of the differential calculus, adapted particularly to the needs of students in engineering. 5 hrs., throughout the year. M Tu W Th F, 8. Prescribed, Freshman year, in the Colleges of Engineering. Open to other students who have passed in Solid Geometry and Plane Trigonometry. 3B. Elements of Analysis, with Applications; Second Course. Associate Professor EDWARDS, Dr. WILCZYNSKI, Mr. WHITNEY, Dr. PUTNAM, and Dr. McDONALD. Continuation of Course 3A. Differential and integral calculus, with applications to geometry. 3 hrs., throughout the year. M W F, 8, 9. Prerequisite: Course Prescribed, Sophomore year, in the 3A, or its equivalent. 4. Plane Trigonometry. Dr. WILCZYNSKI, Dr. LEHMER, Dr. PUTNAM, The development of the general formulæ of plane trigonometry. Practice in the use of logarithmic tables; applications of trigonometry to the solution of triangles and to mensuration in general. 2 hrs., either half-year. First half-year, Tu Th, 9, 10, 11; second half-year, Tu Th, 10, 11. 5. Plane Analytic Geometry. Dr. LEHMER, Dr. BLAKE, Dr. PUTNAM, and Dr. McDonald. The analytic geometry of the straight line, the circle, and the conic sections, including a discussion of the general equation of the second degree, and some special examples in higher loci. 3 hrs., either half-year. M W F, 9, 10. Prerequisite: Course 4. 6. Solid and Spherical Geometry. Mr. WHITNEY, Dr. LEHMER, Dr. BLAKE, and Dr. McDONALD. The fundamental propositions of the Euclidean geometry of space. 2 hrs., either half-year. Two sections, each half-year. 9, 10. 7. Spherical Trigonometry. Tu Th, Mr. WHITNEY. The development of the formulæ of spherical trigonometry, the solution of spherical triangles, problems in spherical mensuration. 1 hr., second half-year. Tu, 4. INTERMEDIATE COURSES. PRIMARILY FOR SOPHOMORES AND JUNIORS. 9. Differential and Integral Calculus; First Course. Professor STRINGHAM. Development of the fundamental principles and formulæ of the differential and integral calculus; applications to various problems in geometry and analysis, such as indeterminate forms, maxima and minima, expansions of functions in series, curvature, length of curves, areas, volumes, centers of position, etc. 3 hrs., throughout the year. M W F, 9. Prerequisite: Course 1 or Course 5. 9B. Differential and Integral Calculus; First Course. Dr. WILCZYNSKI and Mr. WHITNEY. The equivalent of Course 9 or Course 3B. 3 hrs., throughout the year, beginning second half-year. 10. Prerequisite: Course 1 or Course 5. M W F, 10. Problems in the Differential and Integral Calculus. (G. E.) Dr. LEHMER, Dr. PUTNAM, and Dr. McDONALD. 2 hrs., second half-year. Tu Th, 9. Prescribed, Sophomore year, in the College of Civil Engineering; elective in the College of Mechanics, with Mechanical Engineering, Course 8B. 11. Determinants and Theory of Equations. (G. E.) Associate Professor EDWARDS. The theory of determinants and their more important applications to geometry and algebra; algebraic resolution of equations, elimination, elements of the theory of substitutions, and introduction to the theory of invariants. 2 hrs., throughout the year. Tu Th, 9. Open to students who have taken, or are taking, Course 9. 12A. Advanced Analytic Geometry. (G.E.) Dr. LEHMER. General properties of conic sections; introduction to the theory of higher plane curves. 3 hrs., first half-year. Course 5. M W F, 10. Prerequisite: Course 1 or 12B. Analytic Geometry of Three Dimensions. (G.E.) Dr. WILCZYNSKI. The elementary analytic geometry of the straight line in space, the plane, the sphere, and the conicoids, and a discussion of the theory of higher curves and surfaces, including the deter- 3 hrs., second half-year. M W F, 2. Open only to students who Dr. LEHMER. 13. Synthetic Projective Geometry. (G.E.) 3 hrs., second half-year. M WF, 1. 14. Differential and Integral Calculus; Second Course. (G. E.) Dr. NOBLE. Continuation of Course 9. 3 hrs., throughout the year. M W F, 9. Prerequisite: Course 9 or 9B. COURSES FOR GRADUATES AND ADVANCED 15. Analytic Projective Geometry. (G.E.) Professor STRINGHAM. The fundamental principles of projective geometry treated analytically. The principle of duality, cross-ratios, involution, linear transformations of one, two, and three dimensional figures, particularly of loci of the second order and class. 3 hrs., throughout the year. MWF, 10. Prerequisite: Course 12A. *16. Quaternions. Associate Prosessor HASKELL. (G.E.) An elementary presentation of the principles of the subject, with illustrations of its application to geometry and to mechanics. M WF, 2. 3 hrs., throughout the year. 17. History of Mathematics. (G.E.) Professor STRINGHAM. Outlines of the history of mathematical discovery, and of the development of mathematical thought, with special reference to its significance as a factor in intellectual progress. 1 hr., throughout the year. F, 11. 18. Logic of Mathematics. (G.E.) Professor STRINGHAM. Analysis of the foundation principles of geometry and algebra. The number-system and the vector-system of algebra compared. The geometrical theory of proportion, and the irrational. The non-Euclidean geometry. Pre 2 hrs., throughout the year. M W, 11. Designed especially for teachers and prospective teachers of mathematics. requisite: A course in formal logic. *Not given in 1902-03. 19A. Differential Equations. (G.E.) Associate Professor EDWARDS. Theory and methods of solution of ordinary differential equations, followed by a short introduction to partial differential equations. Prescribed, Junior year, in 3 hrs., first half-year. M W F, 10. the College of Mechanics. 19B. Differential Equations. (G.E.) Associate Professor EDWARDS. 3 hrs., second half-year. M W F, 10. have completed Course 19A. Elective to students who *20. Selected Topics in Higher Mathematics. (G.E.) Dr. WILCZYNSKI. A general introduction to some important methods in modern higher mathematics. 2 hrs., throughout the year. Tu Th, 9. 20A. Theory of Probabilities, with special reference to the problems of Life and Endowment Insurance, and of Annuities. (G.E.) Mr. WHITNEY. 2 hrs., first half-year. Tu Th, 10. Students electing this course are advised to elect also Course 22 in History and Political Science (Statistics). HIGHER COURSES. PRIMARILY FOR GRADUATE STUDENTS. Of the following courses it is expected that five or six will be offered each year. In 1902-03 these will be Courses 24, 25, 27, 32, 33, and 40. Students in order to elect any of them must have previously taken the prerequisite intermediate courses; in most cases, at least Courses 9, 11, 14, and 15. *21. Theory of Functions of Real Variables. Professor STRINGHAM. Simple and multiple integrals; line, surface, and space integrals; Laplace's Equation and its applications; series; geometrical applications. 2 hrs., throughout the year. *22 Transformation Groups and Differential Equations. Dr. WILCZYNSKI. An introduction to Lie's Theory; applications to the theory of functions, to the theory of invariants of linear differential equations, and to hydrodynamics. 2 hrs., throughout the year. *Not to be given in 1902-03. ANN'M'T-6 *23. Partial Differential Equations. Mr. WHITNEY. Theory of definite integrals, Fourier's Theorem and applications, introduction to harmonic functions. 2 hrs., second half-year. 24. Theory of Functions of a Complex Variable. Mr. WHITNEY. (Introductory course.) Lectures on the general theory of functions, with special reference to the ideas of Riemann. 3 hrs., first half-year. M W F, 3. 25. Higher Geometry. Dr. BLAKE. Modern developments in the analytical geometry of two and of three dimensions. Application of the differential and integral calculus to algebraic curves and surfaces. 3 hrs., throughout the year. *26. Absolute Geometry. Professor STRINGHAM. An analytical treatment of the absolute geometry of space. 2 hrs., throughout the year. S, 9-11. 27. Elliptic Functions. Dr. NOBLE. Reduction of elliptic integrals, Abel's Theorem, development of elliptic functions in series, applications to various problems of geometry and mechanics. 3 hrs., second half-year. M W F, 2. Prerequisite: Course 24. *28. Abelian Functions. Associate Professor HASKELL. An advanced course in the theory of functions of a complex variable, with applications to the theory of higher plane curves. 3 hrs., throughout the year. Prerequisite: Course 24. *29. Spherical Harmonics. Associate Professor HASKELL. Elements of the theory of spherical harmonics, with special reference to their application in the solution of certain physical problems. 2 hrs., second half-year. *30. Theory of Algebraic Forms. Associate Professor HASKELL. Theory of linear transformation, invariants and covariants of binary and ternary quantics. Applications to the theory of equations, and to higher plane curves. 3 hrs., throughout the year. *Not to be given in 1902-03. |