IGETC Area 2: Mathematical Concepts and Quantitative Reasoning

A study of descriptive and inferential statistics including applications in the behavioral and natural sciences. Topics include classification and analysis of data, probability, distributions, sampling, the binomial, normal, t, F, and chi-square distributions, confidence intervals, hypothesis testing, regression analysis, analysis of variance and non-parametric methods. Calculators and/or computers will be used throughout.

College level course in algebra for majors in science, technology, engineering, and mathematics: polynomial, rational, radical, exponential, absolute value, and logarithmic functions; systems of equations; theory of polynomial equations; analytic geometry.

Techniques of calculus as applied to problem-solving in business and social, behavioral, and natural sciences, including limits, continuity, differentiation and integration in one and several dimensions, optimization, transcendental functions, and the use of computing technology.

Preparation for calculus: the study of polynomial, absolute value, radical, rational, exponential, and logarithmic functions, analytic geometry, and polar coordinates. The study of trigonometric functions, their inverses and their graphs, identities and proofs related to trigonometric expressions, trigonometric equations, solving right triangles, solving triangles using the Law of Cosines and the Law of Sines, and introduction to vectors. This is an accelerated one semester alternative to the two semesters of trigonometry (Math 121) and College Algebra (Math 131).

The first in a two-semester sequence comprising first-year calculus. Topics include functions, limits, continuity, the derivative, differentiation of algebraic, trigonometric and transcendental functions, applications of differentiation, the definite integral, and the use of technology to solve calculus problems.

The second in a two-semester sequence comprising first-year calculus. Topics include methods and applications of integration, sequences and series, Taylor series, an introduction to differential equations, and the use of technology to solve calculus problems.

Topics include vectors, functions of several variables; differentiation and integration in several dimensions; change of variables; parameterized curves and vector fields, line and surface integrals; Green's, Stokes', and divergence theorems.

First order ordinary differential equations, including separable, linear, homogeneous of degree zero, Bernoulli and exact with applications and numerical methods. Solutions to higher order differential equations using undetermined coefficients, variation of parameters, and power series, with applications. Solutions to linear and non-linear systems of differential equations, including numerical solutions. Matrix algebra, solutions of linear systems of equations, and determinants. Vector spaces, linear independence, basis and dimension, subspace and inner product space, including the Gram-Schmidt procedure. Linear transformations, kernel and range, eigenvalues, eigenvectors, diagonalization and symmetric matrices.