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