45. Aesthetics.-An introduction to the history and theory of aesthetics. Mj. Spring, PROFESSOR TUFTS.

46. Le classicisme.-[See XIII, 18.] Mj. Autumn, 11:45, ASSISTANT PROFESSOR DAVID.

47. La réaction contre le classicisme.-[See XIII, 19.] Mj. Winter, 11:45, ASSISTANT PROFESSOR David.

48. The Technique of the Drama.-[See XV, 140.] Mj. Winter, 3:30, PROFESSOR HERRICK.

49. Studies in Romanticism in English Literature of the Eighteenth Century. -Criticism 1725-75. For graduate students only. [See XV, 56C.] Mj. Winter, 9:15, PROFESSOR MACCLINTOCK.

NOTE.-Course 60 may be reckoned for Section II or Section III.

III. COURSES IN COMPARATIVE LITERATURE

NOTE.-These are graduate courses.

60. Types of Old French Literature. [See XIII, 26.] Mj. Winter, 11:45, PROFESSOR NITZE.

61. Germanic Mythology. [See XIV, 145.] Mj. ASSOCIATE PROFESSOR ALLEN. [Not given in 1914-15.]

62. The Romantic School.-[See XIV, 180.] Seminar. ASSOCIATE PROFESSOR SCHÜTZE. [Not given in 1914-15.]

64. The Literary Relations between England and Germany in the Eighteenth Century. [See XIV, 190.] Mj. Summer, 8:00, PROFESSOR HEINZELMANN.

65. The German Court Epic: Hartmann von Aue.-A critical reading of his Iwein with reference to its Old French prototype. Mj. Winter, 9:15, PROFESSOR CUTTING.

See also XIV, 218: German-American Literature. (a) Indian and Emigrant Fiction, M.; (b) German-American Poetry, M. Summer, 11:30, DR. BARBA.

XVII. THE DEPARTMENT OF MATHEMATICS

OFFICERS OF INSTRUCTION

ELIAKIM HASTINGS MOORE, PH.D., LL.D., Sc.D., MATH.D., Professor and Head of the Department of Mathematics.

OSKAR BOLZA, PH.D., Non-Resident Professor of Mathematics (Freiburg i.B.). HERBERT ELLSWORTH SLAUGHT, PH.D., Professor of Mathematics.

GEORGE WILLIAM MYERS, PH.D., Professor of the Teaching of Mathematics and Astronomy, the School of Education.

LEONARD EUGENE DICKSON, PH.D., Professor of Mathematics.

GILBERT AMES BLISS, PH.D., Professor of Mathematics.

ERNEST JULIUS WILCZYNSKI, PH.D., Professor of Mathematics.

JACOB WILLIAM Albert YOUNG, PH.D., Associate Professor of the Pedagogy of Mathematics.

WILLIAM HOOVER, PH.D., Non-Resident University Extension Assistant Professor of Mathematics (Athens, Ohio).

ARTHUR CONSTANT LUNN, PH.D., Assistant Professor of Applied Mathematics.

DAVID RAYMOND CURTISS, M.A., PH.D., Professor of Mathematics, Northwestern University (Summer, 1914).

CHARLES NAPOLEON MOORE, Sc.M., PH.D., Assistant Professor of Mathematics, University of Cincinnati (Summer, 1914).

FELLOWS, 1914-15

ALLEN FULLER Carpenter, A.B.
WILLIAM LEROY HART, S.B.
OLIVE CLIO HAZLETT, A.B.

ALFRED LEWIS NELSON, A.B.
CHESTER HENRY YEATON, A.M.

GENERAL STATEMENT

The regular Junior College courses are courses 1, 2, 3, 6, and 15.

Students who expect to specialize in Mathematics, Astronomy, or Physics should confer with the instructors in Mathematics in planning their courses. They should take courses 1, 2, 3, 18, 19, and 20. It is possible, however, for students of exceptional ability in Mathematics to pass from course 2 to course 18, if course 3 is taken at the same time as course 18. Students who desire to have at least a glimpse beyond the elements of mathematics should elect courses 3 and 15.

The following courses introductory to the Higher Mathematics are intended both (1) for students making Mathematics their principal subject, and (2) for those making Mathematics their secondary subject, in particular for students of Astronomy and Physics: (A) †Differential and integral calculus with applications (3Mj.); (B) †Solid analytics; selected topics in geometry; theory of equations; determinants and elementary invariants; (C) †Analytic mechanics (2Mj.); vector analysis; celestial mechanics (2Mj.); theory of the potential; (D) †Advanced calculus, †differential equations, †theory of definite integrals, elliptic integrals, Fourier series and Bessel functions, elements of the theory of functions; (E) Synthetic projective geometry; analytic projective geometry; differential metric geometry; differential projective geometry; (F) Theory of numbers; theory of invariants; selected chapters of algebra; theory of substitutions with applications to algebraic equations; quaternions.

Groups (A)-(F) indicate six sequences of courses running through the usual academic year from October to June. These sequences vary slightly from year to year; the courses marked (†) are given annually, and the other courses usually once in two years.

The undergraduate student who wishes to specialize in Mathematics should take courses of group (A) as Junior College electives, of (B) in his first Senior College year, and of (C) and (D) in his second Senior College year.

The courses of groups (A)–(F) and the special courses in the Higher Mathematics are intended to give the graduate student a comprehensive view of modern mathematics, to develop him to scientific maturity, and to enable him to follow, without further guidance, the scientific movement of the day in mathematics, and, if possible, to take an active part in it by creative research. The special and research courses vary from year to year. They may be classified, in general, as relating to (a) Algebra and Arithmetic; (b) Analysis; (c) Geometry; (d) Mechanics and Applied Mathematics; and (e) the Foundations and Interrelations of the Mathematical Disciplines as purely abstract deductive systems. Attention is called to courses of type (d) offered by the Departments of Astronomy and Physics.

The proper arrangement of courses is a matter of extreme importance; the best arrangement for any student depends on his previous mathematical studies, and should be determined by conference with some member of the Department.

The courses of the Summer Quarter are designed to meet the needs of those college men and others wishing to study Advanced Mathematics, who are able to spend only the summer in residence. The courses of a series of four summer quarters are arranged so as to give a wide view of modern mathematics.

Scholarship examinations.-The competitive examinations for the Senior College Scholarship and for the Graduate Scholarship in Mathematics are held each Spring Quarter at times and places announced in the Weekly Calendar. Prospective candidates should confer with the Departmental Examiner in Mathematics. Files of papers set at previous Scholarship examinations are accessible in the Departmental Library. Candidates for the Senior College Scholarship will be examined on courses 1, 2, and 3; those for the Graduate Scholarship on courses 18, 19, 20, 31, 32, 47, 48, and 49.

Models.—A collection of Brill's models: plaster and thread models of quadric surfaces, plaster models of cubic and Kummer's quartic surfaces, models of cyclides and surfaces of constant positive and negative curvature, and thread models of three-dimensional projections of four-dimensional regular bodies.

MATHEMATICAL CLUBS

The Departmental Club meets regularly for the review of memoirs and books, and for the presentation of results of research. The club is conducted by the members of the Faculties of Mathematics and Mathematical Astronomy. Graduate students of the departments are expected to attend and otherwise to participate in the meetings of the club.

The Junior Mathematical Club, with fortnightly meetings, is conducted by the graduate students of the departments of Mathematics and of Astronomy and Astrophysics.

HIGHER DEGREES

Master's degree.-Candidates for the Master's degree in Mathematics are expected, on the basis of a principal (or "long") sequence of nine majors of undergraduate mathematics, to offer for examination eight approved courses of groups (B)-(F), including the elements of the theory of functions, and to present a satisfactory thesis on an assigned topic closely related to the subject of one of the courses.

Degree of Doctor of Philosophy.-Candidates for the Doctor's degree with Mathematics as secondary subject are expected to offer for examination nine approved courses in advance of course 20.

Candidates for the Doctor's degree with Mathematics as principal subject are expected (1) to offer for examination the subjects covered by fifteen majors of initial courses of groups (B)–(F), and by a considerable body of special courses, in each case presumably most closely related to the subject of the doctoral dissertation, and (2) to present a dissertation, in finished form, embodying valuable results of mathematical inquiry. The subject of the dissertation may be a topic of pure or applied mathematics or of the history, philosophy, or pedagogy of mathematics.

PREPARATION FOR TEACHING

Courses in the history and the teaching of Elementary MathematicsArithmetic, Algebra, Geometry, Trigonometry, Analytic Geometry, Calculus, Mechanics are offered by this Department and the School of Education.

These courses embody the conviction that elementary students need to have their mathematics made, not easier, but more perfectly intelligible and attractive. To this end it is believed that teachers should more generally appreciate and utilize in instruction the unity of mathematics, as made up of various closely interrelated parts, and the character of mathematics, as an ideal science developed by abstraction from various more concrete domains.

A) Secondary-school positions.-Students who expect to teach mathematics as a major subject in secondary schools should complete at least the following courses in their undergraduate career: (1) Courses in pure mathematics: Trigonometry, College Algebra, Plane Analytic Geometry, Differential and Integral Calculus and Applications of Calculus, Theory of Equations, and the Synoptic course; (2) Courses in applied mathematics: Descriptive Astronomy, Mechanics, and General Physics; (3) The two courses, Principles of Education and Methods of Education, which may be taken either in the Junior College or in the Senior College; (4) Practice teaching in mathematics in the University High School, for which the above courses in education are prerequisite; (5) A course in the Teaching of Secondary Mathematics and a course in the History of Secondary Mathematics.

B) Minor collegiate positions.-Those who look forward to teaching mathematics in normal schools and small colleges should as undergraduates complete at least the following courses: (1) The general courses in education and those in the history and teaching of mathematics mentioned in (3) and (5) above; (2) The content courses specified in (1) and (2) above, together with Advanced Calculus (3 majors).

Candidates for these positions should take at least one year of graduate work leading to the Master's degree in Mathematics and during this year should visit some of the college courses in Mathematics with the purpose of observing methods of teaching. It is the intention of the Department to offer such candidates opportunity, as far as possible, to act as assistants in connection with the collegiate classes, in order that they may gain experience through both observation and practice.

C) University positions.-Candidates for university positions should qualify for the Doctor's degree. Courses in the history of mathematics and in the principles and practice of education are strongly recommended.

COURSES OF INSTRUCTION

I. JUNIOR COLLEGE COURSES

0. Solid Geometry. An elementary course based upon entrance Algebra and Plane Geometry. Mj. Autumn, MR.

NOTE. Students from accredited preparatory schools may present themselves for examination in this subject at the University for college credit.

1. Plane Trigonometry.-Mj. Summer, PROFESSOR SLAUGHT; Autumn, 2 sections, AssOCIATE PROFESSORS LAVES AND YOUNG; Winter, PROFESSOR SLAUGHT; Spring, ASSOCIATE PROFESSOR YOUNG.

2. College Algebra.-Prerequisite: course 1. Mj. Summer, ASSISTANT PROFESSOR C. N. MOORE; Autumn, MR. -; Winter, PROFESSOR WILCZYNSKI; Spring, MR.

3. Analytic Geometry. Elements of plane analytics, including the geometry of the conic sections, with an introduction to solid analytics. Prerequisite: courses 1 and 2. Mj. Summer, PROFESSOR BLISS; Autumn, PROFESSOR WILCZYNSKI; Winter, ASSOCIATE PROFESSOR YOUNG; Spring, PROFESSOR SLAUGHT.

6. College Geometry.-A collegiate sequel to elementary geometry, analogous to college algebra as a sequel to elementary algebra. The course will include systematic study of methods of attack of geometric problems, with applications to various fields including modern geometry of the triangle and geometric conics. Prerequisite: entrance plane geometry. Mj. Summer, ASSOCIATE PROFESSOR YOUNG.

15. Introductory Calculus.-The elementary fundamental principles, methods, and formulas of differential and integral calculus will be carefully studied in connection with simple problems of geometry and the physical sciences. This course is intended primarily for those who do not wish to take the longer course in Calculus (courses 18, 19, and 20). Prerequisite: courses 1 and 2. Mj. Spring, AsSOCIATE PROFESSOR YOUNG.

18, 19. Calculus I, II.-A development of the three fundamental notions of the Calculus: the derivative, the anti-derivative, the definite integral, with especial emphasis on their geometrical interpretations and their relations to problems in geometry, mechanics, and physics. Prerequisite: courses 1, 2, and 3. Two consecutive majors. Autumn and Winter, ASSISTANT PROFESSOR LUNN; Winter and Spring, PROFESSOR SLAUGHT.

18. Calculus I: Differential Calculus. A graphic study of rational algebraic functions and of certain simple irrational transcendental functions, yielding material for a geometric introduction to the fundamental notions and processes of the Calculus. Prerequisite: courses 1, 2, and 3. Mj. Summer, PROFESSOR CURTISS.

19. Calculus II: Integral Calculus.-A course aimed at a comprehension of the nature of integration and of its applications to geometry and physics; solution of numerous problems; use of table of integrals. Prerequisite: course 18. Mj. Summer, ASSISTANT PROFESSOR C. N. MOORE.

20. Applications of the Calculus.-Partial differentiation and multiple integrals. Elements of the theory of Differential Equations and applications of the Calculus to Mechanics. Introduction to Differential Geometry in the plane and in space. Prerequisite: courses 18 and 19. Mj. Spring, ASSISTANT PROFESSOR LUNN. [Not given in 1915.]

25. Graphical Methods in Algebra.-The cross-section paper as a mathematical instrument for the graphical study of the notion of functionality. M. PROFESSOR MOORE. [Not given in 1914-15.]

26. Graphical Analysis.-A brief study by graphical methods of the fundamental principles of Differential and Integral Calculus, with illustrations also of the theory of equations. This course is a desirable supplement to course 18. Mj. ASSISTANT PROFESSOR LUNN. [Not given in 1914-15.]

27. Units and Dimensions.-The theory of units and dimensions as applied to the measurement of concrete magnitudes and the mathematical transcription of physical experiments. Numerical computations and the reduction of observations. Prerequisite: Calculus and General Physics. Mj. Autumn, ASSISTANT PROFESSOR LUNN. [Not given in 1914-15.]

29, 30. Selected Topics in Geometry, I, II.-The fundamental notions of projective geometry treated both analytically and synthetically. The method of abbreviated notation and homogeneous co-ordinates. Theory of determinants, and their application to the geometry of two and three dimensions. Projective and dualistic transformations, and the simpler Cremona transformations. Notions of group and invariant. Prerequisite: courses 1, 2, 3, 18, 19. Two consecutive majors. Autumn and Winter, ASSOCIATE PROFESSOR WILCZYNSKI.

31. Solid Analytics.-This course may be taken simultaneously with course 18; it is an advisable antecedent of course 19. Prerequisite: courses 3 and 18. Mj. Winter, PROFESSOR DICKSON. Shorter course. M. Summer, First Term, PROFESSOR MOORE.