Course Outline for Mathematics 47S
Mathematics for Liberal Arts with Support

Effective: Fall 2019
SLO Rev: 09/13/2018
Catalog Description:

MTH 47S - Mathematics for Liberal Arts with Support

3.50 Units

An introductory study of several mathematical topics. Use of mathematics to make informed decisions in different areas of daily life such as finance and politics. Topics include logic, voting, apportionment, probability, statistics, finance, and graph theory. This course is equivalent to MTH 47 with additional lab hours for students who did not place directly into MTH 47 or for students who place directly into MTH 47 but desire additional instruction.
Prerequisite: MTH 55 or MTH 55B or MTH 53 or MTH 53B or an appropriate placement through the Mathematics Placement process.
1701.00 - Mathematics, General
Letter Grade Only
Type Units Inside of Class Hours Outside of Class Hours Total Student Learning Hours
Lecture 3.00 54.00 108.00 162.00
Laboratory 0.50 36.00 0.00 36.00
Total 3.50 90.00 108.00 198.00
Measurable Objectives:
Upon completion of this course, the student should be able to:
  1. determine the validity of an argument by using truth tables;
  2. solve applied problems involving annuities, sinking funds and amortization;
  3. compare the future value for simple interest and compound interest, including different compounding periods;
  4. determine which method of computing financial charges minimizes the total financial charges on a particular loan and/or credit card;
  5. apply a given voting method to determine the election result when given a description of the voting method and the preferences of a small population of voters;
  6. prepare an argument for or against changing from majority voting to another voting method;
  7. determine the critical voters in a winning coalition given a weighted voting system;
  8. explain how the fairness criterion is violated when given the outcome of a voting method that violates one of the fairness criteria;
  9. apply a given apportionment method to determine the apportionment when given the relevant information about the distribution of the population and the total number of representatives;
  10. determine the absolute and relative unfairness of a given apportionment;
  11. explain the paradox or violation of the quota rule when given the outcome of an apportionment method that has a paradox or violation and describe how it leads to controversy;
  12. diagram a connected graph, determine the degree of each vertex and determine whether the graph contains an Euler path or circuit when given the description of a connected graph;
  13. apply an algorithm to find an Euler path or circuit in a connected graph;
  14. determine whether a sequence is a Hamilton circuit when given a graph and a sequence vertices;
  15. solve the traveling salesperson problem when given a small weighted graph, using a) the brute force algorithm and b) the nearest neighbor algorithm;
  16. use graph theory to create a schedule that satisfies certain criteria;
  17. determine the probability that a specified event will occur;
  18. find the conditional probability of an event;
  19. use expected values to solve application problems;
  20. determine and create the appropriate table, chart and/or graph to present data;
  21. describe a distribution using measures of central tendency and measures of variations;
  22. solve an applied problem that has a normal distribution.
Course Content:
  1. Reflect on Study Skills
    1. Grit and Growth Mindset
      1. How Learning Math is Different
      2. Resources On and Off Campus
      3. Time Management
      4. How to Be an Effective Listener and Take Notes
      5. How to Approach Homework
      6. How to Study for an Exam
      7. Overcoming Math and Test Anxiet
      8. Review
    1. Geometry
      1. Area
      2. Perimeter
    2. Algebra
      1. Graphing Bivariate Data
      2. Linear Regression
  2. Logic
    1. Venn diagrams
    2. Statements
      1. Simple and compound statements
      2. Tautology
      3. Self-contradiction statements
      4. Negation
      5. Converse
      6. Inverse 
      7. Contrapositive
    3. Connectives
    4. Symbolic notation
    5. Validity of an agruement
      1. Common arguement forms
      2. Truth tables
      3. Euler Diagrams
  3. Voting 
    1. Methods
      1. Borda Count
      2. Plurality with elimination
      3. Pairwise comparison
      4. Preference ballot
      5. Approval voting
    2. Fairness Criteria for Voting Methods
      1. Majority Criterion
      2. Condorcet's Criterion
      3. Independence-of-irrelevant alternatives criterion
      4. Monotonicity Criterion
    3. Arrow's Impossibility Theorem
    4. Weighted Voting Systems
      1. Weights and Quotas
      2. Coalitions
      3. Banzhaf Power Index
    5. Applications
  4. Apportionment
    1. Methods
      1. Standard divisors and quotas
      2. Modified divisors and quotas
      3. Hamilton's Method
      4. Jefferson's Method
      5. Adam's Method
      6. Webster's Method
      7. Huntington-Hill Method
    2. Paradoxes and Violations
      1. Population paradox
      2. Alabama paradox
      3. New-states paradox
      4. The quota rule
      5. Absolute and relative unfairness
    3. Applications
  5. Finance
    1. Simple Interest and Compound Interest
    2. Future Value and Present Value
    3. Annuities, Sinking Funds and Amoritization
    4. Applications
      1. Credit card statements
      2. Consumer loans
  6. Graph Theory
    1. Basic Concepts
      1. Walks, paths, circuits
      2. Complete graphs
      3. Connected graphs
    2. Special Graphs
      1. Euler circuits
      2. Hamilton circuits
      3. Trees
    3. Graph Algorithms
      1. Fleury
      2. Nearest Neighbor
      3. Brute Force
      4. Kruskal
    4. Applications
      1. Traveling Salesman Problem
      2. Scheduling
  7. Probability
    1. Basics of probability
    2. Conditional probility
    3. Expected Value
    4. Applications
  8. Statistics
    1. Tables, charts and graphs
    2. Measures of central tendency
    3. Measures of variation
    4. Normal distribution
    5. Applications
Methods of Instruction:
  1. Lecture/Discussion
  2. Problem Solving
  3. Presentation of audio-visual materials
  4. Group Activities
  5. Class and group discussions
Assignments and Methods of Evaluating Student Progress:
  1. Exercises from the textbook such as the following. Campus Life must schedule weekly meeting times for the six organizations listed below in such a way that organizations with members in common meet at different times. Use graph coloring to determine the least number of different meeting times and to decide which organizations should meet at the same time. (A table was given.)
  2. 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.
  3. 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.
  4. What is the benefit of the Borda count method over the plurality method?
  1. Homework
  2. Quizzes
  3. Projects
  4. Exams/Tests
  5. Class Participation
  6. Class Work
  7. Final Examination
Upon the completion of this course, the student should be able to:
  1. Analyze mathematical problems critically 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. Miller/Heeren/Hornsby/Hereen (2016). Mathematical Ideas (13th). Pearson.
  2. Pirnot (2014). Mathematics All Around (5th). Pearson.
  • Scientific calculator
Abbreviated Class Schedule Description:
An introductory study of several mathematical topics. Use of mathematics to make informed decisions in different areas of daily life such as finance and politics. Topics include logic, voting, apportionment, probability, statistics, finance, and graph theory. This course is equivalent to MTH 47 with additional lab hours for students who did not place directly into MTH 47 or for students who place directly into MTH 47 but desire additional instruction.
Prerequisite: MTH 55 or MTH 55B or MTH 53 or MTH 53B or an appropriate placement through the Mathematics Placement process.
Discipline:
Mathematics*