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