pt. 1. Numbers: The natural numbers : counting, addition, and multiplication. Subtraction and the negative. Division and fractions. Irrational numbers. Imaginary and complex numbers

pt. 2. Algebra: Preliminary considerations. The fundamental operations. Simple equations in one unknown letter. Systems of simultaneous simple equations. The division transformation. Factors of rational integral expressions. Highest common factor and lowest common multiple. Rational fractions. Symmetric functions. The binomial theorem. Evolution. Irrational functions : radicals and fractional exponents. Quadratic equations. Discussion of the quadratic equation : maxima and minima. Equations of higher degree which can be solved by means of quadratics. Simultaneous equations which can be solved by means of quadratics. Inequalities. Indeterminate equations of the first degree. Ratio and proportion : variation. Arithmetical progression. Geometrical progression. Harmonical progression. Method of differences : arithmetical progressions of higher orders : interpolation. Logarithms. Permutations and combinations. The multinomial theorem. Probability. Mathematical induction. Theory of equations. Cubic and biquadratic equations. Determinants and elimination. Convergence of infinite series. Operations with infinite series. The binomial, exponential, and logarithmic series. Recurring series. Infinite products. Continued fractions. Properties of continuous functions.