Course Learning Outcomes

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The textbook content, assignments, and assessments for Mathematics for Liberal Arts are aligned to the following learning outcomes:

Module 1: Historical Counting Systems

  • Explore the counting and number system used by the Inca
  • Become familiar with the evolution of our current counting method
  • Convert between Hindu-Arabic and Roman Numerals
  • Become familiar with the history of positional number systems
  • Identify bases that have been used in number systems historically
  • Convert numbers between bases other than 10
  • Use two different methods for converting numbers between bases

Module 2: General Problem Solving

  • 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 to calculate area
  • Solve problems using basic geometry to calculate volume
  • Proportions, similar triangles, ratios applied to geometric problems
  • Define and implement a “solution pathway” for solving mathematical problems
  • Calculate sales tax, property tax
  • Calculate flat tax, progressive tax, and regressive tax

Module 3: 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.
  • 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 4: 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
  • 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
  • Define an Euler path, and an Euler circuit
  • Use Fleury’s algorithm to determine whether a graph has an Euler circuit

Module 5: Fractals

  • Generate a fractal with random variation
  • Calculate Fractal Dimension using scaling relation
  • 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 6: Theory and Logic

  • 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
  • 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
  • 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 7: Voting Theory

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

Module 8: Growth Models

  • 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
  • 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 9: Finance

  • 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
  • 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 10: Statistics: Collecting Data

  • 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 11: 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 12: Probability

  • 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
  • Compute a conditional probability for an event
  • Use Baye’s theorem to compute a conditional probability
  • Calculate the expected value of an event