Syllabus for "Basics for Advanced Mathematics"

Investigations of arithmetic textbooks were conducted to determine what the authors considered important and essential to a good arithmetic course. An effort was made to discover correlations among the texts. Listed, in no particular sequence, were my beliefs of what was important and essential in such a course. These essentials were: Vocabulary, definitions, self explanatory explanations, practical and understandable examples, varied and numerous practice problems, homework problems, and reliable suggested tests. Due to the recent trend to introduce Modern Mathematics in the Secondary Schools, consideration was given to a more practical course which would include the use of letter symbols, a study of right triangles, and uses of exponents and radicals. None of the texts were considered adequate. Excellent illustrations and explanations of certain topics were paraphrased and included in this report. All of the authors agreed that a good course in arithmetic began with an understanding of the four operations of arithmetic. Most of the texts started with a study of fractions. Some of the texts had ample problems and satisfactory methods of explanations. None of them contained a satisfactory amount of material on all the essentials suggested by the author. This conclusion verified a previously studied conclusion and provided the stimulus for the preparation of this report, which the author believes will result in a textbook suitable and adequate for the times.Natural Scienc