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