MATHEMATICS.
NINTH YEAR.
Elementary Algebra.
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.
For the benefit of those students who are not preparing for the University and are not studying mathematics for its own sake, a special effort is made to make the content of the course as rich as possible; that is, to select topics that afford material for mathematical thinking and at the same time have vocational value.
The following are the subjects considered: factors, remainder theorem, factor theorem, fractions, fractional and negative indices, surds, and complex quantities (graphic treatment), theory of quadratic equations, graphs, simultaneous equations, proportion and variation, logarithms.
Second Term.
Either Solid Geometry or Trigonometry. These subjects are begun but once a year. All students finishing two and a half years’ work in Mathematics may take whichever course is offered in the second half of their third year. Original work and solution of practical problems required.
TWELFTH YEAR.
First Term.
Either Solid Geometry or Trigonometry.
Second Term.
This course is a continuation of the work in Algebraic Theory designed especially for engineering students and for others who wish to continue advanced work. The student who is pursuing Mathematics for its vocational value and who does not intend to go to the University need not elect it, since the first term of Algebraic Theory, with Solid Geometry and Trigonometry, will give him sufficient equipment. The following topics are studied: synthetic division, simultaneous quadratic equations, special methods for higher equations, determinants, mathematical induction, binomial theorem, summation of series.