Numbers: The natural numbers-counting, addition, and multiplication Subtraction and the negative Division and fractions Irrational numbers The imaginary and complex numbers 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 A 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 The general 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 Answers Index.