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About Yale Alumni Magazine | View Entire Issue (March 15, 1899)
YALE ALUMNI WEEKLY ae Cpeciga tye ES ‘ ae 3 5 ne igs 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. <> > 4 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.
