AA/AS Degree



|AA/AS Degree | | |MODESTO JUNIOR COLLEGE |Date Originally Submitted: |4/28/1998 |

|Non-Degree | | |COURSE OUTLINE |Date Updated: |2/17/2004 |

|Noncredit | | | |

|I. |DIVISION: |Science, Mathematics, and Engineering |DIV./DEPT. NO: |51/2500 |

| |PREFIX/NO.: |MATH 130   |COURSE TITLE: |Finite Mathematics |

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| |Formerly listed as: |      | Date Changed: |      |

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|II. |ALSO OFFERED AS: | |

| |Div: | |Prefix/No.: |            |Title: |      |

| |Div: | |Prefix/No.: |            |Title: |      |

| | |

|III. |COURSE INFORMATION: |

| |Units: 3 or Variable Units: X=1/2 unit A=1 unit B=2 units C=3 units D=4 units |

| |Total Hours: Lecture: 52.50 Lab:       Other:       |

| |Explain Other hours:       |

| |Transfer Credit: CSU – UC – CAN – MATH 12 |

| |General Ed: AA/AS Area: CSU GE Area: IGETC Area: |

| |Offered Only: Fall – Spring – Summer – Eve – Not offered every semester – |

| |

|IV. |PREREQUISITE(S)/COREQUISITE(S)/RECOMMENDED FOR SUCCESS: |

| |(Please check all that apply and list below. Also attach appropriate documentation forms) |

| |Prerequisite (P) – Corequisite (C) – Recommended for Success (R) – Limitation on Enrollment (L) – |

| |Satisfactory completion of MATH 90 or qualification by MJC assessment process |

|V. |CATALOG DESCRIPTION: |

| |Set theory, probability and counting techniques, Markov chains, matrices and linear systems, linear programming, |

| |applications to business and behavioral and social sciences. |

|VI. |FIELD TRIPS REQUIRED? |Yes | |No | |Maybe | |

| |

|VII. |GRADING: |A-F Only | |CR/NC Only | |CR/NC Option | |Non-Graded | |

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|VIII. |REPEAT PROCEDURES: |Credit: |No | |*Yes | |Maximum Completions: |   |Maximum Units: |    |

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| | |Non-Credit: |No | |Yes | |Maximum Completions: |   |

| |*(If course is repeatable, attach a memo with the appropriate justification)       |

|IX. |EXPLAIN FEE REQUIRED: |      |

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PREREQUISITE SKILLS

Before entering the course, the student will be able to:

A. graph lines and find the equation of a line, given sufficient information.

B. effectively use function notation to describe mathematical relationships.

C. determine the domain and range of a given function.

D. given a relation between two variables, determine if the relation is a function.

E. graph linear, quadratic, absolute value, and simple cubic functions using transformations.

F. solve systems of linear equations in two or three variables by choosing the most effective method for the given problem.

G. solve linear, quadratic, absolute value, and rational inequalities.

H. solve quadratic equations with real and complex solutions by completing the square and using the quadratic formula.

I. graph quadratic functions by determining and using the vertex and stretching constant.

J. add, subtract, multiply, and divide complex numbers.

K. convert radicals to rational exponents and vice versa.

L. add, subtract, multiply, divide, or compose two given functions.

M. find the inverse of a given function.

N. graph exponential and logarithmic functions using transformations.

O. solve exponential and logarithmic equations.

P. simplify expressions using the properties of logarithms.

Q. identify the equations for and sketch the graphs of conic sections.

R. list a requisite number of terms of a given arithmetic, geometric, or recursive sequence.

S. determine the general term of a given arithmetic or geometric sequence.

T. determine the sum of a fixed number of terms of an arithmetic or geometric series, and determine the sum of an infinite geometric series when it exists.

U. solve problems involving permutations, combinations, and probability.

V. given an applied problem, analyze the problem, select an appropriate mathematical model, and use that model to solve the problem. Models used include: linear, quadratic, exponential, logarithmic, systems, and conic sections.

OBJECTIVES (Expected outcomes for students)

Upon successful completion of the course, the student will be able to:

A. Perform matrix operations including addition, subtraction, scalar multiplication, transpose, and matrix multiplication.

B. Find the multiplicative inverse of a square matrix by using Gaussian Elimination.

C. Solve a system of linear equations by using the inverse of the coefficient matrix.

D. Write a linear programming problem in algebraic form (define the variables, write the constraints and objective function).

E. Solve a linear programming problem by graphing (graph, determine the vertex locations, and determine the maximum and minimum values of an objective function).

F. Solve a maximum linear programming problem by using the Simplex Method.

G. Convert minimum or mixed constraint linear programming problems to standard maximum form and solve by the Simplex Method.

H. Write the dual of a linear programming problem and solve the dual by the Simplex Method.

I. Solve the primal system by using the dual.

J. Use sensitivity analysis to analyze the benefits of changing available resources.

K. Perform set operations including union, intersection, and complement.

L. Graph sets and set operations on Venn Diagrams.

M. Apply the Fundamental Counting Principle, permutations, and combinations to various combinatorics problems.

N. Use the Binomial Theorem in counting problems (optional).

O. Calculate the probabilities of events using various combinatorics methods.

P. Find the probabilities of events using unions, intersections, complements, and conditional probabilities.

Q. Determine if events are independent.

R. Represent events and their associated probabilities using tree diagrams.

S. Apply Baye’s Theorem to solving probability problems.

T. Calculate probabilities using binominal trials.

U. Find the expected value of a probability distribution.

V. Write the distribution matrix and the transition matrix for a Markov Process problem.

W. Calculate stable distribution matrix (optional).

X. Use linear regression to determine the best fit line to data points (optional).

Y. Solve applications problems specific to each method in A-X above.

CONTENT

A. Matrices

1. Gaussian Elimination

2. Arithmetic

3. Multiplicative inverse

4. Markov Processes

5. Simplex Method

6. Applications

B. Linear Programming

1. Algebric form

2. Geometric solution

3. Simplex method

a. Maximization

b. Minimization

c. Mixed constraints

4. Dual method

a. Maximization

b. Minimization

c. Mixed constraints

5. Applications

C. Sets

1. Operations

2. Subsets

3. Venn Diagrams

4. Applications

D. Probability

1. Fundamental Counting Principle, permutations, combinations

2. Probability trees

3. Independence

4. Conditional probability

5. Formulas using union, intersection and complement

6. Baye’s Theorem

7. Binomial Trails

8. Expected value

9. Applications

E. Markov Processes

1. Distribution matrix

2. Transition matrix

3. Stable distribution matrix

4. Applications

TEACHING METHODS

A. Methods to achieve course objectives:

1. Lectures which develop theoretical material

2. Demonstrations of mathematical techniques, applications, and problem-solving strategies by both instructor and students

3. Applications of material to specific problems

4. Computer and calculator demonstrations

B. Typical assignments used in achieving learner independence and critical thinking:

Homework assignments and/or in-class exercises require students to analyze a given problem, select an appropriate procedure to solve the problem, apply the procedure, and evaluate the adequacy of both the result of the procedure and the procedure itself.

TEXTBOOKS AND OTHER READINGS (Typical)

A. Required texts:

Goldstein, Larry J., Schneider, David I., Siegel, Martha J.; Finite Mathematics and Its Applications, 8th Edition, April 2003, Prentice Hall

B. Other readings:

SPECIAL STUDENT MATERIALS (i.e., protective eyewear, aprons, etc.)

METHODS OF EVALUATING STUDENT PROGRESS

A. Tests and quizzes at regular intervals throughout the semester

B. Assigned homework

C. Final examination

All of the above requires students to:

A. demonstrate skill in performing mathematical techniques.

B. demonstrate knowledge of mathematical vocabulary.

C. Solve problems by identifying the question and the given information, selecting an appropriate procedure for solution, applying the procedure, and assessing the validity of the solution and the procedure.

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