MATHEMATICS

Those students who take mathematics as their major work should take the courses in mathematics numbered 1, 3 (or 2, 4), 6, 8a, 8b, 10, 11, 15, 16, 17. They should also make sixteen hours' credit in either German or French. They are advised to take also physics 1, 3.

I. ADVANCED ALGEBRA.-This course is offered for those students who wish to cover in five hours of mathematical work the subject of college algebra and that of plane and spherical trigonometry (Math. 3). The course presupposes a thorough working knowledge of elementary algebra through simultaneous quadratics. The same subjects are considered as in course 2, but more briefly. I.; last seven weeks; daily; 10; (2). Mr. MILNE.

12. ADVANCED ALGEBRA.-This course is for those students who wish to cover in five hours of mathematical work the subject of college algebra and that of plane trigonometry (Math. 4.)

The following topics are considered: Progressions, undetermined coefficients, binomial theorem, logarithms, permutations and combinations, probability, convergence of series (or determinants), and the theory of equations, with special reference to the solution of numerical equations of the third and fourth degree. Sections A to O are for engineers, sections P to T are for students of the College of Science, and the College of Literature and Arts. I.; last eleven weeks; daily; section A, 1; section B, 11; section C, 9; section D, 10; section E, 1; section F, 8; section G, 10; section H, 2; section I, 8; section J, I; section K, 9; section L, 2; section M, 10; section N, 3; section O, 10; section P, 11; section Q, 1; section R, 2; section S, 9; section T, 10; (3). Assistant Professor RIETZ, Assistant Professor SLOCUM, Mr. MILNE, Dr. COAR, Mr. PONZER, Miss WHITE, Mr. LYTLE, Dr. NEIKIRK, Mr. RISLEY, Mr. EMMONS, Mr. REDDICK.

3. PLANE AND SPHERICAL TRIGONOMETRY.-This course covers the same ground in plane trigonometry as course 4. In addition to the work outlined there, about four weeks are spent on the general principles and applications of spherical trigonometry. I.; first eleven weeks; daily; 3; (3). Mr. MILNE.

Prerequisite: Solid and Spherical Geometry.

4. PLANE TRIGONOMETRY.'-Sections A to O are for engineers, sections P to T are for students of the College of Science, and the 'Two sections, N, J, repeat the work in the second semester.

College of Literature and Arts. I.; first seven weeks; daily; section A, 1; sections B, 11; section C, 9; section D, ro; sections E, I; section F, 8; section G, 10; section H, 2; section I, 8; section J, FI; section K, 9; section L, 2; section M, 10; section N, 3; section O, 10; section P, II; section Q, I; section R, 2; section S, 9; section T, 10; (2). Assistant Professor RIETZ, Assistant Professor SLOCUM, Mr. MILNE, Dr. COAR, Mr. PONZER, Miss WHITE, Mr. LYTLE.

Section U is taught on Tuesdays and Thursdays throughout the first semester, at the eighth hour, for students registered in the preliminary medical course.

5. TEACHER'S COURSE.-In this course special attention is given to a discussion of the methods of teaching algebra and geometry, the position of mathematics in the secondary school course, the correlation of mathematics with allied subjects, a comparative study of the leading text-books, and a brief history of elementary mathematics. Tu., Th.; 2; (2). Mr. COAR.

6. ANALYTICAL GEOMETRY.-The aim is to acquaint the student with analytical methods of investigation and to familiarize him with the general properties of conics, including a discussion of the general equation of the second degree and its geometrical interpretation. Special emphasis is placed upon the use of algebraic processes as a means of demonstrating geometrical properties of loci. To this is added a brief course on the analytical geometry of three dimensions, including co-ordinate systems in space, the relations of points, straight lines,and planes in space, as also the general properties of surfaces of second order. Sections A to O are for engineers, sections P to R are for students of the College of Science, and the College of Literature and Arts. II.; daily; section A, 1; section B, 11; section C, 9; section D, 10; section E, 1; section F, 8; section G, 10; section H, 2; section I, 8; section J, II; section K, 9; section L, 2; section M, 10; section N, 3; section O, 10; section P, 11; section Q, 1; section R, 8; (5). Assistant Professor RIETZ, Assistant Professor SLOCUM, Mr. MILNE, Dr. COAR, Mr. PONZER, Miss WHITE, Mr. LYTLE, Dr. NEIKIRK, Mr. RISLEY, Mr. EMMONS, Mr. REDDICK.

Prerequisite: Mathematics I, 3 or 2, 4.

7. DIFFERENTIAL CALCULUS.-The principles of the differential calculus are developed, and applied to functions of one and of several variables, with special reference to the needs of engineering "Two sections, N, J, repeat the work in the second semester.

students. I.; section A, 8; section B, 8; section C, 8; section D, 1; section E, 1; section F, 1; section G, 10; section H, 10; section 1,8; section J, 8; (5). Assistant Professor RIETZ, Assistant Professor SLOCUM, Dr. COAR, Mr. MILNE, Mr. PONZER, Miss WHITE, Mr. LYTLE.

Prerequisite: Mathematics 6.

8a. DIFFERENTIAL AND INTEGRAL CALCULUS.-A general introduction to the principles of differential and integral calculus. I.; daily; 8; (5). Professor TOWNSEND,

Prerequisite: Mathematics 6.

8b. DIFFERENTIAL AND INTEGRAL CALCULUS (Advanced Course). -A continuation of Sa. The application of calculus to geometry and mechanics, begun in 8a, is extended throughout the course. II.; Tu., Th.; 1; (2). Professor TowNSEND.

Prerequisite: Mathematics 8a.

I.,

9. INTEGRAL CALCULUS.-This course together with mathematics 7 constitutes a year's continuous work in calculus. The general principles of the integral calculus are developed with usual applications to geometry, centers of gravity, moments of inertia, etc. A brief introduction to ordinary differential equations is also included. II.; section A, 8, M., W., F.; section B, 8, M., W., F.; section C, 8, M., W., Th.; section D, 1, M., Tu., Th.; section E, I, M., Tu., Th.; section F, 1, M., W., F.; section G, ro, M., W., Th.; section H, 10, M., W., Th.; section I, 8, Tu., Th., F.; section J, 8, Tu., Th., F.; (3). Assistant Professor RIETZ, Assistant Professor SLOCUM, Mr. MILNE, Dr. COAR, Mr. PONZER, Miss WHITE, Mr. Lytle.

Prerequisite: Mathematics 7.

IO. THEORY OF EQUATIONS.-A continuation of the theory of equations given in college algebra (Math. 1, 2). It is based on Burnside and Panton's Theory of Equations, Part I., II.; M., W., F.; 2; (3). Professor ToWNSEND.

Prerequisite: Mathematics 2, 4 (or 1, 3), 6.

II.

THEORY OF DETERMINANTS.-The general principles and properties of determinants, including determinants of special form and the functional determinants-Jacobians, Hessians, Wronskians. The application of determinants to the theory of equations, analytical geometry including linear transformation. II.; Tu., Th.; 2; (2). Mr. MILNE.

12. THEORY OF INVARIANTS.-The general development of the theory of invariants, both from the geometric and from the algebraic

side. Applications of invariants to systems of conics and higher plane curves. I.; M., W., F.; 2; (3). Assistant Professor RIETZ. Prerequisite: Mathematics 8b (or 9), 11.

13a. FUNCTIONS OF REAL VARIABLES.-The two courses in functions (13a, 13b) are a continuation of the work done in calculus (8a, 8b, or 7, 9). Under functions of real variables, considerable attention is given to the fundamental ideas of the analysis, including rational and irrational numbers, mengelehre, single and double limits and their application to questions of continuity of functions of one or two variables, uniform, convergence of series, etc. The existence of derivatives, condensation of singularities, definite integrals, differentiation and integration of series are also discussed. I., II.; M., W., F.; 3; (3). Professor TOWNSEND.

Prerequisite: Mathematics 8a, 8b (or, 7, 9), 10.

13b. FUNCTIONS OF A COMPLEX VARIABLE.-A general introduction to the theory of functions of a complex variable. The methods of Weierstrass and Riemann are followed. I., II.; M., W., F.; 3; (3). Professor TOWNSEND.

Prerequisite: Mathematics 8a, 8b (or, 7, 9), 10.

14. METHOD OF LEAST SQUARES.-The fundamental principles of the subject. The following subjects are studied: Law of probability and error, adjustment of observations, precision of observations, independent and conditional observations, etc. I.; Tu., Th.; 2; (2). Assistant Professor STEBBINS.

Prerequisite: Mathematics 8a, or 9.

15. SEMINARY AND THESIS.-I., II.; Tu., Th.; 3; (3) Professor TOWNSEND, Assistant Professor RIETZ, Assistant Professor SLOCUM.

16. DIFFERENTIAL EQUATIONS. For students in the courses of engineering and of mathematics and of astronomy. It embraces the following topics: General linear equations with constant coefficients, special forms of differential equations of higher order, integration in series, etc. I.; M., W., F.; 11; (3). Professor SHATTUCK.

Prerequisite: Mathematics 8a, or 9.

17. SOLID ANALYTICAL GEOMETRY.-A general review of the position of the plane and the right line in space and the more general properties of surfaces of the second degree. The classification and special properties of quadratics, and a brief introduction to the theory of surfaces in general. II.; M., W., F.; 9; (3). Professor TOWNSEND.

Prerequisite: Mathematics 8a (or 7), II.

18. HIGHER PLANE CURVES.-This course includes the general theory of algebraic curves, together with the application of the theory of invariants to higher plane curves. Special study is made of curves of the third and fourth order. II.; M., W., F.; 2; (3). Assistant Professor SLOCUM.

Prerequisite: Mathematics 12.

20. CALCULUS OF VARIATIONS.-This course has for its aim merely to acquaint the student with those elements of the science which are most needed in the study of the higher subjects of mathematical astronomy and physics. II.; M., W., F.; 11; (3). Professor SHATTUCK.

Prerequisite: Mathematics II, 16.

21. SPHERICAL HARMONICS.-This course is introduced by a short course of lectures and study of certain trigonometric series. Fourier's Theorem for developing any function of a variable in a series proceeding in sines and cosines of multiples of the variable is derived and the limitations of its validity investigated. This is followed by the study of Lagrange's, Laplace's, and Lamé's functions and their applications to astronomical and physical problems. I.; M., W., F.; 1; (3). Assistant Professor SLOCUM.

Prerequisite: Mathematics II, 14, 16.

22. POTENTIAL FUNCTION.-The potential function is defined and its properties derived and discussed. The potential of various bodies, such as of wire, a spherical shell, a sphere, ellipsoid of revolution, etc., is computed. Poisson's and Laplace's Equations are derived and discussed. Green's propositions with kindred and similar subjects are considered. II.; M., W., F.; 1; (3) Assistant Professor SLOCUM.

Prerequisite: Mathematics 21.

23. MODERN GEOMETRY.-This course includes, in general, a consideration of homogeneous coördinates, duality, descriptive and metrical properties of curves, anharmonic ratios, homography, involution, projection, theory of correspondence, etc. I.; M., W., F.; 2; (3). Dr. Coar.

Prerequisite: Mathematics 8a or 7, 11.

24. ALGEBRAIC SURFACES.-In this course are considered the application of homogeneous coördinates and the theory of invariants to geometry of three dimensions, and also the general theory of surfaces, together with the special properties of surfaces of the third and fourth order. II.; M., W., F.; 2; (3). Dr. COAR.

Prerequisite: Mathematics 17, 18.