The Rice Thresher (Houston, Tex.), Vol. 50, No. 26, Ed. 1 Wednesday, May 1, 1963 Page: 10 of 16
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Ten
THE THRESHER
WEDNESDAY, MAY 1, 1963
Mathematics Department
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MATHEMATICS 100
Drs. Brown and CNeil
Elementary Analysis
Despite a wave of criticism
following the semester exams,
math 100 has emerged from the
course evaluation program vir-
tually unscathed. Even though a
high percentage of students fail
this course every year—at the
semester, 20% of the class re-
ceived 5's—students were gen-
erally favorable in their analy-
sis of the course's problems. The
only major sources of dissatis-
faction were the extremely fast
pace and the "unrealistic" tests.
Next year, look for a major
change in professors. There will
be at least three sections, to be
taught, tentatively, by Dr. Mac-
Lane and two new additions to
the faculty: Dr. Keith Miller,
currently a post-doctoral fellow,
and Dr. George Innis, who
comes to Rice from Harvard and
received his Ph.D. from the Uni-
versity of Texas.
The outlook for next year is
the same old Math 100 taught
by a new set of faces. What will
happen is anybody's guess.
MATHEMATICS 101
Dr. Durst
Fundamental Concepts of
Mathematics
Logic, set theory, and intro-
ductory calculus will be the sub-
jects of math 101 next year. The
course will be taught by Dr. O'-
Neil.
Math 101 is not intended for
students who will pursue mathe-
matics beyond the freshman
year. However, those who do not
expect to need a knowledge of
calculus will find a variety of
interesting material. Although
the material is not by any means
simple, the work load is lighter
than that of math 100. For these
reasons, academs will probably
be better off in math 101.
MATHEMATICS 200
Drs. Johnson and MacLane
Advanced Calculus
Math 200 has traditionally
been a course in advanced cal-
culus, whose purpose is pri-
marily to acquaint the student
with the fundamental ideas of
mathematical analysis, while
giving him the techniques with
which he can effectively solve
problems. The course begins
with the familiar topics of
Math 100; but the material is
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viewed more thoroughly and
rigorously.
From this beginning the
course typically moves through
such topics as sequences, theor-
ies and techniques of definite
integration, antiderivatives, the
improper integral, infinite ser-
ies, the differential and integ-
ral calculus of functions of sev-
eral variables, and vector analy-
sis.
Next year the course will be
taught in two sections, under
the able tutelage of Dr. John-
son and Dr. McLane, both of
whom haw taught the course
singly in past years.
Most students in Math 200
consider the homework, al-
though slightly on the difficult
side, to be representative work
in the ideas and mechanics of
elementary analysis. Both pro-
fessors are noted for their ex-
tremely organized lectures, and
there will be problem sessions
for discussion of the more try-
ing homework problems.
The textbooks have been
Fulk's Advanced Calculus and
Kazarinoff's Analytic Inequali-
ties. . Most students approve
Fulks with few reservations; al-
though Kazarinoff is almost
universally disparaged, th^ book
is admitted to contain some
highly useful problems. Exams
have varied from pure "re-
gurge" to highly original.
The gifted and interested ma-
thematics student usually takes
Mathematics 210 for his sopho-
more mathematics, 1 e a v i n g
Math 200 open mainly to stu-
dents majoring in science or en-
gineering. These students are of
a more practical bent than the
subject matter would indicate;
nearly everyone taking the
course in the past complained of
the emphasis on theory rather
than applications. However the
course sems to be an excellent
compromise between the poles
of teaching pure theory and pure
technical skill.
MATHEMATICS 210
Dr. Bray
Differential and Integral
Calculus
The aims of Math 210 are by
and large those of Math 200,
but Math 210 is designed for
the gifted student, the subject
matter is a bit more advanced.
In past years, Dr. Bary has de-
emphasized the formal study of
sequences and series,--and has
put- in their place such* topics
as the differential geometry of
a curve in space, partial frac-
tions, implicit functions, and
transformations with an intro-
duction to the idea of conformal
mapping. In this course there is
heavy emphasis on functions of
several variables and on multi-
ple integrals with transforma-
tions of those integrals.
Although the course was de-
signed for those students with
high standing in Math 100, car-
lessness in registration of stu-
dents has had the result that
the members of the class have
been of noticeable non-uniform
ability. In order to remedy this
situation, no one will register
for Math 210 this spring; all
registrations for sophomore ma-
thematics will be for Math 200.
The first day of class in Math
210, volunteers for 210 will be
called for, and their qualifica-
tions will be carefully checked.
Dr. Bray is well-known at
Rice, not only for his mathe-
matical proficiency, but also for
his skill as a teacher. Nearly
all his students have agreed that
few teachers have such a deli-
cate feel for the needs of the
student; if anything, Dr. Bray
is inclined to go too slowly ra-
ther than confuse the class.
Homework is very light in
this course, but it is intended to
be more theoretical than practi-
cal ; it takes more than mechani-
cal skill to do it. Dr. Bray sel-
dom dwells at length on fine
points in his lecture, but he
carefully outlines the mainline
structure of a proof on the
board, with a verbal indication
of the rigor involved. Because
the student has such a light
homework load, he is expected
to provide himself the minimum
amount of l-igor that would only
make for a dull lecture if be-
labored in class. Dr. Bray is of-
ten heard to ask students to
rewrite their notes.
The exams are mainly for
reproductions of work done in
class, but it is not uncommon
for original problems to be
found on them. As there is no
textbook, the quizzes come com-
pletely from the notes.
The most common criticism of
the course is that it fails to
push the able student. Many
pei*sons in the class have felt
that more material could be
covered than is presently cov-
ered. In order to facilitate the
speed-up, a textbook has been
recommended, a text wherein
additional approaches to the
subject matter could be found,
and a text that would enable a
greater quantity of more diffi-
cult homework to be assigned.
With the addition of any good
textbook, Math 210 would be a
very substantial, rewarding
course in elementai-y analysis.
MATHEMATICS 300
Dr. Jones
Differential Equations and
Advanced Calculus
As taught this year by Dr.
Jones, Math 300 was an excel-
lent course in all the basic as-
pects of differential equations
and Fourier analysis. During
the first semester, ordinary
first- and second-order equa-
tions were covered, with meth-
ods of solution and existence
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and uniqueness theorems, in-
cluding power series and regu-
lar singular points.
The second semester deals
with Legendre's equation and
Legendre polynomials, the Pi-
card existence theorem, systems
of equations, 'N-th order equa-
tions, Laplace transforms, par-
tial differential equations, and
Fourier series. The course will
be taught by Dr. Jones again I
next year, and will cover the
same topics.
The outstanding features of
the course are Dr. Jones' lec-
tures and original homework
problems, which are given with
a fresh, original approach. His
tests are unique and creative,
and are the major cause of com-
plaint. The engineering and sci-
ence majors in the course com-
plained that there was not
enough emphasis on the prac-
tical applications of differential
equations and on the various
methods of solution, and that
this neglect was reflected in
the tests and homework. From
this it sems desirable that there
be two 300-level courses in dif-
ferential equations, one stress-
ing the practical aspects of the
subject for the scientists and en-
gineers and one similar to this
year's course for the math ma-
jors. In general, though, Math
300 this year has been a great
improvement over courses in
the subject in previous years,
and has provided a solid ground-
ing for further study in the
field.
MATHEMATICS 330
Algebra
The coming year will find
Math 330 split between Dr.
Durst (first semester) and John
McMillan (second semester).
First semester topics will in-
clude groups, rings, fields, the
Dedekind cut definition of real
numbers, and polynomials. Vec-
tor spaces and matrices will be
studied in the spring; the text
will be Finite Dimensional Vec-
tor Spaces by Paul Halmos, who
gives an extremely lucid account
of the subject. Because of the
way the material is divided be-
tween the semesters, the change
of instructors at midterm should
not interrupt the continuity ap-
' preciably.
Math 330 is a must for math
majors. Vector spaces are ex-
tremely important in mathema-
tical economics, so mathematic-
ally minded economics majors
should consider taking the
course. Beginning next year,
math 330 will be a prerequisite
for Math 441. The homework
load is traditionally light and
the coverage of material thor-
ough.
MATHEMATICS 400
Drs. MacLane and Douglas
Theory of Function of a Complex
Variable
Mathematics 400 is a course
in the theory of functions of a
complex variable. It is usually
taken by math majors, physics
majors, and an occasional chem-
ist and graduate engineering
student. The course was changed
quite drastically this year under
- the direction of Drs. Douglas
and MacLane. Important inno-
vations include adoption of of-
ficial texts (Hijle, v. 1 and 2)
and replacement of the usual
development of the number sys-
tem and classical real analysis
by more advanced topics of
function theory.
This year's Math 400 student
was exposed to a very compre-
hensive treatment of basic ma-
terial by Dr. MacLane and was
thereby, hopefully, prepared for
Dr. Douglas's discussion of cer-
tain special topics in the second
semester, (e.g., normal families,
Vitali's Theorem, the Riemann
Mapping Theorem, and the The-
orem of Picard).
Success in Math 400 depends
heavily on the student's mastery
of the basic concepts introduced
in Mathematics 200 and 210.
This course is quite substantial
and requires a considerable
amount of time and effort on
the student's part. There was a
certain amount of criticism in
the fall semester because home-
work assignments were often
long and sometimes unprofit-
able. This situation has been
alleviated somewhat this semes-
ter by selective problem sets.
Despite the criticism above,
Math 400 is one of the better
courses in the Mathematics cur-
riculum and will continue to be
next year.
MATHEMATICS 410
Dr. Jones
Differential Equations and an
Introduction to the Caulculus
of Variations
This is a coui'se in advanced
ordinary and partial differential
equations. Essentially the same
topics are covered as those in
Math 300 although the discus-
sion is more general. More em-
phasis is placed on partial dif-
ferential equations; e.g., the
Dirichlet Problem is given much
attention.
Dr. Jones is an excellent and
lucid teacher. His problem sets
the very instructive and quite
challenging.
Next year the course will be
taught by Dr. Miller, who also
works in the field of partial dif-
ferential equations. Under his
guidance the course will un-
doutedly retain its excellence.
MATHEMATICS 441
Modern Algebra
Math 441 will be taught by
Dr. O'Neil and will treat ad-
vanced modern algebra. Studies
of matrix theory and of finite
groups will begin where Math
330 leaves off. Theory of equa-
tions and Galois theory will be
treated in the second semester.
The material will closely paral-
lel that in Albert's Modern
Higher Algebra, but the book
will not be used as the text.
MATHEMATICS 442
Dr. Brown
Topology
Mathematics 442 is a senior-
graduate course in topology. Via
abstractions from the basic
point set notions of Math 200,
the concept of a general topo-
logical space is introduced. Dur-
ing the course of the fall se-
master, these spaces are classi-
fied and their essential features
are investigated. These and
other aspects of set theoretic
topology comprise the semes-
ter's work. In the spring semes-
ter algebraic devices are inject-
ed into the discussion, facilitat-
ing the treatment of such topics
as covering spaces and homo-
topy theory.
Dr. Brown's lectures are in-
teresting, well organized, and
quite demanding. His approach
is fresh, and the course mater-
ial is further vitalized by a se-
lection of unusual yet highly
pertinent problems.
Next year the course will be
taken over by Dr. Innis who for-
tuitously researches in the gen-
eral area of topology. In sub-
stance the course will probably
be unchanged.
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The Rice Thresher (Houston, Tex.), Vol. 50, No. 26, Ed. 1 Wednesday, May 1, 1963, newspaper, May 1, 1963; Houston, Texas. (https://texashistory.unt.edu/ark:/67531/metapth231237/m1/10/: accessed July 18, 2024), University of North Texas Libraries, The Portal to Texas History, https://texashistory.unt.edu.; crediting Rice University Woodson Research Center.