Content Overview

Course Materials	YES	NO
OHM Questions?	X
Editable Text?	X
Video Support?	X – embedded in text
Written Assessments/ Test?	X
Workbook?		X

Text

Math in Society , edited by David Lippman, Pierce College Ft Steilacoom.  Development of this book was supported, in part, by the Transition Math Project and the Open Course Library Project. Topics covered in the course include problem solving, voting theory, graph theory, growth models, finance, data collection and description, and probability.  Student learning outcomes include:

Topic Overview

This course is delivered in 11 modules including the following topics:

Module 1: Historical Counting Systems

• Explore the counting and number system used by the Inca
• Identify numbers represented by a Quipu
• Recount the importance of the development of a positional numeration system and describe its implications for our current numeration system
• Describe the development and use of different number bases
• Convert a number from base 10 to another base
• Identify and write numbers using the two numeration systems developed by the Mayans

Module 2: General Problem Solving

• Solve problems involving percents, proportions, and rates.
  • Describing quantities and how they change
  • Write an equivalent fraction or decimal given a percent
  • Find a percent of a whole
  • Calculate absolute and relative change given two quantities
  • Express a relationship as a rate
  • Write a proportion equation given two rates or ratios, solve the proportion equation
  • Determine when two quantities don’t scale proportionally, or more information is needed to determine whether they do

  Solve problems using basic geometry

  • Area
  • Volume
  • Proportions, similar triangles, ratios applied to geometric problems

  Use mathematical problem solving and estimation techniques.

  • Define and implement a “solution pathway” for solving mathematical problems
  • Calculate sales tax, property tax
  • Calculate flat tax, progressive tax, and regressive tax

Module 2: Measurement

• Units of Measurement
  • Define units of length, weight, and capacity and convert from one to another.
  • Perform arithmetic calculations on units of length, weight, and capacity.
  • Solve application problems involving units of length, weight, and capacity.

  Systems and scales of measurement

  • Describe the general relationship between the U.S. customary units and metric units of length, weight/mass, and volume.
  • Define the metric prefixes and use them to perform basic conversions among metric units.
  • Solve application problems involving metric units of length, mass, and volume.
  • State the freezing and boiling points of water on the Celsius and Fahrenheit temperature scales.
  • Convert from one temperature scale to the other, using conversion formulas.

Module 3: Graph Theory

• Elements of Graph Theory
  • Define and use the elements of a graph to optimize paths through the graph
  • Identify the number of vertices and edges on a graph
  • Determine whether a graph is connected
  • Define the degree of a vertex of a graph
  • Determine the difference between a path and a circuit

  Shortest Path

  • Use Dijkstra’s algorithm to find the shortest path between two vertices
  • Given a table of driving times between cities, find the shortest path between two cities

  Euler Paths

  • Define an Euler path, and an Euler circuit
  • Use Fleury’s algorithm to determine whether a graph has an Euler circuit

Module 4: Fractals

Generate fractals given an initiator and generation rule

• Generate a fractal with random variation
• Calculate Fractal Dimension using scaling relation

Complex Numbers

• Identify and make arithmetic calculations with imaginary numbers
• Plot complex numbers on the complex plane
• Define a recursive sequence that will generate a fractal in the complex plane
• Determine whether a complex number is part of the Mandlebrot set

Module 4: Set Theory and Logic

• Organize Sets and Use Sets to Describe Relationships
  • Describe memberships of sets, including the empty set, using proper notation, and decide whether given items are members and determine the cardinality of a given set
  • Perform the operations of union, intersection, complement, and difference on sets using proper notation
  • Describe the relations between sets regarding membership, equality, subset, and proper subset, using proper notation
  • Be able to draw and interpret Venn diagrams of set relations and operations and use Venn diagrams to solve problems
  • Recognize when set theory is applicable to real-life situations, solve real-life problems, and communicate real-life problems and solutions to others

  Introduction to Logic

  • Combine sets using Boolean logic, using proper notations
  • Use statements and conditionals to write and interpret expressions
  • Use a truth table to interpret complex statements or conditionals
  • Write truth tables given a logical implication, and it’s related statements – converse, inverse, and contrapositive
  • Determine whether two statements are logically equivalent
  • Use DeMorgan’s laws to define logical equivalences of a statement

  Analyzing Arguments With Logic

  • Discern between an inductive argument and a deductive argument
  • Evaluate deductive arguments
  • Analyze arguments with Venn diagrams and truth tables
  • Use logical inference to infer whether a statement is true
  • Identify logical fallacies in common language including appeal to ignorance, appeal to authority, appeal to consequence, false dilemma, circular reasoning, post hoc, correlation implies causation, and straw man arguments

Module 6: Voting Theory

• Preference Ballot Voting
  • Given the results of a preference ballot, determine the winner of an election using the plurality method
  • Identify flaws in the plurality voting method
  • Identify situations that may lead to insincere voting
  • Given the results of a preference ballot, determine the winner of an election using the instant runoff voting method
  • Identify situations when the instant runoff voting method produces a violation of the Condorcet Winner
  • Given the results of a preference ballot, determine the winner of an election using the Borda Count
  • Identify situations where the Borda count violates the fairness criterion
  • Given the results of a preference ballot, determine the winner of an election using Copeland’s method
  • Identify situations where Copeland’s method violates the independence of irrelevant alternatives criterion

  Approval Voting

  • Given the results of an approval ballot determine the winner of an election
  • Identify how approval voting can violate the majority criterion

Module 7: Growth Models

• Linear and Geometric Growth
  • Build a recursive equation that models linear or exponential growth
  • Build an explicit equation that models linear or exponential growth
  • Make predictions using linear and exponential growth models

  Logarithms and Logistic Growth

  • Use logarithms to solve exponential growth models for time
  • Identify the carrying capacity and growth rate of the logistic growth model
  • Use the logistic growth model to make predictions

Module 8: Finance

• Simple and Compound Interest
  • Calculate future value and payments for savings annuities problems
  • Calculate present value and payments for payout annuities problems
  • Calculate present value and payments for loans problems
• Annuities and Loans
  • Determine the appropriate financial formula to use given a scenario by recognizing key words and examining frequency of deposits or withdrawals, and whether account is growing or decreasing in value
  • Analyze a home mortgage refinance scenario, forming judgments by combining calculations and opinion
  • Solve a financial application for time using logarithms

Module 9: Statistics: Collecting Data

• Data Collection
  • Define the population and the parameters of a study
  • Discern between a census and a population
  • Define the sample and statistics of a study
  • Classify data as categorical or quantitative
  • Identify an appropriate sample for a study
  • Identify possible sources of sampling bias
  • Identify different techniques for sampling data

Module 10: Statistics: Describing Data

• Present categorical data graphically using a frequency table, bar graph, Pareto chart, pie charts, pictograms
• Present quantitative data graphically using histograms, frequency tables, pie charts, or frequency polygons
• Define the measures of central tendency for a sample of data including mean, median, mode
• Define measures of variation of a sample of data including range, standard deviation, quartiles, box plots

Module 11: Probability

• Computing the Probability of an Event
  • Describe a sample space and simple and compound events in it using standard notation
  • Calculate the probability of an event using standard notation
  • Calculate the probability of two independent events using standard notation
  • Recognize when two events are mutually exclusive
  • Calculate a conditional probability using standard notation
• Applications With Probability
  • Compute a conditional probability for an event
  • Use Baye’s theorem to compute a conditional probability
  • Calculate the expected value of an event

Length: One semester

Delivery: This course has been taught face to face, and online.

Below is a detail of a problem set. You can view them here, enter “guest” for the username, no password necessary. Problem sets include a formative pre-test, a set of questions that align to each page of text, and an end of chapter quiz.