Website owner:  James Miller

Algebra

Elementary algebra. Numbers and number systems. Negative numbers. Rational, irrational and real numbers. Fields.

Exponents. Algebraic expressions, terms and operations. Removal of parenthesis. Multiplication and division of polynomials.

Special products. Methods for factoring polynomials with integer coefficients. Highest common factor. Relatively prime polynomials. Lowest common multiple.

Fractions. Rules. Reduction to lowest terms.

Radicals. Laws. Simplification. Reduction of the index. Rationalization of the denominator.

Methods of solving equations in one or more unknowns. Conditional equation. Solution set. Function. Linear systems. Quadratic equations.

Ratio, proportion, variation. Arithmetic, geometric, harmonic progression. Permutations. Combinations. Binomial formula. Inequalities.

Finding roots of polynomial equations. Remainder, factor theorems. Synthetic division. Variation of sign. Descartes' Rule of Signs. Standard division formula. Depressed equation.

Solution of linear systems by determinants. Properties of determinants. Evaluation of determinants. Minor. Cofactor. Cramer's Rule. Homogeneous systems.

Mathematics of finance. Simple and compound interest. Conversion period. Amount of an annuity. Present value.

Number systems. Rational, irrational, real and complex numbers. Open and closed intervals. Fields. Absolute values, conjugates of complex numbers. Laws.

Products, quotients and roots of complex numbers in polar form. De Moivre's theorem. Roots of unity

The exponential and logarithmic functions

Trigonometry: formulas, identities, solution of triangles

Rational expressions, rational algebraic fractions, partial fractions, expressing a proper algebraic fraction as a sum of partial fractions

Systems of linear equations. Equivalence, independence, dependence, consistency