# MTH 1301 - Ideas in Mathematics

Text:

*Excursions in Modern Mathematics*,
2nd Custom edition for Baylor University – Pearson, 2014 - by Peter Tannenbaum

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