MATHEMATICS. IRVING STRINGHAM, Ph. D., Professor of Mathematics. Students in the College of Letters, or of Social Sciences, or of Natural Sciences, must include the subject of Analytic Geometry as an essential part of their programme of mathematical studies. They may satisfy this prescription by electing Course 1 in their Freshman year; but those who desire to continue their mathematical studies beyond the first year should elect Courses 2, 4, and 5. Course 6 is strongly recommended to all students who have not already studied Solid Geometry. Course 1 should not be chosen as a preparation for more advanced mathematical studies. Students in the College of Commerce must include in their mathematical studies Courses 2, 4, and 5. Students in the College of Agriculture may elect either Courses 2, 4, 5, and 6, or Course 3A, if they enter with credit in Solid Geometry and Plane Trigonometry. Course 3A is prescribed to Freshmen and Course 3B to Sophomores in the Colleges of Engineering and of Chemistry; Course 10 to Sophomores in the College of Civil Engineering; Course 19A to Juniors in the College of Mechanics. These courses are also open to students in any of the other colleges who have the necessary preparation. Students wishing to make a specialty of Mathematics should consult the members of the department as early as possible. The following *On leave 1903-04. programme may serve as a proper sequence: Freshman year: Courses 2, 4, 5, 6; Sophomore year: Courses 9, 12, 13; Junior year: Courses 11, 14, 15; Senior year: Courses 18, 19, 20. Students wishing to take mathematics with reference to its applications to Astronomy and Physics, should elect Course 9, 14, 19, and · if possible, 23 and 24. The Group Elective. A thorough knowledge of algebra, plane trigonometry, plane analytic geometry, and the differential and integral calculus is prerequisite to Group Elective work. Teachers' Certificates. The department will, in general, recommended as qualified to teach mathematics in high schools, only such graduates as have passed with credit in Courses 2, 4, 5, 6, 9, 11, 12a, 12B, 13, 18. It is also of great importance that the prospective teacher of mathematics should be well informed on the relation of mathematics to other sciences, and he should to that end devote a considerable portion of his time to at least one of the closely related sciences. The department further reserves the right to exact a practical test of the candidate's ability to present a clear and interesting exposition of subjects taught in the high schools. INTRODUCTORY COURSES. FOR FRESHMEN AND SOPHOMORES ONLY. 1. Elements of Analysis. Professor STRINGHAM and Associate Professor HASKELL. The methods of higher algebra, trigonometry, analytic geometry and the calculus, with some account of their historical development. 3 hrs., throughout the year. M W F, 9; Tu Th S, 8. Prescribed (except as provided above) to Freshmen in the Colleges of Letters, Social Sciences, and Natural Sciences. 2. Algebra. Assistant Professor NOBLE, Mr. WHITNEY, and Dr. PUTNAM. The progressions and other simple series, inequalities and limits, exponentials and logarithms, permutations and combinations, binomial theorem for any index, expansion of functions in series, convergency of series, determinants, elements of the theory of equations. 3 hrs., either half-year. M W F, 9, 10. 3A. Elements of Analysis, with Applications; First Course. Associate Professor EDWARDS, Assistant Professor NOBLE, Dr. LEHMER, Mr. WHITNEY, Dr. BLAKE, Dr. PUTNAM, and Dr. McDONALD. A practical course in algebra, analytic geometry, and the elements of the differential calculus, adapted particularly to the needs of students in engineering. 5 hrs., throughout the year. M Tu W Th F, 8, 9. 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. LEHMER, Dr. BLAKE, 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 3A, or its equivalent. Prescribed, Sophomore year, in the Colleges of Engineering and of Chemistry. 4. Plane Trigonometry. Dr. LEHMER, Mr. WHITNEY, and Dr. McDONALD. 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. Associate Professor EDWARDS, Associate Professor HASKELL, Assistant Professor NOBLE and Dr. PUTNAM. 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, 10; Tu Th S, 9. Course 4. 6. Solid and Spherical Geometry. Prerequisite: Assistant Professor NOBLE, Dr. BLAKE and Dr. McDONALD. The fundamental propositions of the Euclidean geometry of space. 2 hrs., either half-year. Two sections, each half-year. Tu Th, 9, 10. 7. Spherical Trigonometry. Dr. LEHMER and Dr. PUTNAM. The development of the formulæ of spherical trigonometry, the solution of spherical triangles, problems in spherical mensuration. 1 hr., second half-year. INTERMEDIATE COURSES. 9. Differential and Integral Calculus; First Course. Associate Professor HASkell. 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: Courses 2, 4, and 5. 9B. Differential and Integral Calculus; First Course. Assistant Professor NOBLE and Mr. WHITNEY. The equivalent of Course 9 or Course 3B. 3 hrs., throughout the year, beginning second half-year. M W F, 10. Prerequisite: Courses 2, 4, and 5. 10. Problems in the Differential and Integral Calculus. (G.E.) Mr. WHITNEY, 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.) Assistant Professor Noble. 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, 11. Open to students who have taken, or are taking, Course 9. 12A. Advanced Analytic Geometry. (G.E.) Dr. McDONALD. 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. LEHMER. 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 determination of curvature, by the methods of the differential calculus. 3 hrs., second half-year. M W F, 2. Open only to students who have taken, or are taking, Course 9 or 9B. 13. Synthetic Projective Geometry. (G.E.) 3 hrs., first half-year. M W F, 10. Dr. LEHMER. *14. Differential and Integral Calculus; Second Course. (G.E.) Assistant Professor NOBLE. Continuation of Course 9. 3 hrs., throughout the year. M W F, 10. 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. M W, 11; F, 1. Prerequisite: Course 12A. *16. Quaternions. (G.E.) Associate Professor HASKELL. An elementary presentation of the principles of the subject, with illustrations of its application to geometry and to mechanics. 3 hrs., throughout the year. M W F, 2. 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. 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. *Not to be given in 1903-04. |