20222023 College Catalog [ARCHIVED CATALOG]

MAT 172  Finite Mathematics 3 Credits, 3 Contact Hours 3 lecture periods 0 lab periods
Sampling of finite mathematics which includes mathematics of finance, linear business functions, systems of equations, matrices, geometric and simplex methods of solving linear programming problems, logic, sets, combinatorics, basic probability, probability distributions, and Markov chains.
Prerequisite(s): Within the last three years: MAT 151 with a grade of C or better or satisfactory score on the mathematics assessment exam. GenEd: Meets AGEC  MATH; Meets CTE  M&S.
Course Learning Outcomes
 Solve linear programing problems.
 Calculate and apply probabilities.
 Solve problems involving real world applications.
Performance Objectives:
 Apply the mathematics of finance.
 Graph and evaluate linear functions, including those applying to business.
 Solve systems of linear equations using algebraic methods.
 Perform algebraic operations with matrices.
 Solve systems of linear equations using matrices; use Gaussian elimination with augmented matrices; use inverse matrices.
 Solve linear programming problems geometrically.
 Solve linear programming problems using the simplex method.
 Apply basic symbolic logic including truth tables.
 Represent sets using Venn Diagrams and perform set operations.
 Use the principles of counting (including the multiplication principle, combinations, and permutations) to solve counting problems.
 Calculate probabilities using conditional probability, independence, and Bayes’ theorem.
 Define random variables, differentiating between continuous and discrete; identify probability distributions.
Optional
13. Apply Markov chains, finding transition and distribution matrices. Outline:
 Mathematics of Finance
 Simple interest
 Compound interest
 Future and present value of an annuity
 Amortizations
 Linear Functions
 Graphs and equations of lines
 Linear cost, revenue, and profit functions
 Linear supply and demand functions
 Solve Systems of Linear Equations
 Solve two equations with two unknown variables
 Breakeven points
 Equilibrium points
 Matrices
 Equality of matrices
 Algebraic operations on matrices
 Find the inverse of a nonsingular matrix
 Use technology
 Write matrices which represent a system of linear equations
 Solving Systems of Linear Equations using Matrices
 Gaussian elimination
 Solve a system of equations using inverse matrices
 Describe in detail the solutions of dependent systems
 Applications of systems of linear equations
 Use technology
 Linear Inequalities and Linear Programming
 Graph systems of linear inequalities in two variables
 Solve linear programming problems geometrically
 Applications of linear programming
 Solve Linear Programming using the Simplex Method
 Standard maximization problems
 Standard minimization problems
 Duality problems
 Applications of linear programming
 Logic
 Propositions and connectives
 Apply truth tables to compound proposition
 Sets
 Define sets including universal, empty, sub, complement, and power
 Define and perform set operations
 Draw Venn Diagrams representing sets
 Counting
 Number of elements in a set
 Number of subsets of a set
 Multiplication principle
 Inclusionexclusion principle
 Permutations
 Combinations
 Applications
 Probability
 Sample spaces, simple outcomes, compound outcomes
 Find the probability of an event
 Draw tree diagrams
 Conditional probability
 Independence
 Bayes’ theorem
 Applications
 Random variables
 Binomial distribution
 Normal distribution
 Expected value
 Markov chains (Optional)
 Properties of Markov chains
 Transition and state matrices
 Regular Markov chains
 Absorbing Markov chains
