7a. Prerequisite(s): (Course and/or other preparation/experience that is REQUIRED to be completed previous to enrollment in this course.)

Completion of Math. D or equivalent with a grade of "C" or better, or placement by matriculation assessment process

7b. Co-requisite(s):  (Courses and/or other preparation that is REQUIRED to be taken concurrently with this course.)

7c. Advisory: (Minimum preparation RECOMMENDED in order to be successful in this course.  Also known as “Course Advisory”.)

9b. Catalog Description:

Introduces students to the art and application of mathematics in the world around them. Topics include mathematical modeling, voting and apportionment, and mathematical reasoning with applications chosen from a variety of disciplines. Not recommended for students entering elementary school teaching or business.

10. Student Performance Outcomes: (Outcomes for all credit courses must indicate that students will learn critical thinking and will be able to apply concepts at college level.  Outcomes must be related to items listed in Section 11.)

a. Solve problems at a post-intermediate algebra level from a variety of different mathematical subject areas, especially topics not usually covered in a traditional mathematics course.
b. Analyze given information and develop strategies for solving problems involving mathematical and logical reasoning.
c. Recognize and apply the concepts of mathematics as a problem-solving tool in other disciplines and contexts.
d. Utilize linear, quadratic, exponential, and logarithmic equations, systems of equations, and their graphs to analyze mathematical applications from various disciplines.
e. Compare and contrast apportionment methods and voting systems, using an appropriate level of mathematics to support any conclusions.

11. Course Content Outline: (Provides a comprehensive, sequential outline of the course content, including all major subject matter and the specific body of knowledge covered.)

I. Mathematical Modeling
A. Applications of linear and quadratic functions and graphs, using tools such as regression lines, optimization, matrices, and linear programming
B. Exponential and logarithmic function applications such as growth and decay problems, logistic equations, business and financial applications, and resource analysis
C. Modeling with other mathematical tools and algorithms: applications such as symmetry, tilings, group theory, circuits, networks, and scheduling

II. Voting and Apportionment
A. Apportionment Methods
B. Voting systems
1. Mathematics of Voting systems
2. Weighted voting systems

III. Mathematical Reasoning: Development of mathematical reasoning through study of topics such as numeric and geometric patterns, sequences, probability and chance, and combinatorics

IV. Other Topics from Higher Mathematics:
A. Modular arithmetic and cryptology
B. Topics from pure mathematics such as logic, set theory, game theory, non-Euclidean and fractal geometry, and chaos theory

12. Typical Assignments: (List types of assignments, including library assignments.)

a. Reading Assignments: (Submit at least 2 examples)

1. Read selections in the textbook concerning the Fibonacci sequence. Come to class prepared to discuss the everyday places we find Fibonacci numbers and why they might occur in nature with others.

2. Read the selection in the textbook regarding Hamilton's and Jefferson's respective proposals for the first apportionment of the House of Representatives. Also, find and read "The Papers of Alexander Hamilton Vol XI" and "The Works of Thomas Jefferson Vol VI". Come to class prepared to discuss the absolute unfairness of each of these apportionment systems compared to the current Huntington-Hill method.

b. Writing, Problem Solving or Performance: (Submit at least 2 examples)

1. Explain, mathematically, the Alabama Paradox. (Alabama Paradox: In 1880, it was calculated that if the House of Representatives was increased from 299 members to 300 members, Alabama would lose one representative.)

2. Create a voting system with 4 members in which 1 person has veto power. Calculate the Banzhaf Power Index for the system using the text's "alternative definition". Compare this system to a voting system with 5 members in which one person equals one vote. Calculate the Banzhaf Power Index for this system and use it in your discussion.

3. Use the Division Algorithm to show that the remainder when a number n is divided by m is equal to the position n would be on a mod m clock.

4. Public Key Encryption: Using the 2 public numbers 7 and 143, encode the following string of numbers: "2 83 3 61 38".

5. A farming cooperative mixes two brands of cattle feed. Brand X costs $25 per bag and contains 2 units of nutritional element A, 2 units of nutritional element B, and 2 units of nutritional element C. Brand Y costs $20 per bag and contains 2 unit of nutritional element A, 9 units of nutritional element B, and 3 units of nutritional element C. The minimum requirements for nutrients A, B, and C are 12 units, 36 units and 24 units respectively. Find the number of bags of each brand that should be mixed to produce a mixture having a minimum cost per bag. What is the minimum cost per bag?

c. Other (Terms projects, research papers, portfolios, etc.)

SECTION D

SECTION E

SECTION F

SECTION G