## Course Content and Outcome Guide for MTH 105 Effective Winter 2016

- Course Number:
- MTH 105
- Course Title:
- Math in Society
- Credit Hours:
- 4
- Lecture Hours:
- 30
- Lecture/Lab Hours:
- 20
- Lab Hours:
- 0
- Special Fee:

#### Course Description

Explores concepts and applications of logic rules, basic probability and statistics as well as personal finance models. Investigates problem solving techniques (algebraic and nonalgebraic) as well as some nontraditional mathematics topics such as social choice or discrete mathematics. Integrates technology where appropriate. The PCC Mathematics Department recommends that students take MTH courses in consecutive terms. Prerequisites: (MTH 95 or MTH 98) and placement into WR 121. Audit available.#### Addendum to Course Description

This class is a terminal course, thus it does not directly support other courses in mathematics and other disciplines. As such, students wishing to take MTH 112 must still take MTH 111. The course serves the purpose of exploring mathematical ideas/concepts that can support a variety of disciplines. This course should be rigorous in that it challenges student to contemplate, understand, and synthesize mathematical concepts. The students should be able to communicate their understanding in a variety of ways. Instructors are encouraged to use technology to enhance the learning experience.

#### Intended Outcomes for the course

Upon completion of the course students should be able to:

- Use formulas and perform relevant calculations pertaining to personal finance in order to make informed financial decisions
- Make and interpret calculations and graphical displays of numerical data in order to perceive and infer patterns within data sets
- Calculate and interpret theoretical and empirical probabilities in support of making predictions and decisions in the presence of uncertainty
- Use logical reasoning to describe and critique arguments and recognize common logical fallacies
- Support conclusions using logical thought, reflection, explanation and justification
- Use appropriate representations to effectively communicate, orally and in writing, quantitative results and mathematical processes

#### Course Activities and Design

All activities will follow the premise that formal definitions and procedures evolve from the investigation of practical problems. It is the goal of this class that the investigation of practical problems will drive a desire to learn the mathematics necessary to understand and explain the practical application. In-class time is primarily activity/discussion emphasizing problem solving techniques. Activities will include group work.

#### Outcome Assessment Strategies

- At least one individual or group project culminating in a written report and/or an oral presentation.
- In-class exam: proctored, closed book examination
- At least two of the following additional measures:
- Take-home examinations
- In-class exams
- Graded homework
- Quizzes
- In-class activities
- Portfolios

- Optional Additional Assessment Strategies
- Individual student conference
- Attendance

#### Course Content (Themes, Concepts, Issues and Skills)

**COURSE CONTENT:**

- Logical Reasoning and Problem Solving (roughly 10-20% of the course)
- Describing and Critiquing Arguments
- Understanding the Language and Rules of Logic
- Recognizing Common Logical Fallacies
- Non-Algebraic Problem Solving Strategies

- Probability and Statistics (roughly 30% of the course)
- Counting Rules
- Calculating and Interpreting Basic Probabilities
- Expected Value (e.g., Lotteries, Raffles)
- Measures of Central Tendencies and Spread
- Interpreting Graphical Displays of Data
- Understanding Margin of Error and Polls
- Interpreting Distributions
- Recognizing the Misuse of Data

- Financial Literacy (roughly 20% of the course)
- Percent Sales and Income Tax
- Simple and Compound Interest
- Annuities
- Loans and Credit Cards

- Additional Math Topics - At least one of the following topics should be covered in some depth (roughly 30% of the course)
- Apportionment
- Fair Division
- Voting Theory
- Exponential Growth/Decay Models
- Logistic Growth Models
- Game Theory
- Queuing Theory
- Coding/ Code Checking (Error coding)/ Code Breaking/Cryptography
- Set Theory
- Counting techniques Combinations, Permutations
- Boolean Algebra
- Graph Theory
- Fractal Geometry
- Non-Euclidian Geometry
- Tilings
- Symmetry and Shapes in Nature
- Math in Art
- Math in Music
- Cryptography
- Sequences and Series
- Fermi Approximations
- Historical Numbers
- Proportional Reasoning
- Scheduling