-consurning
interesting
anil to permit the analysis of lalge,
calculations
is indicated in the surThis widespread application
data sets.
coLrses usinq
vey by the fact that 86 percent of the sLatistics
and 74
the computer involve tlata analysis as a student activity,
In fact, many courses have been
percent invofve probl em-solving.
Ievel lhat are devoted enat the upper untlergraduate
introduced
tirely
lo the use of the computer as a toof in data analysis.
courses tliffers
The pattern of computer use in statisLics
AL shaLler colleges the
according to the size of the school.
written
software or a package protentl to use locaIly
faculty
univelsitles
one
At the larger
vided by the computer vendor.
packages
marketeal data analysis
or more of the commercially
and are useal by the students.
are available
indicate that there is approximaCely
The survey results
equal usage of lhe three mosl popular packages, Minitab (40
The BMDP
courses), sAs (38 courses), and sPss (36 courses).
Minilab has more of
package \^ras reported
in use in f7 courses.
and over 70
than the other three,
orientation
an instructional
The other three
percent of its use was in undergraaluate courses.
and about 60
data analysis,
are intenaled for res earch-oriented
percent of the courses using these packages !"ere graaluate
courses taught in
This survey only inclualed statistics
courses.
many slatistics
departments of mathenatics and/or statistics;
and these probably make
courses are taught in other departments,
The only
software packages.
use of alata analysis
even greater
other software package reporteal in use by more than one responalent was the Tanis package (reporteal in four upper_1evel unalergraduate courses ) .
77
Cornputer-orienled,
published
materials
are used most often
packages.
with
soft\irare
Specifica]Iy,
of the 8l courses
in \rhich
published
material
v/as used, 75 used manuals for one of the four
packages
software
listed
above.
The Minitab
handbook \das used in
(83 percenl] of Lhose in ivhi c. tl^e package was used),
l3 courses
The data analysis
packages (SAS, SPSS, BMDP) all had their
manuals in use in about half
of the courses using the software.
The only computer-oriented
textbook
reporteal
in use was
Stalistical
Analysis:
A Computer Orienteal Approach by
Af i'-i and Azen.
This book Dresents statisLics
wiLh the assumppackage is available.
tion
that
a data analysis
ft was reported
in use in t.wo graduate
courses.
B e c a L r s eo f t h e c o m p u t a t i o n a l o r i e n t a t i o n o F i h e c o n p u t e r u s e
in statistics,
there is sti11 a heavy use of batch mode (42 percent of respondenls) and farge mainframe computers (73 percent).
The trend a\ray from batch toward time-sharing
is present in statislics,
but the move is slower than in many other disciplines.
Computer Use in Calculus
lus
Of the traditionaf
undergraduate
lyas the first
to have significant
' : . '
' m i h : l 6 e
i h
mathematics courses,
amounls of computing
i h i c
. c d a r r l
calcu-
' r a h a l r r h a
^ r
use here is more heavily orienLed Eoward prob.Lem-solving Lhan for
all mathematics courses, less toward simulation or tutorial
and
driII
acLivities.
A qreaL deal of instrucLjon in programming Ls
associated with single-variable
caIculus,
very littIe
with multivariable calculus,
The pattern of materiafs in use has shifted
somenhat since
our fast survey,
The most popular computer-calculus
text (but
stilI
not in widespread use) is Smith's Interface:
Calculus anal
t h e C o - " r p u L e r( s e e L h e b i b l i o g r a p h y ) .
The onf y!-rher
texts mentioned by more than one respondent were Stroyan,
Orth, Lelnbach,
and Dorn-Bitter-Hector
, The last two were more popular in our
previous
survey, but Smith and Orth \rere relatively
neu then, anal
Stroyan was not yet in print.
The leading text in the previous
survey v/as Lhe CRICISAI'{ book, which has virtually
disappeared,
as
did several of the others mentioned last time,
Computer Use in Linear Algebra
A s q T a st . h e c a s e w i l h c a l c u l u s ,
activity
in linear atgebra is
orienteal more tov/ard probl em-so1ving, less toward simulation,
tutorial,
or dril1.
BUL much less programming instruction
is
associated with this course.
The usual type of computing activily relieves
the studenl of routine
but tedious computations
to
aflow more attention
t.o t.he central
ialeas.
The leading texts in
1a
this
area are Mc]-augtllinr Wi1liams,
of the three are CONDUIT packages.)
and Fraleigh.
(Note
that
two
Computer Use in Differential Equations
equations
It is novr almost standard for a differ.ential
unit on numerical methods,
at leasl a brief
course to include
on a
although the computation may be done (with some difficufty)
g
r
o
w
i
n
g
recognition
Lhat a
At any ra!e, there is
calcufator.
methods of solution
is a
course that incluales only analytic
selalom be ones needed in pracfraud, since these methods will
is reflecteil
in the fact that virtually
tice.
This conviction
equations being released includes
every new book on differen1:ial
A few of the better
ones are
a chapter on numerical methods.
The ones mentioneal most often by
in this bibliography.
listed
In this course, both
our respondents were Hagin and Braun'
(numerical solution of differential
problem-solving
equations)
(the same thing,
anal perin an applieal context,
and simulation
appear
appear oftenr
other activities
haps with graphical
output)
This course is a natural for graphics, and we exvery little.
programs will be
pect that the present crude character-graphics
replaced as graphics terminafs and micros become more widesplead.
Computer Use in Finite Mathematics, Liberal Arts
Mathematics. and Teacher Education
These courses are grouped together because the boundary
Typical Lopics for inclusion
in
fines beti,reen them are tuzzy.
f
j
n
i
t
e
c
o
m
b
i
n
a
L
o
r
i
c
s
,
such courses dre sets, symbolic logjc,
probability,
matrices,
elementary linear progranuning, finite
I
f
t
h
e
course is
Markov chajns, and elemenLary sLatistics.
m
o
r
e on problemFinite Mathematics,. the emphasis may be
titled
and
solvingr if Liberal Arcs, more on conceptual relaLionships
(
e
l
e
m
entary
p
r
o
s
p
e
c
t
i
v
e
patterns of thought.
If there are enough
junior
more
emptrathele may be
and
high) teachers to be taughl,
and numeration systems, anal on statistics
sis on arithmetic
(rQ's, stanines, eLc.), buL otherlrise these studenLs are Iikely
to satisfy
a requirement by taking one of lhe other types of
that is becoming stanalard
In all three cases, a nevt feature
in BAsIc) and elementary conis a unit on prograruning (usually
Some of this may be used for problemcepts about compulers.
(
b
oLh more LikeIy in finite math courses),
solvirg and simulation
lake
alrill
and tutorial
activities
and some of the freshman-level
place in these courses.
books
The most popular computer-related
Anton-Kofman, and
in l:he finite
math area are Dorn-Mccracken,
19
Williams,
and in the liberal
arts category,
mentioneal any such book in connection with
aimeal at teachers.
Smith.
a course
No responalent
specifical.ly
Computer Use in Precalculus Mathematics
The subject maLLer for these courses is algebra, trigonometry, elementary funcLions, and/or anatyLic qeometry.
They are
often considereal remedial (depending on college entrance require(basic skills),
ments), sometimes terminal
sometimes leading
tolvard a standaral calculus sequence (as the name suggests).
In
this area, the computer is much more ]ikety
to be useal for drill,
tutorial
management, and test' generation
and scor., instrauctional
ing, anal much less for problem- solving,
simulation,
or programming instruction,
The only text mentioned more than once was
Lecuyer.
But note that the primary activities
here require
soft\^rare support,
noL a student text.
Most of the software systems
developed for precalculus courses are heavily site-dependent.
One
that is not (and that sho\rs some promise of aalding something useful to drill
and practice)
is the package aleveloped by Delmer and
Smullen.
Computer Use in Operations Research, Modeling, and
Linear Progranming
These are areas that resemble computer science and numericaf
analysis
in that conputer use is often manalatory, sophisLicated,
vell-understood.
anal carried
provided on
out by packaged routines
Iarge computing systems.
These are also courses that are likely
to be taught in departments other than mathematics in schools
Iarge enough to support,
for example, a department of operations
research.
The only reason .for not aliscussing these courses separately,
as we did with the others,
is because there are so few of
them.
Computets are used in these courses primarity
for pr:oblemsolving,
sinulation,
and data analysis.
However, solving a problem in one of these areas is likely
to mean much mole than it
aloes in calculus,
anal t'he simulations
are likely
to be much more
ambitious than in a differential
equations course.
20
Computer Use in Computer Science and Numerical Analysis
to discuss these
lvhile we have disavoweal any intention
that may be
areas, our survey sholved a few things about textbooks
The most popular computer science book (at leasL
of interest.
for courses taught: in mathematics ilepartments ) is that by cear
(sRA).
There were many books in use for numerical analysis, but
the most popular ones ivere Stark, Gerald, Conte-aleBoor, and
attention
A new book that is alreaaly attracting
Johnson-Riess.
dozens of proThere were literalIy
is Burden-Faires-Reynolals.
grafiuning texts
too many to single
identified
in the survey--far
out only a few.
Computer Use in Other Mathernatics Courses
in table 4, the responses were
For the other courses listetl
growing from our prebut definitefy
few in number anal scatteretl,
is that there is a
The message for mathematicians
vious survey.
potentiaf
every course in the
use for computers in practically
symfor number lheory,
cooal materials
already exist
curriculum.
Litt]e
seems to have been done yet
bolic logic,
and probabil.ity.
with organized materials
for mode].n or abstract algebra courses.
one woultl expect that graphics
devices would be put to ltork in
geometry anal lopology
and they alreaaly have been for lhe
coutses,
for example, in advanced calculus'
study of Fourier analysis,
27
5. Prospects for the Future
Since the bulk of the materials
development in mathematics
has been for courses in the calculus/linear
algebra/differential
equations
range, the unmet neeals are nolv largely
at the lowest
and highest levels of the course spectrum.
On the one hand, much
remains to be done in the development of cost-effective
CAI, CMI,
and CATC for large enroflment, remedial precalculus courses.
On
the other hand, there is very little
available
in the way of organized materials
for explolation
of algebraic structures
in an
abstract algebra course, for example. or for the use of graphics
in an advanced calculus or beginning topology course.
An upper-Ieve]
course for lrhich a new development is under
way is linear proqramminq,
The existing
naLeriafs range from
problem solvers (a good example is the LINPROproself-contained
gram in lhe HP User Contributed Library)
producto sophisticated
packages, such as IBM's MPS. A nev/ teaching-orienteal
tion-type
package v/ill utilize
a program that does one simplex step at a
time and aflo!9s lhe student to make decisions
interactively
about
such things as Lhe focation of the next p-ivoL,
I n t h o s e a r e a s w h e r e g o o d s u p p l e m e n t a r y m a t e r i a f s n o v r 'e x i s t ,
the next phase will
be greaLer integration
of computer materials
into standatd textbooks,
thus making the suppfements obsofete.
(This has alreaaly begun, but the process is slow, anal supplements
will be wilh us for some time vet. )
The qreatest need in sLaLisEics also is tl-e tlevelopment of
Eextbooks Lhat inLegrate t\e use of Lhe computer inLo the course.
Many of the survey responalents who are using the computer in
their
statistics
courses are afso using texts that are \rritten as
it compuLersdid not exist.
Several Eextbooks have atLempted
this integration,
but none .of these has receiveal widespread acceptance.
There have been many reasons for this, but one that is
unique to the computer orientation
of the texts is that many of
the leachers of statistics
were.not familiar
enough with computers and did not have time to ]earn mote.
Exploralory data anaLysis, -ade popular by J.Id. Tukey, is
having a great impact on statistics
courses orienteal toward alata
analysis.
Ttlere will be an increased use of the computer to implement t'he techniques,
as weII as to improve stualent unalerstanding of the concepts involved.
Packages have alreaaly been developed that incotporate
these techniques,
and an enhanceal version
of Minitab will
include thenr.
22
.
t'li1]h computer costs decreasing
rapidly,
and with the coming
The microof lhe microcomputer,
many problems can be overcome.
computer also wilL influence the availability
of and practicalily
of computer graphics.
SomemaLeriafs are currenL.Ly under developmenl LhaL uLilize graphics, but trdnsferabil ity and t\e cost oI
I4icrocomouters
L h e e q u - i p m e n Lh a v e b e e n d e L e r r e n t s i n L I ^ e p a s t .
vTith graphics capabilities
will
facilitate
these applications
in
bol:h mathematics anal statistics.
The e-Cfective use o-[ CAI beyond Lhe rouLine dri]I
and praci
n
h
i
g
h
l
y
tice 1eve1, especially
conceptual courses like mathemaappears
to
depenal
better
cornmunicatlons devices than
tics,
on
teletypes
with
limited
character
sets, restricted
dilow-speeal
uncertain
response
times
from
a
time-shared
rection
of motion,
and
microcomputers can
In addition to graphics displays,
computer.
p
r
o
v
i
d
e
g
r
a
p
h
i
c
s
t
o
u
c
h
s
e
n
s
e
,
or light pen input,
already
tablet,
controllable
response time, tone generators, and voice synthefuture,
they !,r'i11 have videosizers,
and in the not-too-alistant
there
as well.
while it won't happen quickly,
disc capabilities
will
FvFnirral lv hc trrre CAI at all 1eve1s of mathematics,
An
system,
develexample that
already
exists
is ]-he VOCAL authoring
syntheoped by patrick
Suppes at Stanford,
\,thich uses a voice
(in addition
to give auditory
information
1]o visual
inforsizer
l:o the studenL,
under program contol.
mation
on a cRT display)
An application
oE this
system co a course in symbolic logic is
described
in a paper by Tryg Ager anal James MacDonald in the NECC
Proceedings.
l{e predicted
reports
that
systems
like
PLATo
in our previous
and MACSYMA vr'ouId have little
impact
mathematics
for
on college
the foreseeable
future.
With respect
to PLATO, that
is more certain
no!r, since there is Iitlfe
appropriate
courseware on the
system no\^r, and the capabilities
of the system dre r.apidly
at a fraction
being exceedeal by micros,
of the cost and under
M A C S Y M Ac o u l d h a v e s o m e v a l u e ,
total
control
of the user.
espe-ial1r/
in
ia^
-^,trcac
if
Fha
r++am^+
F^
^r^-
Tt is safe to say that it
v i d e i t o v e r E D U N E Th a d n o t f a i l e d .
won't appear on a micro any time soon (but muMATH, a much smaLfer
symbolic manipulation system, is available on several micros).
According to rumors, MACSYMAmay soon become a conrnercial proaluct,
like SPss and SAs, and it nay then be available
on a more \rialespread bassLs, including possibly on EDUNET.
At the other end of the technological
scafe, calcufator
capabilities
continue to develop, and the distinction
between them
has a
and computers is beginning to b]ul.
Ohio Slate University
project
under lvay to develop materials
to support the
lafge-scale
Another of
use of prografirmable calculators
in calculus
courses.
in the previous
report was that teachers of mathour predictions
of finding
an
ematics r^toulal continue lo nove in the direction
appropriate
mir. of the available
computational
tools to support
anal we continue to see lhat process
their
educational
objectives,
at work.
In the three years since our previous
report \ras written,
developments have been as we expected,
except that \ire did not
rea11y appreciate
how fast changes in micros $/ould come on the
scene.
Our summary of future prospects
then is slill
appropriatre
now, and we inalufge in the luxury of quoting ourselves:
"To summarize, the following
devefopments point toward a
rapid increase in the use of numerical
computation
in mathepressures
matics courses:
fraom outside the mathematics
departments; availability
of calculators
anal minicomputers;
and the availabitity
of transferable,
easy-to-use packages
for the novice,
supported by sounal text materials,
and capable of running on existing
equipnent,
-Lr may be an overstalement to cal] t.his a revolutionary
change, but it appears that mathematics courses (other than those attended by
small numbers of majors headed for graCluate study in pure
mathematics) ivill look very different
from those of 20 or
even 10 years ago.
The potentially
dramatic effects of computer graphics
probably
on the teaching of mathematics witl
no1: appear on a *idespreaCl basis as fast as their
alevelopers
prealict, primarily
for economic reasons.
Developments in
hardware and soft$/are wilI
certainly
continue.
and costs
vrill continue
to alecrease.
Ho\tever, the impact of these
probabfy continue to be limited
alevelopments wiIl
to relatively
few campuses until
there is a consensus among mathematics teachers that we can no longer afford
to do vrithout
these tooIs. "
6. Information Sources
Journals
in parentheses ate
Note that abbreviations
next section to inalicate sources of reviews.
The American
Mathematical
used in
the
(AMM)
Monthly
journal
for college
The most widely read and influential
teachers of mathematics,
Percentage of computer-related
Telegraphjc reviews especontent is small but growing.
ciaIIy
helpful
for keeping track of new books anal materi-
American Stati6tician
Computing department anal Teacher's
Statistical
Corner are
computrnq Kevlews I cK,
Reviev,/ing journal
of the Association
for computing MaI
n
c
l
u
d
e
s
r
e
v
i
e
w
s
o
f
m
a
t
h
e
m
a
tics and statistics
chinery.
textbooks
thac involve
comDutinq.
creative
computing
(cc)
Good reOrienteal towaral microcomputers
and their
uses.
Educational
applications
vievrs of equipment and software.
tentl to be more at the secondary level than al the collegiate.
as wel1.
Lots of games and business applications
Ealucational
Published
articles.
itournal
of
i.n Malhematics
sludies
in
Hollanal.
the American
PLlbI ishes
u6efu1
Contains
A6sociation
statistical
book
many conputer-related
reviews.
25
(.lAsA)
Mathematics
Magazine
(MM)
directly,
but many useful
Intended to reach unilergraduates
compuler-relateal content
as well.
articles
for instructors
sunmaries of culrent
Helpful brief
increasing gradually.
books anal articles.
Mathematics
Teacher
(MT)
Many articles
by college faculty members, but readers are
prinarily
high school and junior college teachers.
Ouite
plus announcemenls of
a fe\d computer-related
articles,
producls, services,
computers.
anil publicaLions
involving
SIAM Review ( SR)
applications
of
classroom Notes seclion for significant
many of
for cLassroom presentalion,
mathematics suitable
Helpful
book reviews
the use of computers.
\dhich involve
Two-Year
College
Mathematics
Journal
Contains a Computer Corner
occasional longer articles
(TYCMJ)
for short notes, plus
section
content.
lvith computer-related
Other Information Sources
(AMTRAC). lbg
Ad Hoc Conunittee on Applied Mathematics Training
in the Undergraduale Mathematics curricu_
RoIe of Applications
conmittee
chaired by
Report of a National
Research council
Argues for applications
in ttle mathematics
Peter Hilton.
curriculum,
basic competence in computer progfanuning for
every mathematics major, and use of stualents' computing
knowledge in appropriate courses.
Committee
on the U n d e r g r a d u a t e
dations
fol
an lJnderqraaluate
Berkeley,
CA:
Mathematics.
Program in M a l h e m a t i c s .
P r o q r a m i n Computational
Recommen-
cuPM,1971,
Conunittee on the Undergraduate Program in Mathematics.
dations
on Undergraduate Mathematics courses lnvolving
computing.
Berkeley, cA: CUPM, 1972.
Reconmen_
Conmiltee
diun of
on the Undergtaduate
CUPM Recorunendations.
Program in
Belkelev,
A CompenMathematics.
C A : C U P M ,1 9 ? 5 .
items anal the
Incluales the two previous
T e l e g r a p h i c r e v i e w : A M M8 3 ( 1 9 7 6 ) : 7 3 .
c-Tota-=IEi:
onference
1965 GCMCreporl.
(CcUc).
on CompuLers in the lJnderqraduaLe curricula
1970ma u;fversity
of rowa weeg computing center,
1978.
The mathematics
CCUC/l l'hrough CcUc/9.
Annual proceealings,
8, anal 9 ale
sections in nurnbers l, 2, 3,5,
and statistics
particularly
useful.
Replaced by the National Ealucational
Computing Conference in 1979 (see below).
Cartand, S.J,,
Mathematical
r975 .
Calculus and Cornputinq. Washinqton: American
ed.
Association
of A"nerica,
Society anal Mathematical
Pamphlet presenting case stualies from nine different
and a
schoots, sample problems, help on getting started,
iography.
bibl
The Influence of computing on Mathematicql
Lasalfe, J,P., ed.
Providence, RI: Arerican Mathematical
Research anal Education.
society, 1974.
P r o c e e d i n g s o f t h e A M S S y m p o s i u ' n i n A p p l i e d Mathematics
of Montana, August, 1 9 7 3 . C R 1 6
held at the University
(19?5) :Revie!r' No. 28683.
eds.
R.C., and NeIdei, J.A.,
Milton,
Nev/ York: Acaalemic Press, 1969.
statistical
computation.
fncludes two papers on
Proceealings of a conference.
ttith computers, plus several other
teaching of statistics
pertinent papers.
A M M7 7 ( 1 9 7 0 ) : 9 0 8 '
(Ul'lAP).
lndex
Project
Undergraduate Mathematics Applications
a n a l D e s c r i p L i o n s o f A v a i I a b I e M a t h e m a t i c s M o d u l e s . Newton,
EDC/UMAP.
moalules in variorls stages
Lists hundreds of applications
computerfew are specifically
of alevelopmentr relatively
stage are thoroughly class_
Units in final
related.
(regularly
other UMAP publications
tesleal anal revie\ted.
u p d a t e d ) i n c l u d e : U M A Pc a t a l o 9 , U n i t s a m p l e r s , U M A P
(newsletter),
and various monographs.
Projections
27
MA:
National
Etlucational
T1te Universily
of
Computing Conference (NECC). Iowa City:
lowa Weeg Conputing Center, 1979.
NECC is the successor
to CCUC. Merger with several
otttel
groups anal conferences resulteal in fewer disciplineorienteal papers, more empha6is on neu technofogy,
anal
quality.
higher overall
Only lwo papers on mathematics,
both containing
useful
information
on computer graphics.
-\-'/
7. Materials of Interest
as having pomaterials
have t)een identified
The follo\ting
Additional
information
instruction.
use for mathematics
tential
to
the
authots
or
by
writing
about these units can be obtaineal
by
lhose
materials
distributed
publishers,
For information
aboul
refer
to
Journal
abbreviations
coNDUIT, see the CoNDUIT Catalog'
Monthly
previous
Most
reviews
in
the
section.
the list
in the
(AMM) are telegraphic
revierds consisting
of complete blbliographanal brief
comments.
ic information
Calculus
A l 1 e n , R . C . , , J r . , a n d w i n g , M.C. Probfems for a computer
PrenLice-HaII,
Orienteal Calculus Course, E n g l e w o o dC l i f f s :
1973
Consists of statements of problems for a calculus lab, se(with programs anal outpul),
an appenalix on
lected solutions
A
M M8 f ( 1 9 7 4 ) :
F o R T R A N ,a n d a c c o m p a n y i n g s o l u t i o n s m a n u a l .
805.
Barr, R.C.r Gallie, T.M., Jr.; Hodel, M'J.i Hodel, R'E.;
MArHPROGRAM:
Murray, F.J.r Snilh, D.A.r anal Smith, D,A., II.
c
i
t
y
:
C
oNDUIT, 1980.
f
o
r
C
a
l
c
u
l
u
s
'
I
o
v
r
a
A Computer Supplement
Package consists of a single program to tabulate up to seven
a
and alefinetl recursively),
sequences (possibly interrelated
problem
and
an
inextensive
set,
stualent manual with an
students use the program to sofve probstructorrs
manual.
and multivariable
calculus by inlems in single-variable
i
n
i
t
b
e
fore running the
d
e
f
i
n
i
t
i
o
n
s
o
f
a
l
g
o
r
i
t
h
m
s
serLing
program.
Available
in BASIC from CONDUIT, and in FoRTRAN,
PL/I, and APL versions from the authors at Duke Univelsity.
M. The CaIculus
Bogart, K,, and Vitale,
I\fentworth, NH: cOMPress, 1974.
Short text on calculus
problems in population
plicalions.
of
Population'
motivateal by
of elementary functions,
growth and supported by computer ap-
G.G. Computer Applications
Dorn, W.S.r Hector, D.L.; and Bitter,
for Calculus.
Boston: Prindle, Weber, and Schnidt, 19?2.
conlains
many possible
applications
29
of
compuling
in
calcu-
fus.
M a y b e m o r e u s e f u l as a source of ialeas for instructors than as a text for s t u d e n t s ,
fhe programs are in
FORTRANand BASIC, with appendices on each language.
For a
r e v j - e w , s e e A M MB 0 ( f 9 7 3 ) : 1 0 3 .
Fossum, T,V,, and catteralam, R.W.
An Apptoach to Pr.oblem Solvinq.
and Co. , 1980.
Calculus
ulenvlew?
a n a l the
- tL :
Com u t e r :
Scott,
Foresman
Supplementary text intended to illustrate
anal reinforce
concepts and develop algorithmic
problen-solving
techniques, with emphasis on analysis anal interpretation
of
numerical results.
Sixteen "core" sections,
five ,,supplementaly" sections,
and appendices on flowcharts,
BASIC,
and error analysls.
Each section contalns at least one
algorithm
presented both by flowchart
and by BASIC program.
Hamming, R.W.
lrouqnlon
mlrt
Calculus
Lan,
and the Computer Revofution.
Boston:
19tt8.
ShouId be required reading for instructors,
but may be
too terse for students,
No conputer problems or programming are included.
A M M7 6 ( 1 9 5 9 ) : 5 7 6 . M . r 6 3 l t 9 7 1 ) t 2 a 2 ,
H e n r i k s e n , M . , and Lees, M.
SinqIe Variable Calculus with an
I ntroduction
to Numerical Methods.
New York: Worth Publishers,
19?0
Integrated calculus text with
propriate
for honors students.
Horn,
R.
nunerical applications,
apAMM 78 ( 1 9 7 1) : 5 5 6 - s 5 ? .
for a Calculus Computer Labofatorv.
of M a t h e m a t i c a l
Sciences,
ilohns Hopkins
Notes
Department
1916.
Packaged programs in BASIC, plus
To appear as a CONDUIT package.
an excellent
L a x , P . D . r B u r s t e i n , S.2. i anal Lax, A.
Calculus
tions and Computinq. V o l s , 1 a n d 2 .
New York:
1976, 1979.
Baltimore:
Univers ity,
problem
set.
irith
Appl icaSptinger-Verlag,
Represents a restructuring
of the calculus course as an
introaluction
to applied mathematics.
The appendix contains
F O R T R A Ns o l u t i o n s t o s e v e r a l p r o b t e m s .
A M M8 3 ( 1 9 7 6 ) : 7 5 ? .
30
Leinbach, L.C.
Calculus with the computer:
Prentice-Ha11, I974.
EnglewoodcI iffs:
Manual.
A l,aboratory
stualent-oriented
manual intended to supplement any calculus
ririth
appendices
on BASIC and FORTRANand a solutions
course,
manual . AMM 81 ( 1974 ) : 190 .
L y n c h , R . V . i o s l b e r g , D . R . ; a n d K u l 1 e r , R . G . Calculus
Lexington, MA: xerox, 1973'
Computer Applications.
vith
Ambitious
calculus
text lrith an appenalix on computer
c a t i o n s a n d n u m e r i c a l m e t h o d s . A M M8 0 ( f 9 7 3 ) : 1 0 8 2 .
Calculator
CaIcufus.
PaIo
Alto:
Page-Ficklin,
appli-
1975.
covering
An alternative
to many of the books in this list,
exercises
but with computalional
most of the same topics,
Could be used to introaluce
to be done with a calculator.
lvith use of the computer deferred
numerical methods earIy,
necessary for problems beyontl the
until
it becomes clearly
S R 2 0 ( 1 9 7 8) :
A M M8 3 ( 1 9 7 6 ) : 3 9 4 .
reach of the calculator.
196-197.
McNeary, S. S.
of Calculus
Inlroduction
to Cornputational MeLhods for
1973.
Englewood Ctiffs:
Prentice-Ha1l,
Students
to or follo$ring second-semester
Text for a course parallel
p
r
o
g
r
a
m
s
u
s
e
F o R T I I A N . A M M8 0 ( 1 9 7 3 ) : 9 6 2 .
calculus.
The
(
1
9
7
4
)
:
R
e
v
i
e
v
r
'
cR 15
No. 26316.
Swarthmore, PA: APL Press,
Calculus in a Nev/Key.
Orth, D.L.
t97 6.
A reworking of traditional
calculus topics in an algebraic
anal concepts
and atgorithmic
framework, using APL notation
(
1
9
7
8
)
:
R
e
v
i
e
w
c
C 3,5 (7977)l
c
R
N
o
.
3
2
4
8
0
.
throughout.
19
LO2.
shaDilo,
(iscrj,
L.
University
ui
rndividualized
supplementarv calculus
Instruction
n,
of Minnesota.
program for diagnosing
student difficulties
A computer-tutor
have been attempteal off-Iine.
with problems \,those 60lutions
to severaf different
Program has been moved successfully
via
EDUNET. Relateal aranal
can
also
be
accessed
computers
(
1
,
9
7
7
)
t
4
7
6
4
A
I
.
a
p
p
e
a
r
s
i
n
A
M
M
8
4
ticle
3l
Smith, D.A.
Interface:
Houghton
Mailr-i;:--19;6-
Calculus
anal the
Boston:
Computer.
stualent-oriented
enrichment text and 1ab manual, with append i c e s o n F O R T R A N ,B A S I C , a n d P L / I , a n d a n i n s t r u c t o r ' s
manual with complete solutions
and suggestions
for use.
Also
available
with two character-graphic
s programs as CONDUIT
p a c k a g e + M T H l O 5 . A M M8 3 ( 1 9 7 6 ) : ? 5 6 . C C 3 , 1 ( J a n . 1 9 7 7 ) .
Smith, D.A.
S u r f a c e : A T h r e e - D i m e n si o n a l c r a p h i c s M o d u l e f o r
Multivariable
Calculus.
Iowa Citv: CONDUIT,1978.
graphics package to support the stualy of functions
character
P r o g r a m a v a i f a b l e i n F O R T R A No r B A S I C ,
of two variables.
plus stualent manual .
Related article
appears in MM 50
1 I 9 7 7) t 7 4 3 - 1 4 7 .
Stenberg,
W., and Walker,
R.J.
Calculus:
Presentation.
Tallahassee:
Center for
;i;;tio;=?
University,
science
I968.
anal Mathematics
A Computer
Research in
(cRrcrsAM),
Oriented
CoIlege In-
Floriala
state
Integrated course presenting a nontraditional
ordering of
topics.
Widely used for a number of years, but a iecent
ad in AMM announced liquidation
of remaining
stock by
CRICISAM, Relateal publications
include:
AMM78 (r971):
284-29I.
T Y C M , I( F a l 1 1 9 7 I ) : 5 I - 5 4 .
Stroyan,
Algebra.
K.D.
Compuler Laboratory
Iowa City:
in
Calculus
and Linear
CONDUIT, I9?B
Package consists
of a laboratory
manual and 27 BASIC
programs to support a four-semester
calculus
sequence vrith
linear algebra in the.third
semester.
A M M8 6 ( 1 9 ? 9 ) : 3 2 O .
Statistics and Probability
Afifi,
A . , a n a lA z e n , S .
Oriented Presentation,
Press, 19?9,
Statistical
Anal
s i s : A C o muter
Ne\r York: Acaalemic
A textbook which integrates
the use of alata analysis
packages into an advanced undergraduate
or gfaaluate course
with emphasis on applied statistical
techniques.
JASA 69
( 1 , 9 7 4 ) . 2 7 9 . A M M8 6 ( 1 9 7 9 ) : 5 1 7 .
Computer Exercises
\
Dershem, H.
wenlworth,
for
Elementary Statistics.
A package containing
49 exercises,
2a FoRTRAN subprograms,
anal 5 data sets for use in a precalculus
statistics
course.
To appear as a CONDUIT package.
DlXOn,
W.J.,
ed.
llMUP
lJromedla1
of california
cilbert,
N.
Statistics.
Computer Proqrams.
Berkel ey:
Press,
Philadelphia:
Saunalers, I976
for
Descriptive,
inferential,
anal nonparametric statistics
Computational
exercises
using comnonmathematics majors.
puter programs provialed on puncheal carals with accompanying
nanual.
A M MA 4 ( I 9 ' 7 ' l ) . 2 2 9 .
Groeneveld,
R.A
g:ilc-!4919.
An Introaluction
New Y o r k :
Marcef
to
Probabil it
and Stati
slics
De
Intenaleal for a course follo\ring
cafculus of one variable.
Forty-eight
short,
interactive
BASIC programs are provided
Brief introduction
for examples and simulations.
to BASIC
on
in an appendix.
A1I programs in the text are available
tape from the alrlhor at Tovra State University.
AMM a6
(I979):517.
K l e c k a , w . R . ; N i e , N . H . i a n d H u l 1 , C.H.
Mccraw-Hil1, 1975.
Cood handbook for
belolr.
courses using
SPSS Primer,
SPSS.
See afso
Ne\d York;
Nie,
et
aI
and
Kossack, C.F.,
and Henschke, C.1.
Introduction
to Statistics
Holden-Day,
1975.
computer Programming.
san Francisco:
rhrr^^,,-r-^r\/
crAria+i-s
for students
text
of social
sciencesi
includes
three
chapters
on FoRTRAN and numerous FORcR 17
TRAN programs
\rhich illuslrate
statistical
concepts.
(1976):Review No. 29618.
AMM84 (197?):670.
McNeil, D. R.
YOrK: Warev, rvl/.
.
N"t
A supplement for a course in exploratory
data analysis
including APL and FORTRANimplemenlalions
of the techniques.
JASA 73 (19?8):887. cc 3,6 (Nov. I9?1)z)-24.
Steinbfennel,
K,; anal Bent,
the Social
Sciences,
seconal
Nie, N.H.i Hul1, C.H.i ilenkins, J.c.;
D.H.
SPSS: Statistical
Packaqe for
edition.
New York:
Yccra$r-Hi11,
Reference manual for SPSS a s w e l l a s f o r t h e s t a t i s t i c a l
techniques
available
wil:h t h e p a c k a g e .
AMM 83 ( 1976 ) : ?7 .
For those using version
? or 8 of SPSS, there is an SPSS
Upalate, also published
1979.
by M c c r a w - H i 1 1 ,
Richaralson, R.H., and Stones, D.H. Quantitative
Anafysis.
Io!r'a City: CONDUIT,1978.
Experimental
Seven moalules designed for use \4rlth an applied
statistics
course.
Accompanying FORTRANprograms are interactive
and utilize
random sampling and graphical analysis,
No
calculus ]trrereouisite.
Ryan, T.A.i ;loiner, B.L.; and Ryan, B.F.
Manual.
Universitv
Park, PA: Statistics
iiifE-state
univer;ity.
MINITAB
11 Re ference
Pennsyl -
Department,
Intendeal for precalculus
statistics
coursesi system conplotting,
tains compuCalional,
and simufation
routines
with
extensive error-checking
anCldiagnostics;
available
in
transferable
form.
R y a n , T . A , r J o i n e r , B . L . i a n d R y a n , D , F . MINITAB Student
Handbook,
North Scituate,
MA: Duxburv P r e s s .
Now avai Labl e
from Wadsworth Publishinq Co., BeI'nont., cA.
Supplemental text
Minitab package.
SAS Introductory
for statistics
course
, I A S A7 2 ( 1 9 7 7 ) : 9 3 3 ,
Guide,
Ra]eigh,
NC: SAS InstituLe,
Beginner's guide to the statistical
see also the next lisling.
SAS User ' s Guiale, 1 9 7 9 e d i t i o n .
1979.
The co-nplete
story
Kalelqn,
on SAS in
vrhich uses the
a very
Analysi6
Nc:
5lt5
reatlable
1978.
system (SAS).
.tnstltuter
forn-
Scalzo, F., and Hugtles, R. Elementary Computer-Assisteal
Statistics,
reviFed edition.
New York: Van Nostranal, 1978.
Elementary
statistics
text
lvith
34
accompanying
BASIC programs
for per.forming calculations.
A M M 8 4 ( 1 9 ? 7) : 6 7 0 .
( 1 9 7 ' 7) .
Revieli: 86 (19?9):607.
Sne11, J.L,
Introaluction to Probability
Theory with
EnglewoodCl ifts:
Prentice-HaI1, 1975.
cR l8
Computinq.
probability
Introductory
textr
makes use of BASIC programs
!o -iIlusLraLe concepLs by simulation.
A l a M8 2 ( I 9 7 5 ) : 1 0 3 f .
Tanis, E.
Labor.atory Manual for Probability
Inference.
I o w a C i t y : C O N D U I T ,I 9 7 8 .
and Statistical
Laboratory exercises for mathematical statistics
coutse,
lrith 58 batch or interactive
F O R T R A Ns u b p r o q r a m s .
Weed, H.D.
Descriptive
NH: coMPress, 1978.
Statistics,
second ediLion.
Wentworth,
supplement to intr:oductory statistics
textsr includes four
BASIC programs for elementary alescriptive
statistics
calcup
a
c
k
a
q
e *sTAll4.
A
l
s
o
a
s
C
o
N
D
U
I
T
lations.
available
Linear Algebra
Agnew, J., and Knapp, R.C. Linear Afqebra with
Monterey, cA: Brooks/cole,
1978.
Well-written,
one-semester text with
compuLer programs in every chapter.
Fraleigh,
J .B.
@.
City: CONDUIT,1977.
Applications.
applications
and
A M M8 6 ( 1 9 7 9 ) : ? 0 .
Iotda
Package consisting of seven BASIC programs and a supplementary texl vrith computer projects
lo enhance gtanalaral
I iha^r
Kolman,
York:
^1a6hr.:
B.
Macmillan,
^^'rrc6q
N"t
1976.
lncludes
a chapter on numerical
Iinear
algebra.
Appendix
contains many computer projects
of vaiying
levels
of diffic u l t y , p l u s c o m m e n t s o n A P L a n d B A S I C . A M M8 3 ( 1 0 7 6 ) : 3 9 3 .
Mclaughlin,
IOWa
UALy:
D.E.
A Computer Olienled
Course
in
Linear
^r^6117.
LUNjJU
Package consisting
of a textbook and FORTRANsubroutines
for
reduction
to echelon form, Cram-Schmidt process,
characterpolynornial, and simplex algorithm.
istic
Uses computing to
illustrate
theory anal t.o emphasize the algorithmic
nature of
linear algebra.
Exercises ask stualents to write simple prodr>ms rrci.d
Steinberg,
D.I.
Hil r , 1974.
"ha elnnried
subroutines.
Computational
Matrix
Algebra,
New York:
Mccraw-
Stanalaral sophomore-level
text
rvilh coverage
through
eigenvalues
and Jordan
form;
emptrasis on computational
methods,
No programs are provideal or required.
CR 16 (19?5):Revie\^,
No. 27663.
AMM81 (1974):926.
Williams,
G.
Computational
A1lyn and B a c o n , f 9 7 5 .
Linear
Algebra
with
Mode]s.
Boston:
Covers standaral topics plus numerical methods v/ilh an unusua1ly broad array of applications.
About 20 BASIC programs
anal accompanying computer exercises
are provided
in an appendix.
A M Ma 2 \ 1 9 7 5 ) : 5 4 3 .
Differential Equations
Boyce, W.8., and DiPrina,
R.C.
and Boundary Value Problems,
Elementalv
Dif ferential
Equations
third
edition.
New York: Wilev,
r977 .
Stanalard text for pos.t-calculus
courses up to one year in
lengtht many different
one-sernester courses can be extracted.
Thorough chapter on numerical methods: no programs provided.
Also available
in shorter version without material
on boundary value problems.
A M M8 4 ( 1 9 7 7 ) : 6 6 4 - 6 6 5 , 7 5 2 t 8 6
( 1 9 ? 9) : 5 9 9 - 6 o 0 .
Braun, M,
edition.
Differential
New York:
Equations anal their
Applications,
Springer-Ver1ag,
1978.
second
Moalern, complete text in ODE's with many interesting
appliFORTRANand APL programs illustrate
numerical
cations.
solutions.
An appenalix gives a brief
introduction
to APL.
A M MB 2 ( 1 9 7 5 ) t t 0 2 9 i a 4 ( 1 9 7 7 ) t 6 6 4 - 6 6 5 , s R 2 r ( I 9 7 9 ) t 2 6 4 -
36
Buck, R.C.,
Equations.
and Buck,
Boston:
E.F.
Introtluction
to Differential
nougt'toffi
coursei one
or two-quarter
Standaral text for a one-semestel
No programs
chaptet and an appenalix on numerical methods.
providedt use of a pocket calculator
is suggesteal for numerA M M8 3 ( 1 9 7 6 ) 2 1 5 3 - 7 5 4 .
ical problems.
Calter,
P.
Solution
Numerical Means.
Equations by Graphical
of Differential
N e w L o n , I 4 A : E D C / U M A P ,1 9 7 6 .
anal
equations
ol alifferential
Supplementary module for calculus
and
p
h
y
s
i
c
a
l
a
p
p
l
i
c
a
t
i
ons
p
r
e
s
e
n
t
a
n
d
b
i
o
l
o
g
i
c
a
l
t
o
courses
a
week.
in
about
Can
be
covered
means of solving
them.
A First course in Differential
Hagin, F.c.
P r e n t i c e - t t a 1 1, 1 9 7 5 .
Cl iffs:
Equations.
Englewooal
Standaral one-semester text in which numerical methods are
two
in each of the first
taken up early and often (a littte
c
o
n
s
i
d
e
r
a
t
i
o
ns
a
n
d
c
o
m
p
u
t
a
t
i
o
n
a
l
chaplers, alI of chapter 3,
f
l
o
w
c
h
a
r
t
s
a
n
d
s
o
m
e
I
n
c
l
u
d
e
s
in the chapter on series).
s a m p l e p r o g r a m s i n B A s I c a n d F O R T R A N . A M M8 3 ( 1 9 7 6 ) r 7 5 3 - ' 1 5 4
Numerical Solution of oralinary Differential
Mclauqhln, D,E.
l
o
w
a City: Regional computer cenLer, universiLY
EquaLions.
ot
Iota;-Tq73 .
Multitithed
course noles, intended as a computer-ori ented
equations course.
t
o
a standaral differential
supplement
Elementary Numerical Techniques for Oralinary
Van Iwaaralen, ,J.L.
Di fferenLial EquaLions. wenLworlh, NH: CoMPress, 197?'
manuaf
of student manual, instructor's
Package consisting
and 19 BASIC programs to supplemenl standard ODE coursest
units may be taken up one at a tlme \then the corresponaling
material
is being covereal. To appear as a CoNDUIT
analylic
Dackaoe.
Ziebur, A.D.
Dickenson.
Topics in
197O.
Differential
Equal:ions.
in ordinary
covers the standard topics
useal
as a tool
the computer is
tionsr
z
e
n
t
r
a
l
batt
fur
79 1I972):1148-1I49.
( 1 9 1 2 ' )t L 5 a , R e v i e w n o . 3 4 0 0 2 .
37
Belmonl,
cA:
alifferential
equaAMM
to teach theory.
Mathematik 288
Finite Mathematics
Anton, H.,
edition.
and Kolman,
New York:
B.
Applied
Finite
Mathematics,
AcadefriE-EEEEEI-li9J3-i--
second
well-written
book with good p r o b l e m s , e x a m p l e s , a p p l i c a tions.
Chapter on computing uses BASIC ( replacing
FORTRAN
in the first
Also a v a i l a b l e i n e x p a n d e d e d i t i o n
edition).
with intuitive
introduction
A M M8 5 ( 1 9 7 8 ) : 5 1 1
to calcufus.
8 6 ( 1 9 ? 9) : 1 4 0 .
Dorn, W.S., anal Mccracken, D.D.
Introaluctory
with Computing.
New York: Wiley, 1976.
Computer use is fully
integrateal using
R e v i e w N o . 2 9 9 5 9 , A M M8 3 ( 1 9 7 6 ) : 3 9 4 .
Scalzo,
F., and Hughes,
Colleqe Mathematics.
Finile
BASIC.
R.
A Cornputer Appr.oach !o
New York: Petrocelli/Charl-er,
Mathematics
cR 17 (1976):
Tntroductory
1977.
Topics include algebra, matrices, elementary linear programming, symbolic logic,
elementary probability
and statistics,
and programs provialed in the text to solve problems related
L o e v e r y t o p i c . A M MA 5 ( 1 9 7 8 ) : 6 1 .
wilIiams, c.
Finite
Bacon, 1976.
Mathematics with
M o d e ls .
Boston:
AIlyn
and
Contains an early chapter on computing and an appenalil on
BASIC. Many BASIC programs and computer exercises
appear
the text,
throughout
ranging fron multiplying
a matrix by a
scafar to simple games of strategy.
A M M8 3 ( 1 9 7 6 ) : 3 9 4 .
Liberal Arts Mathematics
Dorn, W.S., and Cleenberg, H.J,
Mathemallcs and compulinq:
FORTFAIJ Programming,
New York:
wiIey, 1967.
with
Intenaled for a precalculus,
Iiberal
artsr or teacher ealucation course.
covers topics in calculus,
finite
mathematics,
AMM75 (1968):103.
linear algebra, logic and probability,
Smith, K.J.
Monterey,
fhe Nature of Modern Mathematics,
CA: Brooks/co1e, 1976.
the
38
nature
second edition.
of
mathematical
thought,
numeration systems, computers, elementary abstract
algebra,
number theory,
1ogic, geometry, combinatorics.
probability,
and statisLics.
Early chapter on computers
contains exercises using a computer.
A M M8 1 ( 1 9 7 4 ) : 1 1 2 9 1 1 3 0r 8 3 ( I 9 7 6 ) : 5 7 9 .
Precalculus Mathematics
Burroves, T.C., and Burrovres, S.K.
Algorithmic
Approach.
Nelv York:
Elementaly Functions:
Intext,
1974.
An
Emphasizes algorithms
anal flowcharts;
conputer use is optional .
Appendices on BASIC and FORrRAN. Programs are provided in FORTRANfor graphing,
roots by interval -halving,
polynomfunction
evaluation,
anal rational
roots of integer
ials.
opportunities
for stualents to write prothroughout
qrams for other problem solving.
D e t m e r , R . C . , a n a l S m u 1 1 e n ,C . W . , I I I .
Algebra
Practice.
Iowa City: CONDUIT, 1979.
Dri11
and
Wel l -alocumented CAT packagei consists
of nine moalules covering various algebraic skills.
fhree of the modules aleal
v/ith lvord problems (rectangles,
distances,
and mixtures in
solution)
and offer the student four levels of difficulty.
Hiqqins, G.A., Jr.
The ElenenLary Functions: An Alqorithmic
Approach.
EnqIe\tood Cliffsr
Prent-Lce-Hal1, I974.
Computer use integlated
throughout
in the form of BASIC programs and computer exercises.
Kno\dledge of BASIC is ass u m e d . A M M8 1 ( 1 9 7 4 ) : 1 0 4 . c c 2 , 5 ( s e p t . 7 9 7 6 1: 9 6 .
Iverson, K. E.
A1 ebra:
Addison'wes ley,
PA.
An A1 orithmic
Approach .
Reading,
MAI
availabl e
Press,
Swarthnore,
Covers elementary
functions
using APL notation
throughout.
A M M8 I ( 1 9 7 4 ) : 4 2 0 . c R 1 3 ( 1 9 7 2 ) : R e v i e w N o . 2 2 5 3 0 . C c 3 , 5
( S e p t . 1 9 7 7 ) : 1 O 2.
Iverson,
1976.
K, E.
Elementatv Analvsis.
Covers precalculus
tions,
derivatives
Swarthmore,
PA: APL Press,
algebta,
elementary transcendental
funcanal antialer ivatives , complex numbers,
conic sections,
and recursive
functions,
all i,rith APL notation.
cR 7A lI9'17):Review No, 3L726- cc 3.5 (Sept.
I 9 ' 77 ) t I O 2 .
Lecuyer, E.J.
Introduction
to Cotlege Mathenatics with
graming Language. New York: springer-Verlag.
1978.
a Pro-
Innovative
text for a futl-year
course covering sets, logic,
elementary Iinear atgebra, graphing of functions,
transcenalental functions,
brief
introaluclions
to differential
and
probab'i1ity,
integral
calculus,
anal statistics.
Appendix on
APL; conventionat
and APL notation
used in paraltel
throughout the text.
c R 1 9 ( 1 9 7 8 ) : R e v i e w N o . 3 3 6 5 0 . A M M8 5
( 1 9 7 4) : 6 9 3.
walIace, W,
Terminal.
Functions and Their craphs Usinq a computing
Oshkosh,WI: Universiry oI Wisconsin, 1978.
Multitithed
notes and BASIC.prograns
of functions
via character-graphics
in a state
of development.
for the study of graphs
plots.
Package is still
Number Theory
Kirch, A.M.
Elementary
York: Intext,
1974,
Number Theory:
A Conputer Approach.
New
,rhich applies
lrays.
The
solid
text
the computer
in expected
programs are in EoRTRAN. AMM 8I {1974):926i
A4 (197"1).39a.
A Computer Laboratory
Malm, D,E.
Wentworth. NH: COMPress.1978.
Manual for
Number Theory.
Supplenent to standard texL Eo treat subjecE as an experimental science.
For each topic,
includes descriptions
of
concepts i experiments for before, aluring, anal after
stualy of
topic, references,
Instructoirs
nanual, approxinately 40
(To appear as a
p r o g r a m s i n B A S I C . A M M8 6 ( 1 9 7 9 ) : 3 2 0 .
CONDUITpackage. )
Symbolic Logic
Moor, J.,
analNelson, J.
BERTIE. Wentworth, NHr COMPress,l9?4.
BASIC proqram and a
Package consisting
of ao interactive
Intenaled to teach the skills
student/instructor
nanual.
and to enhance stuneeded for natural
dealuctive derivations
fornulas.
to write and recognize well-formed
dents' ability
Also
systen of naturat alealuction'
Uses the custason-Ulrich
available
as CONDUITpackage +MTEO47'
40