Mechanical skill and accuracy of expression in the formal language of Mathematics are the things emphasized in the first year of Algebra. The course is designed to cover sufficient ground so that the student who studies Algebra for only one year will be able to handle the algebraic processes involved in problems of computation in Geometry and to manipulate formulae, in order that he may read intelligently the popular publications on mechanics. To this end special attention is paid to graphical methods of representation, to the solutions of simple equations in which the unknown may be represented by any letter, and to the solution of the quadratic equation, by the formula method as well as by factoring. Stress is laid upon accuracy of expression, and upon the knowledge of processes, that this elementary work may afford a proper foundation for all future work in Mathematics. Factoring is taught by means of type forms and rules, which the students are required to learn.
The following are the subjects considered: four fundamental operations, linear equations, type product forms, factors, fractions, fractional equations, ratio and proportion, quadratic equations, functionality, simultaneous linear equations (graphical solution), simplification of simple surds. The quadratic equation is used to develop the idea of a variable and of a function of a variable, and to teach graphical methods of solving equations. Stress is laid upon the practical application of the graph to the solution of every day problems.
TENTH YEAR.
Plane Geometry.
Usual theorems and constructions, original exercises, problems of computation.
ELEVENTH YEAR.
Algebraic Theory.
First Term.
The object of this course is to introduce the student to the Theory of Mathematics; therefore the demonstration of principles is insisted upon. A rigorous treatment of simple laws is required.
The course is designed to meet the needs of two classes of students: those who are preparing for the Engineering Course at the University, and those who, while they are not preparing for college, wish to do advanced work in Mathematics and to acquire a broader knowledge of Algebra than that obtained in the first year. It also prepares the students for the Courses in Trigonometry and Solid Geometry that are to follow.