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Study Guides

Mathematics for the Liberal Arts

Course Contents

Logical Fallacies in Common Language
Course Contents at a Glance
Putting It Together: Set Theory and Logic
Learning Outcomes
Assignment: Set Theory Problem Set

Faculty Resources

Discussion: Set Theory
Pacing
Discussion: Logic
Assignments
Assignment: Logic Writing Task

Module 1: Historical Counting Systems

Assignment: Logic Writing Task
Why It Matters: Historical Counting Systems
Assignment: Set Theory Problem Set
Introduction to Early Counting Systems

Module 7: Voting Theory

Entering Answers for Practice Problems
Why It Matters: Voting Theory
The Evolution of Counting and The Inca Counting System
Introduction to Preference Ballot Voting
The Hindu—Arabic Number System and Roman Numerals
Plurality Method
Introduction to Positional Systems and Bases
Instant Runoff Voting
The Positional System and Base 10
Borda Count
Another Method for Converting Between Bases
Copeland's Method
The Mayan Numeral System
Which Method is Fair?
Putting It Together: Historical Counting Systems
Introduction to Approval Voting
Discussion: Historical Counting Systems
Approval Voting
Assignment: Historical Counting Systems Writing Task
Voting in America
Assignment: Exploring The Abacus
Putting It Together: Voting Theory
Assignment: Historical Counting Systems Problem Set
Discussion: Voting Theory
Assignment: Exploring the Abacus
Assignment: Voting Theory Writing Task
Assignment: Historical Counting Systems Writing Task
Assignment: Electoral College Trouble
Assignment: Historical Counting Systems Problem Set
Assignment: Voting Theory Writing Task

Module 2: General Problem Solving

Assignment: Electoral College Trouble
Why It Matters: General Problem Solving

Module 8: Growth Models

Introduction to Proportional Relationships and a Bit of Geometry
Why It Matters: Growth Models
Percents
Introduction to Linear and Geometric Growth
Proportions and Rates
Linear (Algebraic) Growth
A Bit of Geometry
Exponential (Geometric) Growth
Introduction to Solving Problems With Math
Introduction to Logarithms and Logistic Growth
Problem Solving and Estimating
Solve Exponentials for Time: Logarithms
Taxes
Logistic Growth
Putting It Together: General Problem Solving
Putting It Together: Growth Models
Discussion: Problem Solving Application
Discussion: Growth Models
Discussion: Application of Geometry
Assignment: Growth Models Problem Set
Assignment: General Problem Solving Problem Set
Assignment: Growth Models Writing Task
Assignment: General Problem Solving Writing Task
Assignment: Average Daily Balance
Assignment: Geometry Writing Task, Part I
Assignment: Growth Models Problem Set
Assignment: Geometry Writing Task, Part II
Assignment: Growth Models Writing Task
Assignment: Multi-Step Written Problem
Assignment: Average Daily Balance
Assignment: General Problem Solving Problem Set

Module 9: Finance

Assignment: General Problem Solving Writing Task
Why It Matters: Finance
Assignment: Multi-Step Written Problem
Introduction to Simple and Compound Interest
Assignment: Geometry Writing Task, Part I
Simple Interest
Assignment: Geometry Writing Task, Part II
Compound Interest

Module 3: Measurement

Introduction to Annuities and Loans
Why It Matters: Measurement
Savings Annuities
Introduction to US Units of Measurement
Payout Annuities
Units of Length
Loans
Units of Weight
Which Formula to Use?
Units of Capacity
Putting It Together: Finance
Introduction to Systems and Scales of Measurement
Discussion: Finance
Metric System Basics
Assignment: Finance Problem Set
Applications of Metric Conversions
Assignment: Finance Writing Task
Temperature Scales
Assignment: Finance Problem Set
Putting It Together: Measurement
Assignment: Finance Writing Task
Assignment: Measurement Writing Task

Module 10: Statistics: Collecting Data

Assignment: Unit Conversion
Why It Matters: Collecting Data
Discussion: Measurement
Introduction to Data Collection Basics
Assignment: Unit Conversion
Populations and Samples
Assignment: Measurement Writing Task
Categorizing Data

Module 4: Graph Theory

Introduction to Sampling and Experimentation
Why It Matters: Graph Theory
Sampling Methods and Bias
Introduction to Graph Theory Basics
Experiments
Elements of Graph Theory
Putting It Together: Collecting Data
Shortest Path
Assignment: Collecting Data Problem Set
Introduction to Euler and Hamiltonian Paths and Circuits
Discussion: Collecting Data
Euler Circuits
Assignment: Collecting Data Problem Set
Hamiltonian Circuits

Module 11: Statistics: Describing Data

Putting It Together: Graph Theory
Why It Matters: Describing Data
Assignment: Graph Theory
Introduction to Representing Data Graphically
Assignment: Euler and Hamiltonian Circuits
Presenting Categorical Data Graphically
Discussion: Graph Theory
Presenting Quantitative Data Graphically
Assignment: Graph Theory
Introduction to Numerical Summaries of Data
Assignment: Euler and Hamiltonian Circuits
Measures of Central Tendency

Module 5: Fractals

Measures of Variation
Why It Matters: Fractals
Putting It Together: Describing Data
Introduction to Fractal Basics
Assignment: Describing Data Problem Set
Fractal Basics
Assignment: Describing Data Writing Task
Fractal Dimension
Discussion: Describing Data
Introduction to Fractals Generated by Complex Numbers
Assignment: Describing Data Problem Set
Arithmetic With Complex Numbers
Assignment: Describing Data Writing Task
Generating Fractals With Complex Numbers

Module 12: Probability

Putting It Together: Fractals
Why It Matters: Probability
Assignment: Fractals Problem Set
Introduction to Computing the Probability of an Event
Assignment: Fractals Generated With Positive Exponents
Basic Concepts
Discussion: Chaos
Types of Events
Assignment: Fractals Problem Set
Conditional Probability
Assignment: Fractals Generated With Positive Exponents
Introduction to Applications With Probability

Module 6: Set Theory and Logic

Bayes' Theorem
Why It Matters: Set Theory and Logic
Counting
Introduction to Set Theory Basics
Probability Using Permutations and Combinations
Introduction to Set Theory
Expected Value
Union, Intersection, and Complement
Putting It Together: Probability
Cardinality
Assignment: Probability Problem Set
Introduction to Logic Basics
Assignment: Probability Writing Task
Boolean Logic
Discussion: Probability
Truth Tables
Discuss: Final Reflection
DeMorgan's Laws
Assignment: Probability Problem Set
Introduction to Analyzing Arguments With Logic
Assignment: Probability Writing Task
Arguments