You should be able to do each of the following objectives after completing the corresponding chapter.

Chapter 1 - Voting Methods

• Use a preference schedule to find the winner of an election using the plurality, Borda count, plurality-with-elimination, and pairwise comparison methods.
• State what each of the four fairness criteria says.
  
• Explain why a voting method fails to satisfy one of the fairness criteria when given an example.
• Find a ranking of the candidates in an election using the extended plurality, Borda count, plurality-with-elimination, and pairwise comparison methods and the recursive pluality method.
  
• Explain the meaning and importance of Arrow's Impossibility Theorem.
  

Chapter 2 - Weighted Voting Systems

• Interpret and correctly use the notation for weights, players, and the quota.
• Identify players who are dictators, have veto power, or are dummies in a given weighted voting system.
• List all winning coalitions and identify all critical players in those winning coalitions.
• Compute the Banzhaf power distribution of a weighted voting system.
• Compute the total number of coalitions in a system with n players.
• List all sequential coalitions and identify all pivotal players in those coalitions.
• Compute the Shapley-Shubik power distribution of a weighted voting system.
• Compute the total number of sequential coalitions in a system with n players.

Chapter 13 - Collecting Statistical Data

• Identify the target population and N-value, sampling frame, sample, and sample size from a description of a survey.
  
• Distinguish between quota sampling and stratified sampling.
• Identify features of a survey that would produce sample bias and suggest features that would minimize sample bias.
• Distinguish between a statistic and a parameter.
  
• Compute response rate, sampling rate, and sampling error when given sufficient information.
• Attribute sampling error to chance or sample bias based on a reasonable description of a survey.
• Use the capture-recapture method to estimate the size of a population.
• Identify and evaluate various design aspects of a clinical study.
  

Chapter 14 - Describing Data

• Build frequency tables, bar graphs, pie charts, and histograms from a given data set.
• Interpret information given in a frequency table, bar graph, pie chart, or histogram.
• Convert between frequencies and relative frequencies using knowledge of percents.
• Compute the average or mean, median, and first and third quartiles from a given data set.
• Create and interpret a box and whisker plot.
• Compute range, interquartile range, and, for very simple data sets, the standard deviation.
• Use the meaning of the standard deviation to reason about a given data set without computing.

Chapter 15 - Chances, Probabilities, and Odds

• Distinguish when order matters in listing the possible outcomes in the sample space for a random experiment.
  
• List the possible outcomes in the sample space for a random experiment.
• Apply the multiplication rule to count the numbers of possible outcomes in a sample space without listing them.
• Count numbers of ways to select r different objects from n objects when order matters and when it does not using permutations and combinations.
• List the outcomes in an event described in words.
• List a probability assignment for a sample space if given enough information about it.
• Compute the probability of an event when all outcomes are equally likely.

• Know the basic properties of a normal distribution, including:
  
• symmetry,
  
• the fact that median=mean=center,
• the relationship between the points of inflection and standard deviation, 
• the relationship between the quartiles and the mean and standard deviation, and
• the 68-95-99.7 percent rule.
  
• Use these basic properties of a normal distribution to compute various values given enough other values (in written or picture form) from the following list: mean, standard deviation, location of inflection points, quartiles, and percents or amounts of data in certain locations.  (See exercises A, C, and D for examples of what this means.)
  
• Compute various values given enough other values from the following list: data value, standardized score, mean, and standard deviation.  (See exercises B for examples of what this means.)

Chapter 9 - Spiral Growth in Nature

• Perform calculations involving Fibonacci numbers and numbers defined by similar recursive rules.
• Compute Fibonacci numbers using Binet's formula and a calculator.
• Know what the golden ratio is and ways that it arises, including as the ratio of successive large Fibonacci numbers.
• Know what a gnomon is and  evaluate when a given shape has a gnomon.
  
• Use similarity to solve for unknown lengths, including when these are related to gnomons.
• Decide when a rectangle is a golden rectangle.
• Know how Fibonacci rectangles are related to golden rectangles, spirals, and spiral growth.

Chapter 10 - Mathematics of Population Growth

• Use both the recursive and explicit description of the linear growth model.
• Add the terms in an arithmetic sequence using the formula on page 402.
• Use both the recursive and explicit description of the exponential growth model.
• Calculate amounts using the general compounding formula.
• Distinguish between linear and exponential growth.

• List all of the types of basic rigid motions of the plane and identify which are proper (orientation preserving) and which are improper (orientation reversing).
  
• Given two figures related by reflection, find the axis of reflection, and given an axis of reflection, reflect a figure.
• Given two figures related by rotation, find the rotocenter, and given a rotocenter, direction, and number of degrees, rotate a figure.
• Given two figures related by translation, find the vector of translation, and given a vector, translate a figure.
• Given two figures related by glide reflection, find the axis of reflection and vector of translation, and given an axis and a vector, glide reflect a figure.
• List all the reflection and rotation symmetries of a figure.
• Identify the symmetry type of a figure as Z_N or D_N or D_infinity.
• List the five platonic solids and give their numbers of vertices, edges, and faces.

• Give examples of routing problems.
• List vertices, edges, degrees for a given graph.
• Given vertices and edges of a graph, draw a figure to represent the graph.
• Identify when two figures represent the same graph.
• Give or identify examples and non-examples of adjacent vertices, adjacent edges, paths and Euler paths, circuits and Euler circuits, bridges, and connected and disconnected graphs.
• Convert a simple real-life routing problem into an abstract graph.
• Use Euler's Theorems 1-3 to determine whether or not a graph has an Euler path or Euler circuit.
• For graphs that do have Euler circuits or Euler paths, be able to find them by trial and error and by Fleury's algorithm.
• Provide eulerizations and optimal eulerizations of graphs that do not have an Euler circuit.