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STUDENTS may elect Mathematics either from a decided taste for the subject itself, or because they wish to prepare themselves for the thorough study of Physics or of Engineering, or for the sake of the general intellectual benefits which can be derived from a judicious discipline in exact science. Those who have the definite intention of pursuing a continued course of scientific study will find that the scheme of mathematical electives has reference primarily to their wants; and such students, after the first year of elective work, in which they will naturally take Math. 1 and 2 (or 1 alone, with other scientific electives), should consult their professors as to the precise direction of their choice. Those, on the other hand, who merely wish to keep up a moderate amount of Mathematics in order to give variety to literary studies can make a profitable election among courses 1, 2, 3, 4, and 6, in which the presence of such students is distinctly recognized. If they become really interested in their mathematical work, they may add to these studies either 5 or 7; and no student is advised to take Mathematics at all without a fair degree of liking for it and of insight into it.
Math. 1 covers the more elementary parts of the Differential and Integral Calculus; and it is designed to give a practical familiarity with the ordinary methods and leading principles of that subject. It constitutes the introduction to the higher Mathematics; and hence is the first elective to be taken by those who mean to pursue a mathematical course, and at the same time is a good supplement to the Freshman work for general students. This elective is required for Honors in Physics, being essential to a thorough theoretical knowledge of that science.
Students who have taken this course will find great advantage in repeating it during a second year as an extra, if their time will permit.
The work is generally analytical; that is, of the algebraic kind.
Math. 2 is an advanced course in Analytic Geometry. Salmon's Conic Sections, one of the best mathematical text-books in any language, is used in connection with lectures. This course is generally found harder than 1, and students who mean to take the two electives in successive years are advised to take 1 first. Course 2 may be followed by 6 and 8.
Math. 3 is intended, in the first place, for students who wish to keep up a year of elective Mathematics, but prefer to confine themselves to the applications of the elementary branches. This course is also especially useful to students of Astronomy, and may advantageously be taken by mathematical students in addition to some of the more theoretical courses. General students will do well to take 1, 2, and 3, or two of them, in successive years.
Math. 4 is a continuation of the required course primarily intended for candidates for Second-Year Honors.
Math. 5 is a continuation of 1. It is a combination of Courses 5 and 6 in the scheme of the current year, made with the intention of giving more space to the practical methods. This course should be taken by all who desire to gain a real and permanent mastery of the Calculus.
Math. 6 is Analytic Geometry applied to space of three dimensions.
Math. 7 belongs to the professional study of Engineering, but it is also important as a branch of pure Mathematics. It is recommended to those especially who have a taste for pure Geometry.
Math. 8 is a continuation of 2. It is designed to cover Chapters III., IV., VII., XIII., and some other selected parts of Salmon's Conic Sections.
Math. 9. - Analytic Mechanics - may almost be regarded as the summing up of pure Mathematics, for it finds a use for the most advanced methods of analysis, and thus has had much to do in stimulating and shaping mathematical progress. Its object is the development of the theory of force and motion in the most general mathematical forms. The previous study of Physics 1 is an advantage in this course, but not a necessity. Math. 1, 2, 5, and 6 are necessary, but 6 may be taken at the same time. Math. 10 is designed for students who have taken 5 during the current year. The precise arrangement of topics will be determined hereafter in consultation with those who may elect it.
For Second-Year Honors in Mathematics 1 and 2 are required. For Final Honors 5, 6, 8 and 9 should also be taken, with other courses approved by the committee. Physics 1 will be accepted, if the mathematical electives in Mechanics are also offered.
All the mathematical electives will be valuable to students who purpose to study Engineering. Math. 1, 2, 5, and 6 are especially recommended to students of Physics.
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