SUGGESTIONS TO TEACHERS AND STUDENTS. The parts named below embrace very nearly all that is taught year by year to the regular classes at Cornell University; and these parts may be conveniently taken up in their order at a first reading: All of chapter I, all of chapter II except section 8, all of chapter III except sections 2, 7, 9, 11, all of chapter IV except sections 7, 8. The more difficult examples may well be omitted at a first reading. The other parts are taught here to special classes, and they may be reserved for a second reading without breaking the continuity of the subject. When several figures are given to illustrate the same principle, the first figure is easiest followed; the others help the reader to see the generality of the principle and of the proof. When the reasons are obvious, both theorems and corollaries are left without formal demonstration, but students expected to state the proofs. are In most cases theorems are given only in formula; it is best that these formulæ be translated into words. In most cases answers to the examples are not given, and the student is left to test his own results. The testing is counted as not less important than the solution, and the habit of independent thought and self-reliance, so cultivated, as most valuable of all. Only the main lines of the subject are developed in the text; collateral matters are outlined in the examples and left for the student to work out for himself. These examples serve also a more important purpose: No real mastery of any mathematical subject can be got by merely reading demonstrations and solving illustrative numerical examples. To assimilate the principles of the subject, one must work them out afresh for himself, and discover their applications to new lines of thought. Counting upon this problem-solving quite as much as upon the reading of the text, the authors have sought to lay out such work as is most important and most instructive, with only so much of guidance as shall make it easy and attractive. |