YALE ALUMNI WEEKLY
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MATHEMATICS AT. YALE.
An Excellent Past and a Progressive
Present. :
[Copyrighted.]
A steady growth from the first and a
very rapid development in the last ten
years are the features of the history —
of the Department of Mathematics at
Yale. :
In the old days a single professor
taught both Mathematics and Natural
Philosophy, but in 1836, by the election
of Professor Stanley, Mathematics: had
a chair of its own. When Professor
Stanley died in 1853, Professor New-
ton, although only twenty-five years of
age, was appointed to fill the vacancy.
For more than forty years, that is, till
his death in 1896, the Department was
under Professor Newton’s vigorous and
progressive administration.
this time the Department increased from
one professor and two tutors to a staff,
in the Academic Department, of five
professors and four instructors, and in
the Shefheld Scientific School, of two
professors and four instructors,—a total
of seven professors and eight instruc-
_tors. In the Academic Department are
Professors Gibbs, Richards, Beebe,
Phillips, and Pierpont, and the instruc-
tors are Messrs. Strong, Westlund.
Hawkes, and Sellew. In the Sheffield
Scientific School are Professors Clark
and Smith, and the instructors are
Messrs. Starkweather, Lockwood, Mar-
shall, and Granville. 3
The instruction in the undergraduate
department may be considered first.
In looking over the course of study
followed half a century or more ago,
one is surprised at first sight to ob-
serve how small the change is when
compared with that which has taken
place in the Department of Natural
Sciences. In 1836, the year of Profes-
sor Stanley’s appointment to the chair
of Mathematics, the Freshmen studied
Day’s Algebra and Playfair’s Euclid.
In the Sophomore year Euclid was fin-
ished and Solid Geometry, Plane and
Spherical Trigonometry, Logarithms,
Mensuration, Conic Sections, Survey-
ing, and Navigation were taken up. In
the Junior year Astronomy was re-
quired, and Fluxions (the Calculus) was
offered as an optional.
CHANGELESS FORMS.
These studies are largely what are
given to-day. The reason why so little
change has been necessary is to be
found in the fact that Mathematics is
not only one of the oldest sciences, but
also the most exact. Geometry re-
ceived from the Greeks a form so per-
fect that later generations can add but
little. The Elements of Euclid and the
Conics of Apollonius of Perga still en-
joy the admiration they excited twenty
centuries ago. And this is true, though
to a less degree, of the other branches
of Mathematics,—Algebra, Trigonome-
try, Analytical Geometry, and the Cal-
culus, the youngest of which was vener-
able before many of the sciences which
crowd our college curriculum of to-day
were born. 7
But, even under these circumstances,
changes have been taking place in un-
dergraduate instruction in Mathematics.
Perhaps the most radical has been the ©
introduction of the Calculus into the
Sophomore year. To effect this, the
course of study in this year were divided
into two part. The first is the tradi-
tional course in Mensuration, Survey-
ing, and Navigation, under the charge
of Professors Richards and Beebe. The
second, under Professor Phillips, em-
braces Graphic Algebra, Analytical
Geometry, and the Calculus. The ad:
vantages derived from this radical
change are obvious. Students who
wish to make an extended study of
Mathematics or Physics and Astronomy
will reach the Junior and Senior years
prepared for much more advanced work
than hitherto. For these students ad-
vanced courses are now offered in Al-
gebra and Analytical Geometry, Higher
Analysis and Higher Geometry, the last
two being really graduate courses. In
addition a course of much more ad-
vanced character than ever before is
given in the Differential and Integral
Calculus. |
During
GRADUATE INSTRUCTION.
The. development of instruction in
Mathematics in the Graduate School is
as radical and as extensive as in any
of the other departments. In the first
announcement in 1847 of the courses in
the newly foufided Graduate School, or,
as it was then called, the Department
of Philosophy and the Arts, the only
course in Mathematics was one offered
by Professor Stanley on the Calculus
and Analytical Mechanics. On Profes-
sor Stanley’s death, Professor Newton
offered for a number of years “such
branches of higher mathematics” as
might be ‘agreed upon with the stu-
dent.” In 1860 the lectures were di-
vided into three sections, of which
Mathematics and Physics formed one.
Professor Newton had charge of the
Mathematics, and his courses were an-
nounced briefly as “Pure and Mixed
Mathematics.” Professor Loomis had
charge of Astronomy.
The year 1871. is memorable in the
annals of this Department, as it marks
the entrance of. Professor Gibbs into
the school as Professor of Mathemati-
cal Physics. He offered the Theory ot
Wave Motion, Capillarity, and the
Potential Function. The number of
courses offered by him soon grew, and
they now form a stately series of lec-
tures covering nearly the whole range
of Mathematical Physics, an object of
just pride to all the friends of Yale.
In the same year Professor Newton
offered the Calculus, Statics, Dynamics
of .a Particle, Lunar and Planetary
Theories, and Higher Geometry. These
remained, with an ‘occasional change
to courses on shooting stars and
meteors, and the Calculus of Proba-
bilities, the subjects he taught till his
death. In 1873 the department received
the addition of Professor Clark’s in-
struction, who. began to lecture regu-
larly on Definite Integral, Differential
Equations, Determinants, Analytical
Mechanics, Numerical Approximations,
and Least Squares. ,
A STORY OF GROWTH.
Since then the Department has been
steadily growing. In 1884 Professors
Beebe and Phillips began to give grad-
uate instruction, the former turning his
attention to Geodesy and Practical As~
‘tronomy, while the latter devoted him-
self to Geometry, Curve Tracing, and
Map Projection. Professor Phillips in-
augurated a movement at Yale which
has been so successfully carried out in
Germany. It has been his constant ef-
fort. by the construction of geometrical
models and machines, to render graphic
and geometrically intuitive many results
of advanced geometry and the theory of
equations. The collection of mathe-
matical models and machines, has grad-
ually grown under his ceaseless activity
to be one of the largest in the country.
Some details may give a more exact
notion of the field covered by the De-
partment in the last few years (1896-98).
Professor Gibbs, besides his lectures
in Mathematical Physics already alluded
to, gives courses in Vector Analysis,
with its application to Geometry, As-
tronomy, and kindred subjects, and an
advanced course in Multiple Algebra,
which embodies for the most part his
own investigations in this direction. It
is deeply to be regretted that this
author, who is so widely and favorably
known abroad for his epoch-making
researches in Thermodynamics, does
not publish an account of his ideas and
methods in Multiple Algebra.
Professor Clark lectures at present on
Determinants, Theory of Equations,
and Differential Equations;. Professor
Phillips on Advanced Calculus; Profes-
sor Barney on Geodesy and Practical
Astronomy, and Professor Beebe on
Comparison of Orbits and Practica
Astronomy and Surveying. - f
Professor Pierpont devotes himself to
the analytical side of pure Mathematics,
-and has given courses: on- Introduction
to Higher - Analysis, ~ Substitution
Theory, Galois’ Theory of Algebraic
Equations, Functional Theory: of Real
and Complex Variables, Elliptic Func-
tions, Linear Differential Equations,
Modular Functions, Theory of Con-
tinuous Groups, and Theory of Num-
bers. Finally Professor Smith, repre-
senting Modern Geometry, has given,
since his return from Europe in 18606,
Differential Geometry, Modern Geome-
try of the Plane and of Space, Algebraic
Curves and Surfaces, and the Theory ot
limits of the time.
Transformations of Space. In this lat-
ter course the theory of Lie’s contin-
uous groups play a dominant role.
CHANGE IN THE METHOD OF TEACHING.
With this influx of new and thor-
oughly modern courses, a change in the
method of teaching has been made.
Instruction, which in the older days
was often limited to directing the read-
ing of the students and explaning diffi-
cult passages, is now given entirely by
formal lectures. The seminary method,
which is so efficacious abroad in train-
ing young men to be _ independent
thinkers and investigators, has replaced
the old custom of solving ingeniously
devised problems of more or less trivial
nature, which we inherited from Eng-
land, and which the Mathematical
Tripos still unfortunately fosters there.
In close connection with the seminary
is the Mathematical Club, founded in
1877 by Professor Giggs. This is one
of the prominent features of mathemati-
cal life at Yale. The fortnightly meet-
ings, held in the Sloane Laboratory,
are largely attended, and the number
of papers to be presented exceeds the
Two series of papers
were, among others of miscellaneous
character, on the program for the Fall
of 1898: one on the relation between
our intuitional and analytical notions ot
a curve, the other on hypercomplex
numbers, of which the well-known
quarternions are a type.
An important factor in the education
of students of Mathematics at Yale is
found in the recently equipped seminary
library rooms. Two pleasant and con-
veniently situated rooms have been set
apart for this purpose, and friends of
the Department, by donation of money
and books, have provided a_ well-
equipped and thoroughly modern de-
partmental library. There are separate
drawers and shelves for the books and
papers of the students. These rooms
are forming a central place of meeting
for students in the Department, and
everything is done to this end, in the
belief that the daily intercourse of stu-
dents among themselves has an educa-
tional value of great importance.
YALE TEXT-BOOKS.
Yale has always stood for an educa-
tional force; its professors have not
only done their part to advance science
by original contributions, but they have
in an unusual degree helped to make
science accessible by writing excellent
text-books. This has been particularly
true in Mathematics. At the com-
mencement of the century Yale had
taken a prominent position in this re-
pect. The mathematical series of Pro-
fessor Day, afterwards President of the
College, had a widespread popularity.
The series prepared by Professor
Loomis numbered fifteen volumes, and
embraced not only Pure Mathematics,
but its application to surveying, naviga-
tion, and astronomy, as well as a
treatise on the allied subjects of Natural
Philosophy and Meteorology. It is safe
to say that over one hundred thousand
copies of these books have been; sold.
This fact makes comment on their value
superfluous.’ ~The tradition so early
established is being continued. A short
time ago, at the request of Messrs. Har-
per and Brothers, Professor Phillips -
undertook to prepare a new series of
text-books on Algebra, Geometry,
Trigonometry, Analytical Geometry,
and. the Calculus, which are to be fully
abreast of the best methods and ad-
vances in the science. A characteristic
feature is the admirable photogravures
of the figures of Solid Geometry, made
from models in this subject belonging
to the Yale collection. .The constant
efforts of Professor Phillips, already re-
ferred to, to derive all possible benefit
from our geometrical intuition by the
help of models, is thus bearing frwit in
a new and broader field.
- =_
Ce. 2
The Scientific Monthly has announced
that a gold medal of the value of twenty
dollars will.be offered for the best ar-
ticle on some ‘scientific subject, written
by an undergraduate of the Scientific
Department. This has become possi-
ble through the kindness of Professor
Chittenden, who gives the medal this
year. The main object of this offer is
to stimulate undergraduates in all
courses to write on science and for the
Scientific Monthly.
HARVARD-TALE FIGURES, —
A Letter From Dean Briggs of HWar-
vard on the Comparison.
To the Editor of Yate ALUMNI WEEKLY:
Sir:—As a constant reader of the
Yate ALtumni WEEKLY, I am interested
in the Yale and Harvard statistics on
the first page of the WEEKLY for March
Ist. I understand that, in each study,
the method of computation (for Har-
vard, at any rate) was to multiply the
number of undergraduates in every
course by the number. of hours of
instruction given per week, and then to
add the products. As Professor Mor-
gan points out, our two half-courses in
Military Science, each offering three
hours of instruction a week for a half-
year, contained respectively 146 and 99
students. Thus, according to the YALE
ALUMNI WEEKLY, 245 students, each
having what amounted to an hour and
a half of instruction in Military Science
throughout the year, got a total of 367
hours of instruction in Military Science.
This is an entirely fair way of reckon-
ing, yet may need explanation. If Yale
is said to give 14 hours of instruction
in Military Science and Harvard 367,
it seems at first to mean a much greater
discrepancy than really exists in the
amount of instruction offered. Ob-
viously, the fact is that a very much
larger number of students elected Mili-
tary Science at Harvard than at Yale.
Again, as regards Ancient Languages
and Mathematics, the fact that those
studies are prescribed at Yale, and not
at Harvard, is evidence that more im-
portance is accorded to them at Yale
than at Harvard; yet it is not evidence
that more hours of instruction per week
are given to them, unless we accept, as
a definition of an hour’s instruction, an
hour’s imstruction to one undergraduate.
The statistics of the WEEKLY are
clear, when the unit of computation and
the relation of the elective system at
Yale to the elective system at Harvard
are clearly understood. Unless these
things are clearly understood, a reader
might easily be misled. I do not know
whether misleading him would lead him
toward Yale or toward Harvard; and
my letter, like your statistics, is meant
to be wholly non-partisan,
Sincerely yours, |
L. B. R.. Briaas.
Harvard College,
Cambridge, March 6th, 1899.
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Resignation of Prof. Hoppin.
On Monday, March 13th, Professor
James Mason Hoppin announced his
resignation from the Professorship of
the History of Art in the Yale Art
School, thus closing a period of thirty-
eight years of continuous service in the
work of the University.
Professor Hoppin was graduated from
Yale at the age of twenty years, in the
Class of Forty. After graduation, he
studied Law at Harvard and Theology
at Andover, and afterwards in Berlin
University, Germany. ;
After his return to America he be-
came pastor of a church in Salem,
Mass., where he remained for ten years.
In 1861 he was made professor of
Homiletics and the Pastoral Charge
in the Yale Divinity School. He oc-
cupied this position for eighteen years,
finally resigning in 1879 to accept the
professorship ‘) the History of Art in
the Art School. 7
During his life Professor Hoppin has
published several books. Among them
are ‘Notes of a Theological Student;
“Old England: Its Scenery, Art and
People’; “Office and Work of the
Christian Ministry’; “Life of Rear-
Admiral Andrew Hull Foote’; “Memoir
of Henry Armitt Brown’; Homiletics” ;
“Pastoral Theology”; ‘Office of the
Ministry”; “Sermons on Faith, Hope
and Love’; “The Early Renaissance,
and other Essays on Art Subjects,” and
“Greek Art on Greek Soil.”
—_— ~~
a
E. Layton DeForest, 1900S. will be
married to Miss Margie D. Bliven, on
Wednesday, April 12. Among the
ushers will be John F. Archbold, ‘99 so
John H. Inman, 1900 S.; John C. Green-
leaf, ’99 S.; and Eliot Cutter, 1900S.
Mr. deForest and his bride will sail for
Europe on Wednesday, April 19.
