Finite Mathematics | Madison College Outline of Instruction

20804220 Finite Mathematics

Course Information

Description

Finite mathematics provides the necessary mathematical preparation for the understanding of various quantitative methods in modern management theory and the social sciences. The topics included are sets, relations, linear functions, matrix theory, the solutions of linear systems by graphical, algebraic, Gauss-Jordan, and inverse matrix methods, linear programming by graphical and simplex methods, the mathematics of finance, counting and probability, game theory, decision theory, and other related topics.

Total Credits

Course Competencies

Apply mathematical problem solving skills

Assessment Strategies

by completing and submitting for evaluation all in-class and take-home quizzes with passing grades according to the grading scale contained in the syllabus

by demonstrating correct and accurate use of a calculator on all assignments, quizzes, tests, projects, and laboratory work when appropriate

by active participation in class discussions and activities

Criteria

you show your work in a clear and logical manner

you verify your solution

you verify that the solution is within the stated range and reflects appropriate accuracy or precision

you label solutions with appropriate units
Use the fundamental concepts of Algebra

Assessment Strategies

by completing and submitting for evaluation all in-class and take-home quizzes with passing grades according to the grading scale contained in the syllabus

by demonstrating correct and accurate use of a calculator on all assignments, quizzes, tests, projects, and laboratory work when appropriate

by active participation in class discussions and activities

Criteria

you add, subtract, multiply, and divide polynomials

you factor polynomials

you simplify, add, subtract, multiply, and divide rational expressions

you solve linear and quadratic equations using appropriate methods

you solve linear, quadratics and rational inequalities

you apply positive integer exponents, negative integer exponents, rational number exponents to evaluation or simplify expressions

you relate roots to rational number exponents
Determine the properties of and solve linear equations and functions

Assessment Strategies

by completing and submitting for evaluation all in-class and take-home quizzes with passing grades according to the grading scale contained in the syllabus

by demonstrating correct and accurate use of a calculator on all assignments, quizzes, tests, projects, and laboratory work when appropriate

by active participation in class discussions and activities

Criteria

you use the Cartesian coordinate system

you determine the slope of a line from either two points on the line or from the equation of the line

you determine the forms of an equation of a line: standard form, slope-intercept, and point-slope form

you generate equations of lines from given information

you summarize the characteristic of vertical and horizontal lines

you determine if two lines are parallel, perpendicular, or neither

you graph equations of lines

you create linear models based on observed data as given in a problem

you make predictions based upon linear models

you use function notation correctly

you determine the equation of a line of least squares

you compute and interpret the coefficient of correlation
Solve systems of linear equations using various means

Assessment Strategies

by completing and submitting for evaluation all in-class and take-home quizzes with passing grades according to the grading scale contained in the syllabus

by demonstrating correct and accurate use of a calculator on all assignments, quizzes, tests, projects, and laboratory work when appropriate

by active participation in class discussions and activities

Criteria

you solve systems of linear equations using substitution

you solve systems of linear equations using elimination

you apply the methods of transforming a system of equations

you solve systems of equations using echelon form and reduced echelon form

you define an n x m matrix, a square matrix, and elements of the matrix

you define the matrix form of a system of linear equations

you define row echelon form and reduced row echelon form

you perform row operations on a matrix

you solve a system of equations by performing row operations to reduce the augmented matrix to reduced echelon form

you determine if a system of equations is consistent or inconsistent system

you define matrix addition and subtraction, the additive identity matrix, and the additive inverse matrix

you compute the product of a scalar and a matrix

you define matrix multiplication, the multiplicative identity matrix, and the multiplicative inverse matrix

you recognize that matrix multiplication is generally not commutative

you calculate the inverse of a 2x2, 3x3, and 4x4 matrix

you solve linear matrix equations of the form AX=B, where A is a square matrix (2 equations in 2 unknowns, 3 equations in 3 unknowns)

you solve application problems using any method
Solve systems of linear inequalities and linear programming problems

Assessment Strategies

by completing and submitting for evaluation all in-class and take-home quizzes with passing grades according to the grading scale contained in the syllabus

by demonstrating correct and accurate use of a calculator on all assignments, quizzes, tests, projects, and laboratory work when appropriate

by active participation in class discussions and activities

Criteria

you summarize linear inequalities

you summarize equivalent inequalities

you solve linear inequalities algebraically for a variable

you solve linear inequalities graphically

you summarize the boundary line, test points, and feasible region

you solve systems of linear inequalities graphically

you summarize the objective function, and constraints of a linear programming problem

you solve linear programming problems graphically

you summarize basic variables, slack variables, artificial variables, pivots, and indicators in a linear programming problem

you write a linear programming problem in standard form

you determine the solution of a linear programming problem from the last tableau

you solve linear programming maximization problems using the simplex method

you solve linear programming minimization problems using the simplex method

you use the dual of a linear programming problem to solve problems

you solve non-standard problems using linear programming methods

you solve linear programming application problems
Solve problems of a financial nature

Assessment Strategies

by completing and submitting for evaluation all in-class and take-home quizzes with passing grades according to the grading scale contained in the syllabus

by demonstrating correct and accurate use of a calculator on all assignments, quizzes, tests, projects, and laboratory work when appropriate

by active participation in class discussions and activities

Criteria

you compute simple interest

you compute future value for simple interest

you compute compound interest

you compute the present value for compound interest

you compute the effective rate of interest

you define a geometric sequence

you compute the sum of a geometric sequence

you compute the future value of an ordinary annuity

you compute the payment to a sinking fund

you explain the difference between an ordinary annuity and an annuity due

you compute the present value of an annuity

you compute the payment to amortize a loan

you compute an amortization schedule
Determine the probability of a particular outcome

Assessment Strategies

by completing and submitting for evaluation all in-class and take-home quizzes with passing grades according to the grading scale contained in the syllabus

by demonstrating correct and accurate use of a calculator on all assignments, quizzes, tests, projects, and laboratory work when appropriate

by active participation in class discussions and activities

Criteria

you define element, set, subset, union, intersection and complement of sets

you use set builder notation

you create tree diagram to determine set composition

you use Venn diagrams to determine set composition

you determine the complement of set

you form union and intersections of sets

you compute the number of elements in the union of two sets

you summarize experiment, trial, sample space, event, variable, random variable, expected value

you determine if events are mutually exclusive or independent

you compute basic probabilities

you determine the probability of multiple options for an event

you apply rules for computing the complement of an event

you determine if the probability of an event is empirical or theoretical

you determine conditional probabilities

you determine the probability of a series of events occurring

you compute probabilities using Baye's Theorem

you summarize factorial, permutation, combination

you compute the number of ways an event can occur if the event consists of n possibilities in which each possibility can occur more than once

you compute the number of ways an event can occur if the event consists of n possibilities in which each possibility can occur exactly once

you use factorial notation

you computer factorials

you compute permutations of events

you compute combinations of events

you determine if events are to be counted using combinations or permutations

you determine if an event is a binomial experiment

you compute probabilities of binomial events

you generate a probability distribution

you draw a histogram representing a probability distribution

you compute expected value of a generic probability distribution

you compute the expected value of a binomial probability distribution
Solve problems involving the state of the system

Assessment Strategies

by completing and submitting for evaluation all in-class and take-home quizzes with passing grades according to the grading scale contained in the syllabus

by demonstrating correct and accurate use of a calculator on all assignments, quizzes, tests, projects, and laboratory work when appropriate

by active participation in class discussions and activities

Criteria

you summarize a transition matrix, Markov chain, absorbing chain, probability vector, equilibrium vector

you compute products of transitions matrices

you compute a probability vector

you compute the values of an equilibrium vector

you apply the properties of regular Markov chains

you determine if a Markov chain is an absorbing chain

you determine the fundamental matrix

you solve problems involving the state of the system
Make decisions based upon mathematical principles

Assessment Strategies

by completing and submitting for evaluation all in-class and take-home quizzes with passing grades according to the grading scale contained in the syllabus

by demonstrating correct and accurate use of a calculator on all assignments, quizzes, tests, projects, and laboratory work when appropriate

by active participation in class discussions and activities

Criteria

you summarize strategies, saddle points, and payoff matrices

you determine if dominate strategy exists

you determine a saddle point

you determine if a game is fair

you determine the expected value of a game

you determine the optimum strategy of a non-strictly determined game

you solve zero-sum games
Compute basic statistical measures (optional)

Assessment Strategies

by completing and submitting for evaluation all in-class and take-home quizzes with passing grades according to the grading scale contained in the syllabus

by demonstrating correct and accurate use of a calculator on all assignments, quizzes, tests, projects, and laboratory work when appropriate

by active participation in class discussions and activities

Criteria

you summarize mean, median, mode, and midrange

you compute the mean, mode, median, and midrange of a discrete data set

you compute the mean, mode, median, and midrange of a frequency distribution

you summarize deviation from the mean, variance, standard deviation

you compute the variance and standard deviation of a discrete data set

you compute the variance and standard deviation of a frequency distribution

you summarize the standard normal distribution

you compute the z value

you determine the probability of an event that is normally distributed

you determine the mean and standard deviation of a binomial distribution

you determine the probability of an event that is binomial and can be approximated by a normal distribution
Determine the truth or falsity of prepositional statements (optional)

Assessment Strategies

by completing and submitting for evaluation all in-class and take-home quizzes with passing grades according to the grading scale contained in the syllabus

by demonstrating correct and accurate use of a calculator on all assignments, quizzes, tests, projects, and laboratory work when appropriate

by active participation in class discussions and activities

Criteria

you summarize a statement, a compound statement, a connective, a quantifier, both universal and existential, a conditional statement

you write the negation of a statement

you use logic symbols appropriately

you identify conjunctions and disjunctions

you construct truth tables for logical statements

you apply De Morgan's laws

you summarize the characteristics of conditional statements

you write the negation of a conditional statement

you apply the principles of logic to circuits

you write the converse, inverse, and contrapositive of a given statement

you show that two statements are equivalent

you interpret biconditional statements

you determine if an argument is valid or invalid