In preparing this book, the author had especially in mind classes in the upper grades of grammar schools, though the work will be found equally well adapted to the needs of any classes of beginners.

The ideas which have guided in the treatment of the subject are the following:

The study of algebra is a continuation of what the pupil has been doing for years, but it is expected that this new work will result in a knowledge of general truths about numbers, and an increased power of clear thinking.

All the differences between this work and that pursued in arithmetic may be traced to the introduction of two new elements, namely, negative numbers and the representation of numbers by letters. The solution of problems is one of the most valuable portions of the work, in that it serves to develop the thought-power of the pupil at the same time that it broadens his knowledge of numbers and their relations. Powers are developed and habits formed only by persistent, long-continued practi...

In his later work, Freud proposed that the human psyche could be divided into three parts: Id, ego and super-ego. Freud discussed this model in the 1920 essay Beyond the Pleasure Principle, and fully elaborated upon it in The Ego and the Id (1923), in which he developed it as an alternative to his previous topographic schema (i.e., conscious, unconscious and preconscious).

The id is the completely unconscious, impulsive, childlike portion of the psyche that operates on the "pleasure principle...