MAT 111 - Math for Liberal Arts

Unit Objectives:

Outcome 1:    Analyze information objectives using logic and set theory.
     Task 1: Describe a set using set-building notation.
     Task 2: Determine whether two sets are equivalent.
     Task 3: Determine the subsets of a given set.    
     Task 4: Use Venn diagrams to represent one, two, and three sets.
     Task 5: Use Venn diagrams to visualize set relationships.
     Task 6: Represent unions, intersections, and complements using Venn diagrams.
     Task 7: Use Venn diagrams to answer questions about a survey.
     Task 8: Identify English sentences that are statements.
     Task 9: Express statements using logic symbols.
     Task 10: Express the negation of a statement.
     Task 11: Express compound statements into symbolic form.
     Task 12: Use truth tables to determine the conditions necessary for a statement to be considered true.
     Task 13: Use De Morgan’s laws to determine equivalent statements.
     Task 14: Construct truth tables for biconditional statements.
     Task 15: Use truth tables to show that two statements are equivalent.
     Task 16: Write the converse, inverse, and contrapositive of a statement.
     Task 17: Use truth tables to determine validity.
     Task 18: Use forms of valid arguments to draw logical conclusions.

Outcome 2:    Differentiate between various loans and investments.
     Task 1: Calculate sale prices and discounts.
     Task 2: Create a budget.
     Task 3: Calculate simple and compound interest.
     Task 4: Calculate the principle necessary to earn a specific future value in a compound interest account.    
     Task 5: Calculate payments and future values of annuity accounts.
     Task 6: Calculate monthly payments.

Outcome 3:    Apply geometric principles to solve problems.
     Task 1: Solve problems involving angles formed by parallel lines and transversals.
     Task 2: Solve problems involving triangles.
     Task 3: Use Pythagorean’s Theorem to solve problems involving right triangles.
     Task 4: Identify polygons and use their properties to solve problems.
     Task 5: Calculate the area and circumference of geometric figures.
     Task 6: Calculate the volume of three-dimensional figures.
    
Outcome 4:    Apply probability and statistics to make decisions.
     Task 1: Use the fundamental counting principle, permutations, and combinations to determine the number of outcomes for an event and to determine the probability of an event.
     Task 2: Calculate the probability of the union and intersection of two events.
     Task 3: Calculate conditional probabilities.
     Task 4: Compute the expected value of a game.
     Task 5: Determine the mean, median, mode, standard deviation, and boxplot of data set.
     Task 6: Recognize characteristics of a normal distribution and use them to make comparisons.
     Task 7: Create a scatter plot and use it to interpret and analyze data.
     Task 8: Determine a sample’s correlation coefficient.
    
Outcome 5:     Analyze various voting and apportionment rules.
     Task 1: Identify voting counting methods: majority, plurality, plurality with elimination, Borda Count, and pairwise comparison.
     Task 2: Use various counting methods to determine the winner of a vote.
     Task 3: Determine the fairness of a vote based on the Condorcet, majority criterion, monotonicity, and irrelevant alternatives criteria.
     Task 4: Use apportionment methods to divide resources.
     Task 5: Identify players and outcomes of a weighted voting system.