### CCOG for MTH 105 Winter 2024

- Course Number:
- MTH 105
- Course Title:
- Math in Society (MTH105=MTH105Z)
- Credit Hours:
- 4
- Lecture Hours:
- 30
- Lecture/Lab Hours:
- 20
- Lab Hours:
- 0

#### Course Description

#### Addendum to Course Description

Math in Society is a rigorous mathematics course designed for students in Liberal Arts and Humanities majors. The course provides a solid foundation in quantitative reasoning, symbolic reasoning, and problem solving techniques needed to be a productive, contributing citizen in the 21st century.

#### Intended Outcomes for the course

Upon completion of the course students should be able to:

1. Employ mathematical reasoning skills when reading complex problems requiring quantitative or symbolic analysis and demonstrate versatility in the consideration and selection of solution strategies.

2. Demonstrate proficiency in the use of mathematical symbols, techniques, and computation that contribute to the exploration of applications of mathematics.

3. Use appropriate mathematical structures and processes to make decisions and solve problems in the contexts of logical reasoning, probability, data, statistics, and financial mathematics.

4. Use appropriate representations and language to effectively communicate and interpret quantitative results and mathematical processes orally and in writing.

5. Demonstrate mathematical habits of mind by determining the reasonableness and implications of mathematical methods, solutions, and approximations in context.

#### Quantitative Reasoning

Students completing an associate degree at Portland Community College will be able to analyze questions or problems that impact the community and/or environment using quantitative information.

#### General education philosophy statement

Mathematics and Statistics courses help students gain tools to analyze and solve problems using numerical and abstract reasoning. Students will develop their abilities to reason quantitatively by working with numbers, operations, and relations and to reason qualitatively by analyzing patterns and making generalizations.

#### 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

- Must include both:
- At least one individual or group project culminating in a written report and/or oral presentation
- One (or more) individual, proctored, closed-book examination(s) worth at least 25% of the final grade.

- Additionally, at least two of the following additional measures:
- Examinations and/or quizzes (group or individual)
- Projects
- Worksheets/graded homework
- Online homework
- Group or individual activities
- Portfolios

- Optional additional assessment strategies may include, but are not limited to
- Individual student conference
- Discussions
- Participation

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

**COURSE CONTENT:**

- Statistics
- Define and identify populations and samples
- Define and identify sampling methods and bias
- Find and interpret common measures of center and spread
- Graph data using technology
- Interpret graphical displays of data
- Interpret margin of error in the context of polls
- Recognize the misuse of data

- Probability
- Define probability and basic terminology
- Calculating and interpret basic empirical probabilities
- Calculate and interpret basic theoretical probabilities
- Calculate and interpret expected value

- Financial Literacy
- Personal budgeting
- Simple and compound interest savings
- Savings and investment plans
- Loans and credit cards
- Income tax

- Problem Solving and Logical Reasoning
- Logic rules in everyday language
- Set (Venn) diagrams
- Contingency tables
- Proportional reasoning

- Suggested optional topics. May cover up to 25% of class time
- Logical Arguments
- Fallacies
- Correlation and Regression
- Normal Models
- Voting Methods
- Apportionment
- Fair Division
- Voting Theory
- Exponential Growth/Decay Models
- Logistic Growth Models
- Game Theory
- Queuing Theory
- Coding/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
- Sequences and Series
- Fermi Approximations
- Historical Numbers