Course Outline for Mathematics 44
Mathematics for Democracy

Effective: Fall 2024
SLO Rev:
Measurable Objectives:
Upon completion of this course, the student should be able to:
  1. describe a distribution using measures of central tendency and measures of variations;
  2. solve an applied problem that has a normal distribution;
  3. calculate the mean, median, mode, variance and standard deviation for a given data set;
  4. identify the standard methods of obtaining data and identify advantages and disadvantages of each;
  5. identify the sample(s) and population(s) in a data set description;
  6. describe the basic principles of experimental design;
  7. construct and interpret confidence intervals based on corresponding levels of confidence;
  8. describe the difference between the margin of error and the credibility index in polling;
  9. identify mutually exclusive and independent events;
  10. compute probabilities;
  11. calculate probabilities of various independent or dependent events;
  12. strategize how to address a problem using various problem-solving techniques;
  13. translate a statement into a sybolic statement;
  14. use truth tables for validating rules of inference;
  15. apply problem-solving techniques to identify the best voting method for a given situation;
  16. apply the concepts of statistics to understand current polling;
  17. apply logic and problem-solving techniques to identify the ideal voting method for a given context;
Course Content:
  1. Statistics
    1. Tables, charts and graphs
    2. Measures of central tendency
    3. Measures of variation
    4. Normal distribution
    5. Applications
    6. Experimental design
    7. Sampling methods
    8. Polling
  2. Probability
    1. Basics of probability
    2. Combinatorics and probability
    3. Expected value
  3. Logic
    1. Translation of statements into symbolic statements
    2. Truth Tables
    3. Rules of inference
    4. Inductive vs deductive reasoning
    5. Proofs
  4. Problem-solving
    1. Mathematical discovery
    2. Logic and axiomatic thinking
    3. Inductive thinking
    4. Patterns in data
    5. Mathematical experimentation
    6. Construction of Models
    7. Game theory
    8. Strategy
  5. Applications: math in the democratic process
    1. Polling
    2. Voting Theory
    3. Apportionment
    4. Redistricting
Methods of Instruction:
  1. Lecture/Discussion
  2. Group Activities
  3. Written assignments
  4. Hands-on Activities
  5. Class and group discussions
  6. Distance Education
Assignments and Methods of Evaluating Student Progress:
  1. Exercises from the textbook such as the following: Suppose state A has a population of 935,000 and five representatives, whereas state B has a population of 2,343,000 and 11 representatives. Determine which state is poorly represented, and calculate the absolute unfairness for this assignment of representatives. Determine the relative unfairness for this apportionment.
  2. Exercises from the textbook such as the following: The heights of 5-year old girls in the U.S. are normally distributed with a mean of 42.56 inches and a standard deviation of 1.573 inches. 68.27% of 5-year old girls have heights between ______ inches and ______ inches.
  3. Using the given map of a district, determine the scores under the Harris, Polsby-Popper, Reock, Convex Hull, and sum of perimeters methods. Which score indicates that the district might have been gerrymandered? (A map was provided.)
  4. What is the benefit of the Borda count method over the plurality method?
  5. Using the given map with 60% of the precincts for party A and 40% of the precincts for party B, create a gerrymandered redistricting so that party B earns a majority of the representatives. Can you construct a gerrymandered redistricting which will award party A 100% of the representatives? (A map was provided.)
  1. Homework
  2. Quizzes
  3. Class Participation
  4. Exams/Tests
  5. Final Examination or Project
Upon the completion of this course, the student should be able to:
  1. critically analyze mathematical problems using a logical methodology;
  2. communicate mathematical ideas, understand definitions, and interpret concepts;
  3. increase confidence in understanding mathematical concepts, communicating ideas and thinking analytically.
Textbooks (Typical):
  1. Poitrast, Gail (2021). Math for Our World Granite State College https://granite.pressbooks.pub/math502/.
  2. Lee et al., Portland Community College Math Department (2018). Math in Society: Mathematics for Liberal Arts Majors (1.0/e). Portland Community College Math Department https://spot.pcc.edu/math/mathinsociety/.
  3. Lippman, David (2022). Math in Society (2.6/e). Pierce College http://www.opentextbookstore.com/mathinsociety/.
  1. Duchin, Moon, et al (2022). Political Geometry: Rethinking Redistricting in the US with Math, Law, and Everything In Between (1st Edition). Birkhauser.
  2. Lippman, David (2022). Math in Society (2.6). Pierce College.
  • Scientific Calculator
Abbreviated Class Schedule Description:
An introductory study of the mathematics for the Liberal Arts student. Core topics include statistics, probability, logic and proofs, and problem-solving. Applications of these topics will be found in current and historical political processes; examples include statistical analysis of sampling and interpretation of polling, the logical structure of various voting methods, solving the problems arising from the paradoxes with apportionment, and using the geometry of compactness for redistricting.
Prerequisite: MTH 55 or MTH 53 or an appropriate skill level demonstrated through the mathematics assessment process..
Discipline:
Mathematics*