This course is intended for those who do not wish to take the longer course in Calculus (three quarters), but who, nevertheless, desire to round out their previous mathematical work with some knowledge of a subject of such great importance, both in pure mathematics and the natural sciences, as the Calculus. Certain students expecting to take the longer course in Calculus may advisedly take this course as an introductory course. Students of the College of Science may take Course 15 instead of Course 3 as a required course. 17. Integral Calculus.-An elementary course with much practice in connection with applications to problems of geometry, analysis, and physics. Mj. Summer Quarter; 8:00 DR. LUNN Prerequisite: Differential Calculus. 18, 19, 20. Calculus, I, II, III.-The fundamental principles and processes of the differential and integral Calculus, with constant use of graphical methods and with much attention to the solving of problems illustrating all phases of the theory and certain important applications to geometry and mechanics and physics. Three consecutive Majors, Laboratory Method, Autumn, Winter, and Spring Quarters; 2:00-4:00 PROFESSOR MOORE Prerequisite: Courses 1, 2, 3, or their equiva lent. NOTE.-A student exceptionally strong in Courses 1 and 2 may, after conference with the instructor, enter Course 18 without having taken Course 3. SENIOR COLLEGE COURSES [COLLEGE OF EDUCATION, 135] Surveying and Astronomy. This course includes practical work with surveying instruments. Mj. Spring Quarter; 9:30-11:30 Prerequisite: Plane Trigonometry and College Algebra. NOTE.-The registration is limited to sixteen. To cover cost of repairs to instruments each student makes a deposit of $5.00 with the Registrar. 31. Solid Analytics and Determinants. Mj. Summer Quarter; 9:00 ASSISTANT PROFESSOR YOUNG Mj. Autumn Quarter; 12:00 ASSOCIATE PROFESSOR MASCHKE Prerequisite: Plane Analytics and Calculus. 32. Algebraic Analysis.—The complex number system (of ordinary Algebra). Roots of unity. Theory of equations. Infinite series. Mj. Winter Quarter; 12:00 ASSOCIATE PROFESSOR MASCHKE Prerequisite: Plane Analytics and Differential Calculus. 36. Advanced Calculus, I.—The theory of simple and multiple definite integrals and allied subjects, with applications to geometry. Mj. Summer Quarter; 10:30 ASSOCIATE PROFESSOR MASCHKE Prerequisite: Differential and Integral Cal culus. 37. Advanced Calculus: I. Differential Equations.— culus. 38, 39. Advanced Calculus: II. Elliptic Integrals; III. Definite Integrals. With especial attention to the applications. 2Mj. Winter and Spring Quarters; 8:30 ASSISTANT PROFESSOR SLAUGHT Prerequisite: Course 37. [ASTRONOMY 5, 6, 7] Analytic Mechanics, I, II, III. 3Mj. Autumn, Winter, and Spring Quarters; 9:30. ASSISTANT PROFESSOR MOULTON 44. Practice Teaching of Mathematics by the Laboratory Method. For teachers and advanced students who expect to become teachers of Mathematics. Practice work in the laboratory teaching of classes in Algebra, Plane and Solid Geometry, Trigonometry, College Algebra, Analytics and Calculus. Those wishing to reg. ister will confer in advance with Professor Moore or Assistant Professor Young (for the Junior College work), and with Professor Myers (for the University High School work). [COLLEGE OF EDUCATION, 132] The Teaching of Mathematics for Elementary Schools. Mj. Summer Quarter; 11:30 45A, B, C, D. Mathematical Reading and Research. When in the judgment of the Department it is advisable that students undertake definite mathematical reading and research not closely connected with any current lecture course or Seminar, this work will be directed by one or other of PROFESSORS MOORE, BOLZA, MASCHKE, DICKSON [COLLEGE OF EDUCATION, 133] The Teaching of Secondary Mathematics. Mj. Summer Quarter; 10:30 PROFESSOR MYERS GRADUATE COURSES 65. Critical Review of Secondary Mathematics (for Teachers). A brief survey of the subject-matter of Secondary Mathematics as seen in the light of modern mathematics, aiming both to organize the theory of the whole scientifically and to gather the products of this work for use in teaching. Actual drill in solving problems will be introduced as needed. Reports on assigned readings (such as critical comparison of the same topic in leading American and foreign texts) will constitute an important part of the work. Primarily for teachers, actual or prospective, but open also to others. Mj. Summer Quarter; Mon. and Thurs., 3:305:30. ASSISTANT PROFESSOR YOUNG Prerequisite: Working knowledge of Secondary Mathematics.. 71. Theory of Numbers.-Elements of the theory of numbers; introduction to the theory of algebraic numbers; finite and infinite groups; finite and infinite fields. Mj. Summer Quarter; 2:30 ASSISTANT PROFESSOR DICKSON Mj. Autumn Quarter; 9:30 ASSISTANT PROFESSOR YOUNG 78. Multiple Algebra and Quaternions.—An introduction to the general theory of hypercomplex numbers, with particular attention to quaternions and matrices. PROFESSOR BOLZA Prerequisite: Theory of Equations, Solid Analytics, and a certain general maturity. [Not to be given in 1905-6] 81, 82. Finite Groups with Applications I, II.-Substitution groups in connection with the theory of algebraic equations; abstract groups; linear congruence and collineation groups; rotation groups and the simpler of Klein's two treatments of equations of the fifth degree. Seminar discussion of recent results, in particular those of Frobenius. ASSISTANT PROFESSOR DICKSON [Not to be given in 1905-6] 84. Continuous Groups and Differential Equations.— An illumination of the fundamental concepts and theorems of the Lie theory in connection with various classes of problems of geometry and differential equations. ASSISTANT PROFESSOR DICKSON [Not to be given in 1905-6] 94. Theory of Invariants.-The theory of binary quantics ("modern higher algebra") with applications to the theory of equations and to geometry. Mj. Spring Quarter: 11:00 PROFESSOR BOLZA Prerequisite: Theory of Equations and Advanced Calculus. 97. Algebraic Numbers and Forms.—An introduction to the theory in the spirit of Kronecker; application to the Galois theory of algebraic equations. Based on J. König's Einleitung in die allgemeine Theorie der algebraischen Grössen (Leipzig: Teubner, 1903). Mj. Spring Quarter; 12:00 ASSISTANT PROFESSOR DICKSON Prerequisite: Theory of Functions: I, Theory of Numbers. 115, 116. Selected Chapters in the Theory of Functions of Real Variables, I, II.-An advanced course, considering, in particular, recent researches in the theories of point sets, series, definite integrals, and various representations of arbitrary functions. 2Mj. Autumn and Winter Quarters; 12:00 PROFESSOR MOORE 118, 119. Calculus of Variations, I, II.-An advanced course on the theory of maxima and minima of definite integrals, with numerous applications to problems of geometry and mechanics. PROFESSOR BOLZA [Not to be given in 1905-6] 121. Theory of Functions of a Complex Variable, I. An introductory course: Geometrical repre XVIII. THE DEPARTMENT OF ASTRONOMY AND ASTROPHYSICS OFFICERS OF INSTRUCTION *GEORGE ELLERY HALE, S.B., Sc.D., Professor of Astrophysics, and Director of the Yerkes Observatory.† EDWIN BRANT FROST, A.M., Professor of Astrophysics, and Director of the Yerkes Observatory. SHERBURNE WESLEY BURNHAM, A.M., Professor of Practical Astronomy, and Astronomer in the Yerkes Observatory. EDWARD EMERSON BARNARD, A.M., Sc.D., Professor of Practical Astronomy, and Astronomer in the Yerkes Observatory. KURT LAVES, A.M., PH.D., Assistant Professor of Astronomy. FOREST RAY MOULTON, A.B., PH.D., Assistant Professor of Astronomy. GEORGE WILLIS RITCHEY, Assistant Professor of Practical Astronomy, and Superintendent of Instrument Construction at the Yerkes Observatory.† JOHN ADELBERT PARKHURST, S.M., Instructor in Practical Astronomy. FERDINAND ELLERMAN, Instructor in Astrophysics at the Yerkes Observatory.† WALTER SIDNEY ADAMS, A.M., Instructor in Astrophysics at the Yerkes Observatory.† STORRS BARROWS BARRETT, A.B., Secretary and Librarian of the Yerkes Observatory. WILLIAM RAYMOND LONGLEY, A.B., S.M., Assistant in the Students' Observatory (Summer Quarter, 1905). FELLOWS, 1905-6 FRANK LOXLEY GRIFFIN, S.B. PERRY WILSON JENKINS, A.B. INTRODUCTORY The work of the Department of Astronomy and Astrophysics naturally divides itself into two parts: 1. Work at the University, comprising: (a) elementary instruction in general Astronomy, both theoretical and practical; (b) preliminary training in the principles and methods of work underlying the science of Astrophysics, given in part in the undergraduate and graduate courses offered by the Department of Physics; (c) graduate and research work in Celestial Mechanics and Practical Astronomy. 2. Graduate and research work in Practical Astronomy and Astrophysics in the Yerkes Observatory at Lake Geneva. In the work at the University, given by Assistant Professors Laves and Moulton, special emphasis will be laid on the development of the mathematical methods and principles which lie at the basis of the physical sciences. In addition to the annual courses in Descriptive Astronomy, Introduction to Celestial Mechanics, Spherical and Practical Astronomy, Orbits and Ephemerides, and Analytical Mechanics, courses in the various branches of Celestial Mechanics will be given within periods not exceeding three years. The most fundamental subjects will be arranged in a cyclic manner so as to recur at regular intervals, while other more special topics will vary from time to time. The general object of the instruction will be: (1) to furnish the student an adequate mathematical basis for successful work in Celestial Mechanics; (2) to give such experience and preliminary training in the work of observation and reduction as will enable the student to use intelligently and skilfully any of the astronomical or astrophysical instruments of a modern observatory; (3) to direct research work in Celestial Mechanics. In the work at the Observatory attention will be devoted both to the investigations of Practical Astronomy and to those of Astrophysics. The rapid development of the latter science within the last few years has been fully recognized and amply provided for in the design of the Observatory and in its instrumental equipment. The special laboratory facilities will render possible many astrophysical investigations which are necessarily neglected in other institutions. The Observatory will be open to those students only who have completed the necessary preliminary work at the University or its equivalent at other institutions. Undergraduate students, in the S.B. course, who desire to specialize along the line of Astronomy, are recommended to take six Majors in Mathematics, viz.: Differential and Integral Calculus 3; Solid Analytic * Resigned as Director of the Yerkes Observatory. †1905-6 at Mount Wilson (Pasadena), California, on the Expedition for Solar Research. Geometry 1; Advanced Integral Calculus 2; and three Majors in Astronomy, viz.: Descriptive Astronomy, Introduction to Celestial Mechanics, and Spherical and Practical Astronomy. Graduate students working for the Master's degree are recommended to choose three Majors in the Department of Mathematics, viz.: Differential Equations, 1; Theory of Equations, 2; or in the Department of Physics, viz.: Advanced General Physics 3; and six Majors in the Department of Astronomy. Candidates for the degree of Doctor of Philosophy are expected to make their secondary subject either Mathematics or Physics. Students intending to specialize in the lines of Astrophysics will be required to take the work in Theoretical Physics, Advanced Experimental Physics, Sound and Light, and Physical Manipulation. Graduate Scholarships, Fellowships, and Docentships, will be assigned in accordance with the general regulations of the University. Details regarding the appointment of Volunteer Research Assistants and Special Investigators at the Yerkes Observatory may be found on page 144 of this Register. The Departmental Club meets fortnightly on Fridays at 4:00 P.M. in the Ryerson Physical Laboratory, Room 35, 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 Mathematical Astronomy are expected to attend regularly and, so far as possible, to participate actively in the meetings of the Club. The Department of Astronomy at the University occupies at present rooms on the third floor of the Ryerson Physical Laboratory. For the purpose of instruction in Practical Astronomy a Students' Observatory, consisting temporarily of two small buildings, has been provided west of the quadrangles. It is equipped with a modern Warner and Swasey equatorial telescope of 61⁄2-inches aperture, provided with a filar micrometer with position circle, a modern Bamberg broken transit instrument of 3 inches aperture, a Bamberg universal instrument, a Riefler sidereal clock, a chronometer, and various smaller accessories. The laboratory courses offered by the Department of Physics afford excellent preliminary training for the work in Astrophysics. A description of the Yerkes Observatory at Lake Geneva and its equipment will be found on pages 143, 144 of this Register. The publications of the Department are enumerated in the description of the Observatory. The Astronomical Library is open to Graduate students under the same conditions as the Mathematical Library, with which it is associated. The Astronomical Library includes many of the fundamental works on Astronomy, several sets of annals, and a number of journals. |
