College of DuPage FY Fall/17
ACTIVE COURSE FILE
Fall 2017 Only
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 where applicable:
Designed primarily for students planning to major in business, or the behavioral, social, or biological sciences. Topics include sets, counting techniques, probability, modeling, systems of linear equations and inequalities, matrix algebra, linear programming, Markov chains, and game theory. Applications are presented from business and the above 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 or a qualifying A.C.T. math sub-score
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. Recognize 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:
a. Addition, subtraction, and multiplication
b. Inverses
c. Solution of a linear system using matrix inverses
d. Applications, including the Leontief input/output model
4. Linear programming
a. Graphical method
b. Simplex method
5. Sets, Venn diagrams, and counting techniques
6. Basic probability (including independence, conditional probability, and Bayes' theorem)
7. Regular and absorbing Markov chains
8. Applications of probability, such as expected value, decision making, linear regression, and Bernoulli trials (binomial probability)
9. Introduction to game theory
10. Additional Topics - At least 4 hours should be spent on topics chosen from below:
a. Linear regression
b. Cryptography
c. Graph theory
d. Non-linear models
e. Logic and/or Boolean algebra
C. Methods of Evaluating Students:
1. Unit tests at appropriate intervals; quizzes, homework, projects, and a comprehensive final examination, all at the discretion of the instructor
______
Initiator Date Division Dean Date
Sponsor Date
Topical Outline
Suggested
Time in Hours
I. Linear functions and models 4
II. Solution of a linear system by matrix reduction 4
III. Matrix methods
A. Addition, subtraction, multiplication 2
B. Inverses 1
C. Solution of linear system using inverses 1
D. Applications including Leontief model 2
IV. Linear programming 10
V. Sets, Venn diagrams and counting techniques 6
VI. Basic probability including independence, conditional probability and Bayes’ Theorem 10
VII. Regular and absorbing Markov chains 4
VIII. Applications of probability, such as expected value, decision making, linear regression and Bernoulli trials (binomial probability). 4
IX. Introduction to game theory 2
X. 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 algebra 4
XI. Review and Testing 8
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 least four hours of additional material should also be covered.
Chapter 1: Sections 1.2 – 1.4 (Sections 1.1 and 1.5 are optional) You may choose 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 be used. 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-82 or TI-83 graphics 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.