MTH 1301 - Ideas in Mathematics
Tentative Course Outline
- SOCIAL CHOICE
- The Mathematics of Elections: The Paradoxes of Democracy
- The Basic Elements of an Election
- The Plurality Method
- The Borda Count Method
- The Plurality-with-Elimination Method
- The Method of Pairwise Comparisons
- Fairness Criteria and Arrow's Impossibility Theorem
- The Mathematics of Power: Weighted Voting
- An Introduction to Weighted Voting
- Banzhaf Power
- Shapley-Shubik Power
- Subsets and Permutations
- The Mathematics of Sharing: Fair-Division Games
- Fair-Division Games
- The Divider-Chooser Method
- The Lone-Divider Method
- The Lone-Chooser Method
- The Method of Sealed Bids
- The Method of Markers
- The Mathematics of Apportionment: Making the Rounds
- Apportionment Problems and Apportionment Methods
- Hamilton's Method
- Jefferson's Method
- Adams's and Webster's Methods
- The Huntington-Hill Method
- The Quota Rule and Apportionment Paradoxes
- MANAGEMENT SCIENCE
- The Mathematics of Scheduling: Chasing the Critical Path
- An Introduction to Scheduling
- Directed Graphs
- Priority-List Scheduling
- The Decreasing-Time Algorithm
- Critical Paths and the Critical-Path Algorithm
- GROWTH
- Population Growth Models: There Is Strength in Numbers
- Sequences and Population Sequences
- The Linear Growth Model
- The Exponential Growth Model
- The Logistic Growth Model
- Financial Mathematics: Money Matters
- Percentages
- Simple Interest
- Compound Interest
- Consumer Debt
- SHAPE AND FORM
- Fibonacci Numbers and the Golden Ratio: Tales of Rabbits and Gnomons
- Fibonacci Numbers
- The Golden Ratio
- Gnomons
- Spiral Growth in Nature
- STATISTICS
- Censuses, Surveys, Polls, and Studies: The Joys of Collecting Data
- Enumeration
- Measurement
- Cause and Effect
- Graphs, Charts, and Numbers: The Data Show and Tell
- Graphs and Charts
- Means, Medians, and Percentiles
- Ranges and Standard Deviations
- Probabilities, Odds, and Expectations: Measuring Uncertainty and Risk
- Sample Spaces and Events
- The Multiplication Rule, Permutations, and Combinations
- Probabilities and Odds
- Expectations
- Measuring Risk
- The Mathematics of Normality: The Call of the Bell
- Approximately Normal Data Sets
- Normal Curves and Normal Distributions
- Modeling Approximately Normal Distributions
- Normality in Random Events
