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CCOG for MTH 105 Winter 2024

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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

Focuses on developing numeracy through the exploration of present-day applications of mathematics. Includes major topics such as quantitative reasoning and problem-solving strategies, probability and statistics, and financial mathematics; these topics are to be weighted approximately equally. Emphasizes mathematical literacy and communication, relevant everyday applications, and the appropriate use of current technology. This course is part of Oregon Common Course Numbering. MTH 105 and MTH 105Z are equivalent. The PCC Mathematics Department recommends that students take MTH courses in consecutive terms. Prerequisites: (MTH 95 or MTH 98) and (RD 115 and WR 115) or IRW 115 or equivalent placement. Audit available.

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

  1. Must include both:
    1. At least one individual or group project culminating in a written report and/or oral presentation
    2. One (or more) individual, proctored, closed-book examination(s) worth at least 25% of the final grade.  
  2. Additionally, at least two of the following additional measures:
    1. Examinations and/or quizzes (group or individual)
    2. Projects
    3. Worksheets/graded homework
    4. Online homework
    5. Group or individual activities
    6. Portfolios
  3. Optional additional assessment strategies may include, but are not limited to
    1. Individual student conference
    2. Discussions
    3. Participation

Course Content (Themes, Concepts, Issues and Skills)

COURSE CONTENT:

  1. Statistics
    1. Define and identify populations and samples
    2. Define and identify sampling methods and bias
    3. Find and interpret common measures of center and spread
    4. Graph data using technology
    5. Interpret graphical displays of data
    6. Interpret margin of error in the context of polls
    7. Recognize the misuse of data
  2. Probability
    1. Define probability and basic terminology
    2. Calculating and interpret basic empirical probabilities
    3. Calculate and interpret basic theoretical probabilities
    4. Calculate and interpret expected value
  3. Financial Literacy
    1. Personal budgeting
    2. Simple and compound interest savings
    3. Savings and investment plans
    4. Loans and credit cards
    5. Income tax 
  4. Problem Solving and Logical Reasoning
    1. Logic rules in everyday language
    2. Set (Venn) diagrams
    3. Contingency tables
    4. Proportional reasoning
  5. Suggested optional topics. May cover up to 25% of class time
    1. Logical Arguments
    2. Fallacies
    3. Correlation and Regression
    4. Normal Models
    5. Voting Methods
    6. Apportionment
    7. Fair Division
    8. Voting Theory
    9. Exponential Growth/Decay Models
    10. Logistic Growth Models
    11. Game Theory
    12. Queuing Theory
    13. Coding/Cryptography
    14. Set Theory
    15. Counting techniques – Combinations, Permutations
    16. Boolean Algebra
    17. Graph Theory
    18. Fractal Geometry
    19. Non-Euclidian Geometry
    20. Tilings
    21. Symmetry and Shapes in Nature
    22. Math in Art
    23. Math in Music
    24. Sequences and Series
    25. Fermi Approximations
    26. Historical Numbers