College of DuPage FY Fall/19

ACTIVE COURSE FILE

Beginning Spring 2018

Curricular Area: Mathematics Course Number: 1533

Course Title: Finite Mathematics

Semester Credit Hours: 4 Lecture Hours: 4 Lab Hours: 0 Clinical Hours: 0

This course is an IAI approved general education course: M1 906.

Changes from the present course must be accompanied by a yellow Course Revision or Deletion Form.

Course description to appear in catalog including prerequisite whereapplicable:

Students will be introduced to sets, counting techniques, probability, modeling, systems of linear equations and inequalities, matrix algebra, linear programming, Markov chains, and game theory. This course is intended for students planning to major in business, or the behavioral, social, or biological sciences.

Prerequisite:

Math 1428 (or college equivalent) with a grade of C or better or Math 1431 (or college equivalent) with a grade of C or better or a qualifying score on the mathematics placement test.

A. General Course Objectives:

Upon successful completion of the course the student should be able to do the following:

  1. Construct linear functions and models
  2. Solve linear systems by matrix reduction
  3. Calculate matrix sums, differences, products, and inverses
  4. Determine the maximum and minimum values of functions using techniques of linear programming, including the simplex method
  5. Identify intersections, unions, and complements of sets
  6. Construct Venn diagrams
  7. Compute permutations and combinations
  8. Calculate basic probabilities using independence, conditional probability, and Bayes' theorem
  9. Solve problems using Markov chains
  10. Use the basic principles of game theory
  11. Solve application problems of finite mathematics in the areas of business, behavioral, social, and biological sciences
  12. Use technology as an aid in problem solving

B.Topical Outline:

  1. Linear functions and models
  2. Solution of a linear system by matrix reduction
  3. Matrix methods:
  4. Addition, subtraction, and multiplication
  5. Inverses
  6. Solution of a linear system using matrix inverses
  7. Applications, including the Leontief input/output model
  8. Linear programming
  9. Graphical method
  10. Simplex method
  11. Sets, Venn diagrams, and counting techniques
  12. Basic probability (including independence, conditional probability, and Bayes' theorem)
  13. Regular and absorbing Markov chains
  14. Applications of probability, such as expected value, decision making, linear regression, and Bernoulli trials (binomial probability)
  15. Introduction to game theory
  16. Additional Topics - At least 4 hours should be spent on topics chosen from below:
  17. Linear regression
  18. Cryptography
  19. Graph theory
  20. Non-linear models
  21. Logic and/or Boolean algebra

C.Methods of Evaluating Students:

Students will be evaluatedby tests including a final examination. Other methods may includequizzes, homework and projects.

______

Initiator Date Division DeanDate

Sponsor Date

Topical Outline

Suggested

Time in Hours

  1. Linear functions and models4
  1. Solution of a linear system by matrix reduction4
  1. Matrix methods

A. Addition, subtraction, multiplication2

B. Inverses1

C. Solution of linear system using inverses1

D. Applications including Leontief model2

  1. Linear programming 10
  1. Sets, Venn diagrams and counting techniques6
  1. Basic probability including independence, conditional probability and Bayes’ Theorem 10
  1. Regular and absorbing Markov chains4
  1. Applications of probability, such as expected value, decision making, linear regression and Bernoulli trials (binomial probability). 4
  1. Introduction to game theory2
  1. Additional topics: At least 4 hours chosen from below

a. Linear regression

b. Cryptography

c. Graph theory

d. Non-linear models

e. Logic and/or Boolean algebra4

  1. Review and Testing8

Total Hours 62

Textbook for Math 1533

Title:Finite Mathematics for the Managerial, Life and Social Sciences/Twelfth edition

Author: Tan

Publisher: Cengage

Copyright: 2017

The following chapters and sections of the textbook should be covered. At leastfour hours of additional material should also be covered.

Chapter 1: Sections 1.2 – 1.4 (Sections 1.1 and 1.5 are optional)You maychoose to cover the method of least squares as an additional topic.

Chapter 2: Sections 2.1 – 2.7

Chapter 3: Sections 3.1 – 3.3 (Section 3.4 is optional)

Chapter 4: All sections. (This text uses the method of duality to solve standard minimization problems; an alternative method may beused. Artificial variables are not introduced in this text.)

Chapter 5: Omit

Chapter 6: All sections

Chapter 7: All sections

Chapter 8: You may choose to cover expected value and binomial distributions as an additional topic.

Chapter 9: All sections

Appendix A: Optional

Use of Technology in Math 1533

The use of either the TI-83 or TI-84 graphng calculator or computer software is required in this course. This technology should be used to improve the speed and accuracy of complicated calculations in realistic modeling once the concepts of the problem have been developed. Technology could be applied during coverage of any of the following topics:

1.determining equation of the least-squares line of best fit;

2.matrix operations

a.matrix arithmetic,

b.row operations,

c.matrix inverses;

3.solving linear systems

a.Gauss-Jordan method,

b.inverse-of-the-coefficient-matrix method,

c.applications such as the Leontief input-output model of an economy;

4.linear programming problems;

5.Markov chains; and

6.coding theory.

In all Mathematics courses, students with a documented learning disability that specifically requires a calculator as determined by Health Services, will be allowed to use a basic calculator for all test/quiz questions where arithmetic calculations are not the main objective. The specific disability must be verified with Health Services before the accommodation can be made.