Number systems, including our decimal number system based on the number 10, introduce concepts of abstract math. Real, rational and irrational numbers are number systems. Primes, composites,decimals and percents are elements of a number system. Greatest common factors and least common multiples are concepts, which help to solve equations. Mathematical reasoning includes set theory and logic for problem solving. Inductive and deductive reasoning are used in analysis of arguments and in proofs of formulas and theories.
Algebra begins with translating words in algebraic sentences in the GRE preparation guide. College algebra applies ratios and proportions in linear equations to solve problems and determine indirect measurements. Proficiency in college math requires the ability to perform operations on algebraic variables and constants to solve linear equations and inequalities. The student must be able to graph the lines formed by points that satisfy the linear equations. The quadratic formula is used to solve equations in one variable.
Essential college geometry requires graphing points and lines in a plane. Geometry of parallel and perpendicular lines crossed by a transversal creates corresponding, supplementary and congruent angles. Essential college geometry includes the perimeter and area of circles, triangles and polygons. Angles and sides of triangles and polygons are calculated with the Pythagorean theorem. Triangles are the same, similar or congruent. Basic college geometry requires calculation of surface areas and volumes of three-dimensional solids.
Data analysis in the GRE test preparation guide begins with measures of central tendency, the mean, median and mode. Measures of dispersion begin with a range of values from least to greatest. Variance from the mean is calculated by subtracting the mean from each measurement, squaring the difference, summing the squares and dividing by the number of squares. The square root of the variance is the standard deviation. A standard deviation is the amount that a value deviates from the mean.
Matrices are essential college math and the applied math foundation for computer game theory. A matrix is an array of numbers in rows and columns, used to solve systems of linear equations and inequalities. Essential college mathematics requires students to perform operations on matrices. The value of three variables in a system of linear equations is determined by elimination from a matrix of the coefficients of the variables and the constants from the equations.