
MAT 141  Finite Math Credits: 4 Lecture Hours: 4 Lab Hours: 0 Practicum Hours: 0 Work Experience: 0 Course Type: Core A general education course in practical mathematics for those students not majoring in mathematics or science. This course will include such topics as set operations and applications, methods of counting, probability, systems of linear equations, matrices, geometric linear programming and an introduction to Markov chains. Prerequisite: Minimum ALEKS score of 30% or MAT 063 with a C or better. Competencies
 Solve linear equations and inequalities in one variable
 Determine if the sentence is linear
 Isolate the variable
 Change order when operating with a negative factor
 Describe the functions and functional notation
 Define a relation
 Define a function
 Determine the dependency relationship between the variables
 Use f(x) notation
 Graph linear equations and inequalities in two variables
 Describe the Cartesian coordinate system
 Determine the coordinates of sufficient points needed to draw the line of the equation
 Locate and indicate the proper halfplane for an inequality
 Write linear models for verbal problems
 Identify the quantities pertinent to the problem
 Identify extraneous information
 Label clearly the necessary constant and variable quantities
 Write a mathematical sentence that relates the necessary quantities
 Identify, when necessary, missing information
 Perform basic matrix operations
 Define a matrix and related terms
 State the conditions under which various operations may be performed
 Add, subtract, and multiply matrices when possible
 Invert a 2 x 2 or a 3 x 3 matrix, when possible
 Solve systems of linear equations by a variety of methods
 State the possible solutions and the conditions of their appearance for a linear system
 Graph the set of equations on one set of axes
 Use the ‘multiply and add’ method to determine the solution
 Apply row operations to an augmented matrix to determine the solution (GaussJordan method).
 Solve the system by applying matrix algebra
 Identify the feasible region and vertices for a set of linear constraints
 Graph each of the constraints on the same set of axes
 Indicate the intersection of all the halfplanes as a polygon
 Find the coordinates of the vertices of the polygon
 Solve linear programming problems
 Model the limited resource problem in terms of an objective function and a set of constraints
 Graph the constraints
 Apply the Corner Point Theorem
 Confirm the result for reasonableness
 Perform basic set operations, using correct notation
 Define a set and its related terms
 Determine the intersection and union of given sets
 Illustrate the intersection and union of sets with Venn diagrams
 Use set notation to describe a Venn diagram
 Solve counting problems using the multiplication principles
 State the Fundamental Counting Principle
 Determine if a problem is a permutation or a combination
 State the relationship between combinations, Pascal’s triangle, and the binomial coefficients
 Use correctly combination and permutation notations
 Calculate factorials
 Write the sample space and specific events of an experiment
 Define sample space and event
 Distinguish between continuous and discrete outcomes
 Describe a trial of an event
 Write a clear description of an event of interest
 Evaluate the probabilities of basic problems such as dice, cards, coins, and balls
 Define the probability of an event
 Apply the addition rule for combined probabilities
 Apply the multiplication rule for combined probabilities
 Determine if events are mutually exclusive
 Calculate conditional probabilities by various methods
 Calculate conditional probability by formula
 Calculate conditional probability by probability trees
 Determine if events are independent
 Calculate probabilities by Bayes’ formula
 State characteristic properties of probability distributions
 Create a probability distribution form a frequency distribution table
 Create a probability distribution graph
 Relate the area under a probability distribution graph to the probability of an event
 State the random variable of the probability distribution
 Calculate the mean, median, mode, and standard deviation of the random variable
 Calculate the probabilities of events by means of known probability distributions
 Apply Chebychev’s Theorem
 Find the probabilities of events based on normally distributed random variables
 Estimate the probabilities of binomial events by means of a normal distribution
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