 # Finite Mathematics

## COURSE DESCRIPTION:

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, methods of counting, probability, systems of linear equations, matrices, geometric linear programming, and an introduction to Markov chains.

## COURSE COMPETENCIES:

During this course, the student will be expected to:

1. Solve linear equations and inequalities in one variable.
1.1 Determine if the sentence is linear.
1.2 Isolate the variable.
1.3 Change order when operating with a negative factor.

2. Describe the functions and functional notation.
2.1 Define a relation.
2.2 Define a function.
2.3 Determine the dependency relationship between the variables.
2.4 Use f(x) notation.

3. Graph linear equations and inequalities in two variables.
3.1 Describe the Cartesian coordinate system.
3.2 Determine the coordinates of sufficient points needed to draw the line of the equation.
3.3 Locate and indicate the proper half- plane for an inequality .

4. Write linear models for verbal problems.
4.1 Identify the quantities pertinent to the problem.
4.2 Identify extraneous information.
4.3 Label clearly the necessary constant and variable quantities.
4.4 Write a mathematical sentence that relates the necessary quantities.
4.5 Identify, when necessary, missing information.

5. Perform basic matrix operations.
5.1 Define a matrix and related terms.
5.2 State the conditions under which various operations may be performed.
5.3 Add, subtract , and multiply matrices when possible.
5.4 Invert a 2 x 2 or a 3 x 3 matrix, when possible.

6. Solve systems of linear equations by a variety of methods.
6.1 State the possible solutions and the conditions of their appearance for a linear system.
6.2 Graph the set of equations on one set of axes.
6.3 Use the 'multiply and add' method to determine the solution.
6.4 Apply row operations to an augmented matrix to determine the solution (Gauss-Jordan method).
6.5 Solve the system by applying matrix algebra.

7. Identify the feasible region and vertices for a set of linear constraints.
7.1 Graph each of the constraints on the same set of axes.
7.2 Indicate the intersection of all the half-planes as a polygon.
7.3 Find the coordinates of the vertices of the polygon.

8. Solve linear programming problems.
8.1 Model the limited resource problem in terms of an objective function and a set of constraints.
8.2 Graph the constraints.
8.3 Apply the Corner Point Theorem.
8.4 Confirm the result for reasonableness.

9. Perform basic set operations, using correct notation.
9.1 Define a set and its related terms.
9.2 Determine the intersection and union of given sets.
9.3 Illustrate the intersection and union of sets with Venn diagrams.
9.4 Use set notation to describe a Venn diagram.

10. Solve counting problems using the multiplication principles.
10.1 State the Fundamental Counting Principle.
10.2 Determine if a problem is a permutation or a combination.
10.3 State the relationship between combinations, Pascal's triangle, and the binomial coefficients .
10.4 Use correctly combination and permutation notations.
10.5 Calculate factorials .

11. Write the sample space and specific events of an experiment.
11.1 Define sample space and event.
11.2 Distinguish between continuous and discrete outcomes.
11.3 Describe a trial of an event.
11.4 Write a clear description of an event of interest.

12. Evaluate the probabilities of basic problems such as dice, cards, coins, and balls.
12.1 Define the probability of an event.
12.2 Apply the addition rule for combined probabilities.
12.3 Apply the multiplication rule for combined probabilities.
12.4 Determine if events are mutually exclusive.

13. Calculate conditional probabilities by various methods.
13.1 Calculate conditional probability by formula .
13.2 Calculate conditional probability by probability trees.
13.3 Determine if events are independent.
13.4 Calculate probabilities by Bayes' formula.

14. State characteristic properties of probability distributions.
14.1 Create a probability distribution form a frequency distribution table.
14.2 Create a probability distribution graph.
14.3 Relate the area under a probability distribution graph to the probability of an event.
14.4 State the random variable of the probability distribution.
14.5 Calculate the mean, median, mode, and standard deviation of the random variable.

15. Calculate the probabilities of events by means of known probability distributions.
15.1 Apply Chebychev's Theorem.
15.2 Find the probabilities of events based on normally distributed random variables.
15.3 Estimate the probabilities of binomial events by means of a normal distribution.

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