MAT 140 - Finite Math

Unit Objectives:
Outcome 1:    Solve and graph linear equations and inequalities and apply these concepts to practical applications.
        Task 1:    Determine if an equation/inequality is linear.
        Task 2:    Describe the rectangular coordinate system.
        Task 3:    Determine the coordinates of sufficient points needed to draw the line of an equation.
        Task 4:    Locate and indicate the proper half-plane of a linear inequality.
        Task 5:    Apply the idea of linear systems to practical applications.

Outcome 2:    Solve systems of linear equations in two or three variables using graphs, matrix algebra, and Gaussian elimination.
        Task 1:    Locate the intersection of a linear system on a graph.
        Task 2:    Define a matrix and related terms.
        Task 3:    Define the elementary row operations.
        Task 4:    Rewrite a linear system in matrix form.
        Task 5:    State the conditions necessary for which various operations may be performed.
        Task 6:    Solve a system of linear equations using the Gaussian elimination method.
        Task 7:    Use Gaussian elimination to solve a system of equations in matrix form.
        Task 8:    Add, subtract, and multiply matrices when possible.
        Task 9:    Invert a 2 x 2 and 3 x 3 matrix, when possible.
        Task 10:  Solve a matrix equation in the form AX = B.
        Task 11:  Use matrices to solve input-output analysis problems.

Outcome 3:    Solve linear programming problems.
        Task 1:    Determine the constraints and objective function of optimization problems.
        Task 2:    Graph the feasible region for a set of linear constraints/inequalities on the same coordinate system.
        Task 3:    Indicate the intersections of all half-planes as a polygon.
        Task 4:    Find the coordinates of the vertices of the polygon.
        Task 5:    Determine which vertices, if any, optimize the objective function.
        Task 6:    Set up the initial simplex tableau.
        Task 7:    Determine pivot elements.
        Task 8:    Transform the initial simplex tableau into the final simplex tableau by elementary row operations.
        Task 9:    Set up and solve a nonstandard problem.
        Task 10:  Write the dual of a problem and solve it.
        Task 11:   Apply linear programming to solve word problems.

Outcome 4:    Analyze information using set theory, probability, and Markov chains to make decisions.

        Task 1:    Define a set and its related terms.
        Task 2:    Determine the intersection, union, and complement of given sets.
        Task 3:    Illustrate intersections, unions, and complements of sets with Venn diagrams.
        Task 4:    Use set notation to describe a Venn diagram.
        Task 5:    Use sets and set notation to solve problems in counting.
        Task 6:    Apply Venn diagrams to solve counting problems.
        Task 7:    Define sample space for a probability experiment and define a probability event.
        Task 8:    Identify all outcomes in a sample space and outcomes that comprise a particular event.
        Task 9:    Calculate the probability of a simple probability event.
        Task 10:  Describe a trial of a probability experiment.
        Task 11:  Determine if events are mutually exclusive.
        Task 12:  Determine if events are independent.
        Task 13:  Apply the addition rule for compound probabilities.
        Task 14:  Apply the multiplication rule for compound probabilities.
        Task 15:  Calculate conditional probabilities by formula.
        Task 16:  Calculate conditional probabilities by probability trees.
        Task 17:  Calculate probabilities by Bayes’ formula.
        Task 18:  Determine if a problem is a permutation or a combination.
        Task 19:  Apply permutations, combinations, and the binomial theorem to solve problems in counting.
        Task 20:  Solve counting problems using the multiplication principles.
        Task 21:  Define a regular stochastic matrix.
        Task 22:  Set up a transition matrix for a Markov process.
        Task 23:  Predict long-term trends/behaviors using stochastic matrices.