**Annual Report 1896.**

**Mathematics and Astronomy.**

The required work in mathematics extends through the first two years of the course for students in the agricultural department, and throughout the entire four years for those in the mechanical course. The time devoted to the subject in the Freshman year, is spent in the study of algebra and plane geometry. The work in algebra consists of a systematic drill in the fundamental operations, leading up to a study of the equation, both simple and quadratic, the theory of exponents, radicals, the progressions, the binomial formula, and the graphic representation of equations. Especial attention is given to the expression, by means of equations, of the conditions of a problem, and the exact methods of reasoning involved. In the course in plane geometry, beginning with the third term, particular stress is laid upon the original demonstration of propositions, in order best to develop the rigidly logical methods of thought which are the outcome of exact geometrical work. Numerical problems am1 practical applications are given whenever possible. This course extends through the first term of the Sophomore year and is followed by a course in plane trigonometry during the winter term. The fundamental formulas are developed and application of them is made in the solution of right and oblique triangles. The subject of logarithms is studied and sufficient applications are made to thoroughly familiarize the student with this invaluable aid to computation. It is the aim here, as throughout the course, to select such problems and applications as shall have direct bearing upon practical subjects. Practical work in surveying is given during the spring term and this work is continued through the first term of the Junior year, by the agricultural students, while the mechanical students enter upon the subject of analytical geometry, studying first the subject of loci and their equations and the analytical demonstration of many geometrical theorems, and later developing the simpler properties of the conics. A short course in descriptive geometry is also given during the first term. A one-term course in solid geometry is given to the mechanical students, in which are studied the point, the line and the plane in space, the familiar polyhedrons, the cylinder, cone and sphere, including the measurement of these solid figures. The work in calculus begins with the second term of the Junior year and continues through three terms. It includes the differentiation of algebraic, trigonometric, anti-trigonometric, exponential and logarithmic functions, successive differentiation and the integration of simple forms, illustrated by applications to the rectification of plane curves, the areas of plane curves and the surface and volume of solids of revolution. The fundamental formulas of mechanics are developed and illustrated. The more familiar devices for integration are studied and a short time is devoted to the interesting subject of curve-tracing.

The primary aim of the entire course in mathematics is to stimulate original work, to insist upon and develop a capacity for clear thinking and logical, systematic reasoning such as will prove invaluable in any department of study or life, as well as to achieve familiarity with such mathematical principles as are necessary for applied work.

A growing reference library affords an opportunity for wider mathematical reading, the value of which is constantly becoming more fully appreciated by the students.

Several elective courses are offered by the department, and others will be added from time to time as may seem advisable. In pure mathematics courses are offered in college algebra, open to all who have completed the required work in algebra; in modern synthetic geometry, open to all students who have completed the required courses in algebra and plane geometry; in determinants; and an advanced course in integral calculus, open, of course, only to students who have completed the required work in calculus.

In applied mathematics the department offers a course in surveying and civil engineering, giving opportunity to students who have completed the required work to carry the subject farther; a course in analytical mechanics, open to students who have completed one term of the required work in calculus; a course in practical astronomy, in which the simpler problems of practical astronomy are discussed.

In astronomy, in addition to the course above mentioned, a lecture course in physical astronomy is offered in the spring term of the Senior year, the aim of which is to make the students familiar with the general characteristics of the various members of the solar system, and to emphasize the general laws which govern the universe. A four-inch equatorial telescope, an eighteen-inch celestial globe, a large collection of lantern-slides of astronomical phenomena and a small but carefully chosen reference library, add greatly to the resources of the department.