Upon successful completion of this course, students will be able to: use mathematical notations and expressions to represent variables and write algebraic expressions and equations; solve algebraic equations, including linear, quadratic, polynomials, roots, and rational functions; graph a mathematical function and apply basic transformations to the graph and corresponding equation; work with and manipulate exponential and logarithmic expressions; solve systems of linear and basic nonlinear equations and find solution sets of systems for inequalities; and recognize equations that represent conic sections such as circles, ellipses, hyperbolas, and parabolas from mathematic equations and their graphic representations.

Upon successful completion of this course, students will be able to: convert realistic situations into mathematical concepts so mathematical tools can be used to solve them; use Venn diagrams, graphs, charts and similar methods to represent, organize and analyze data; apply principles of logic to prove or disprove statements (both in text and in mathematical form) on the basis of other given statements; identify, manipulate and utilize mathematical expressions including rational, irrational and imaginary numbers, along with mathematical expressions such as absolute value, inequalities and radicals; use principles of algebra and geometry to identify variables and express algebraic expressions on graphs; determine the probability of a specified event or condition or series of events or conditions; and apply principles of statistics, such as averages, normal distributions and standard deviations to identify statistically significant data.

Upon completion of this course, students will be able to: solve systems of linear equations and perform operations on vectors; determine if a given set of vectors is linearly independent and perform linear transformations; determine if the inverse of a matrix exists, calculate the inverse of a matrix, and identify geometric changes of matrices; determine if a vector is in a vector space, identify properties of determinants, and apply Cramer’s rule to solve linear systems; determine whether a given set is a vector space or subspace, find a basis for a column space, and map a vector to its coordinate vector in a basis; find the dimension of a subspace, apply the rank theorem, and map a coordinate vector from one base to another; calculate eigenvalues, determine if a vector is an eigenvector, and diagonalize matrices; determine orthogonality projections and orthogonality of vectors; determine symmetry and orthogonality of matrices, find the matrix of a quadratic form; and find the singular values of a matrix.