El Camino College - Division of Mathematical Sciences

Math 140
Finite Mathematics for Business and Social Sciences
4 units; 4 hours lecture

Catalog Description Course Objectives and Methods of Evaluation
Outline of Subject Matter Planned Instructional Activities

Grading Method: Letter

Associate Degree Credit --- Transfers to CSU and Transfers to UC

Prerequisite: Mathematics 70 with a minimum grade of C or qualification by testing (El Camino College Mathematics Placement Test) and assessment.

Catalog Description:
  This course consists of a study of equations, matrices, linear programming (a geometric approach), sets, counting, probability, probability distributions, statistics, Markov chains, and game theory.
Note: Math 140 was formerly numbered Mathematics 4.

Course Objectives and Methods of Evaluation:

  1. Course objectives (list the major objectives stated as student outcomes in behaviorally measurable terms.)
    1. Graph linear functions.
    2. Use linear functions to model problems from the business and social sciences.
    3. Solve a system of linear equations by: comparison, substitution, elimination, and the Gauss-Jordan technique.
    4. Add, scalar multiply, and multiply matrices.
    5. Find the inverse of a matrix.
    6. Graph linear inequalities in two variables.
    7. Use the graphical method of linear programming to maximize and minimize linear functions subject to a set of constraints.
    8. Find the union, intersection, and complement of sets.
    9. Count the number of elements in a finite set using the multiplication principle, permutations, and combinations.
    10. Find the probability of a given event.
    11. Find the expected value of a random variable.
    12. Computer the mean, the variance, and the standard deviation for a given set of data.
    13. Computer probabilities for binomial random variables directly using the standard normal approximation.
    14. Computer probabilities for normal random variables using the standard normal tables.
    15. Write a transition matrix for a Markov chain and find the steady state vector for this matrix.
    16. Find the transition matrix for a Markov chain after k-transitions and interpret the results.
    17. Find the optimal strategies and payoff for a two-person, zero sum matrix game that is strictly determined and for a matrix game that has mixed strategies.
  1. Methods of Evaluation - Associate Degree Credit Course
    1. Substantial writing assignments are inappropriate for this degree applicable course because:
      1. The course primarily involves skill demonstrations or problem solving.
    2. Computational or non-computational problem-solving demonstrations, including:
      1. Exam
      2. Quizzes
      3. Homework problems

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Outline of Subject Matter
 

Approximate Time

Major Topic

8 hours

I. Applications of Linear Functions

  1. The Cartesian Plane and Graphing
  2. Equations of Straight Lines
  3. Linear Modeling
  4. Two Lines: Relating the Geometry to the Equations

8 hours

II. Systems of Linear Equations

  1. Linear Systems as Mathematical Models
  2. Linear Systems Having One or No Solutions
  3. Linear Systems Having Many Solutions

6 hours

III. Matrices

  1. Matrix Addition and Application
  2. Matrix Multiplication and Applications
  3. The Inverse of a Matrix
  4. More Applications of Inverses

6 hours

IV.  Linear Programming

  1. Modeling Linear Programming Problems
  2. Linear Inequalities in Two Variables
  3. Solving Linear Programming Problems Graphically

12 hours

V. Logic, Sets, and Counting Techniques

  1. Logic
  2. Sets
  3. Applications of Venn Diagrams
  4. The Multiplication Principle
  5. Permutations
  6. Combinations
  7. Other techniques including combinations of all the previous ones
12 hours VI. Probability
  1. Equally Likely Outcomes
  2. Outcomes with Unequal Probability; Odds
  3. Discrete Random Variables and Expected Value
  4. Addition Rules for Probability; Mutually Exclusive Events
  5. Conditional Probability
  6. Multiplication Rules for Probability: Independent Events
  7. Bayes' Theorem
  8. Binomial Experiments
8 hours VII. Statistics
  1. Organizing Data: Frequency Distributions
  2. Measures of Central Tendency
  3. Measuring the Dispersion of Data
  4. Continuous Random Variables and the Normal Distribution
  5. The Normal Approximation to the Binomial Distribution
4 hours VIII. Markov Chains
  1. Combining Matrices with Probability: The Transition Matrix
  2. Regular Markov Chains
4 hours IX. An Introduction to Game Theory
  1. Strictly Determined Games
  2. The Expected Value of Games with Mixed-Strategies
  3. Solving Mixed-Strategy Games

 4 hours

Examinations

Note: Included in each unit above was one hour of review and one hour of testing

Total: 72 Hours

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Planned Instructional Activities:

Lecture, discussion, individual assistance, calculator activities, computer aided instruction

Entrance Skills and Knowledge:

List the required skills and/or knowledge without which a student would be highly unlikely to receive a grade of A, B, C, or Credit (or for Health and Safety, would endanger self or others) in the Target Course.

  1. Solve linear equations at the Intermediate Algebra level.
  2. Evaluate linear functions at the Intermediate Algebra level.
  3. Graph linear functions at the Intermediate Algebra level.
  4. Find the slope-intercept and general forms of equations of lines given two points or a point and the slope at the Intermediate Algebra level.
  5. Solve systems of linear equations by the graphical, substitution, and elimination methods at the Intermediate Algebra level.
  6. Solve and graph linear inequalities and systems of linear inequalities at the Intermediate Algebra level.
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Source of information: Course Outline of Record dated February, 1999


 Last Updated On: 4/20/06