Mar 28, 2024  
2022-2023 General Catalog 
    
2022-2023 General Catalog [ARCHIVED CATALOG]

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MAT 140 - Finite Math


Last Date of Approval: Fall 2019

3 Credits
Total Lecture Hours: 45
Total Lab Hours: 0
Total Clinical Hours: 0
Total Work-Based Experience Hours: 0

Course Description:
This course is a study of the topics of finite mathematics which have applications in nonphysical science areas such as business, economics, psychology, social science, and natural science. Topics included are systems of linear equations and inequalities, linear programming, probability and decision theory. This course will also help students gain mathematical literacy which will be of vital significance when making important life decisions. In addition, this course will help with any career that involves mathematics, decision making, or problem-solving. This course satisfies a general education requirement in the Math/Science area.

Prerequisites: MAT 035   with C grade or better or the necessary score on the mandatory assessment and placement chart found in the course cataglog.
Mode(s) of Instruction: traditional/face-to-face

Credit for Prior Learning: There are no Credit for Prior Learning opportunities for this course.

Course Fees: None

Common Course Assessment(s): None

Student Learning Outcomes and Objectives:
Outcome 1:    Solve and graph linear equations and inequalities and apply these concepts to practical applications.
Outcome 2:    Solve systems of linear equations in two or three variables using graphs, matrix algebra, and Gaussian elimination.
Outcome 3:    Solve linear programming problems.
Outcome 4:    Analyze information using set theory, probability, and Markov chains to make decisions.

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.

 



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