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May 19th

May 19th

# COURSE SYLLABUS FOR Finite Mathematics

Prerequisites Math 131 with a grade of C.

Cata log Description

This course is de signed especially for students in areas such as business, economics, social science, and
non-physical sciences. It emphasizes the concepts and applications of mathematics rather than
mathematical structures. Topics include: vectors, matrix algebra , applications of matrices (including
solution of systems of linear equations), linear programming and the simplex method, set theory, logic,
Boolean Algebra, counting and probability, stochastic process, game theory, Markov Chains,
mathematical modeling, and the mathematics of finance.

Course Objectives: See attached.

STUDENT MATERIALS

A. Textbooks:

Title: Finite Mathematics, An Applied Approach, 8th edition, 1999.

Author: Mizrabi/Sullivan

Publisher: John Wiley & Sons

B. Other Required Materials

TI-83 Plus graphing calculator or its functional equivalent.

Other Course Requirements

N one

Grading policy is established by the individual instructor. A comprehensive final
examination will be given.

 Days Topic or Class Activity 3 Linear Equations 8 Matrices and Systems of Linear Equations 8 Linear Programming 6 Finance 7 Sets and Counting Techniques 11 Probability 7 Markov Chains and Game Theory 6 Logic 57

OBJECTIVES

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

1. De termine the slope and equations of a given line.
2. Find equations of parallel and perpendicular lines.
3. Construct linear models such as supply and demand functions.
4. Solve a system of m linear equations in n variable by getting reduced row echelon form of the
corresponding matrix (with and without graphing calculators).
5. Add, subtract, and multiply matrices .

6. Find the inverse (if it exists) of a given matrix by hand and on the graphing calculator.
7. Determine whether two given matrices are inverse of each other.
8. Solve systems of linear equations using the Matrix Inverse Method.
9. Use the Leontief model to solve problems involving an economy.
10. Set up the model for a linear programming problem.

11. Solve a linear programming problem in two variables geometrically.
12. Solve a linear programming problem using the Simplex method.
13. Solve linear programming problems in minimization using duality.
14. Solve linear programming problems with mixed constraints using two phase method.
15. Use the graphing calculator to solve linear programming problems.

16. Work problems involving simple interest.
17. Work problems involving interest compounded n times a year using the graphing calculator.
18. Find amounts of annuities and payments for sinking funds using the graphing calculator.
19. Find the present value of an annuity using the graphing calculator.
20. Apply combinations including permutations and combinations to model real -world problems.

21. Expand a binomial using the Binomial Theorem.
22. Construct a probability model by finding the sample space and appropriate probabilities for
outcomes.
23. Find the probability of a union of events and of the complement of an event.
24. Determine probabilities using counting technique.
25. Determine conditional probabilities.

26. Use the product rule for the probability of an intersection of events.
27. Determine whether two events are independent.
28. Use Bayes’ Formula to determine conditional probabilities in applied problems.
29. Determine probabilities using binomial models.

30. Find the expected value of a random variable and use it in real-world problems.
31. Define “Markov Chain.”
32. Determine probability distribution vectors after k stages using the kth power of the transition
matrix for a Markov chain.
33. Apply Markov models to real-world problems.
34. Determine whether a Markov chain is regular.

35. Recognize the long term behavior of regular Markov chain.
36. Use a graphing calculator to compute powers of a transition matrix and apply a resulting
equilibrium matrix to find the fixed vector of the matrix.
37. Determine whether a Markov chain is absorbing.
38. Analyze probabilities using the Fundamental Matrix of an Absorbing Markov Chain.
39. Write a game matrix for a two-person conflict.

40. Find the value of a strictly-determined, two-person, zero - sum game .
41. Find expected payoffs in mixed-strategy games.
42. Find optimal strategy and expected payoffs in two-person, zero-sum games by using formulas
and geometrically.
43. Define “conjunction,” “disjunction,” and “negation” and recognize the symbols used in symbolic
logic.
44. Construct truth tables for compound logical statements.

45. Determine whether logical propositions are equivalent.
46. Know the laws of logic in symbolic form including DeMorgan’s Laws.
47. State the converse, contrapositive, and inverse of the implication, p => q; and make the
respective truth tables.
48. Determine whether a compound proposition is a tautology.
49. Do direct and indirect proofs symbolically.
50. Determine whether arguments are valid.

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