Math 1332: College
Mathematics
Lecture Notes
Following are browsable web pages representing my class notes for
the chapters
to be covered from our book, Excursions in Modern Mathematics, 6th
Edition
, by Peter Tannenbaum (before viewing, please read the
note
).
To see some web-based enrichment materials, link to the
textbook home page
, click on your book and then "Jump to" which will let you select a
chapter. There's some really great stuff (like warm-ups and
practice quizzes) there!
Chapter 1: The Mathematics of
Voting
| Section |
|
| 1.1 |
Preference Ballots and Preference Schedules |
| 1.2 |
The Plurality Method |
| 1.3 |
The Borda Count Method |
| 1.4 |
The Plurality-with-Elimination Method |
| 1.5 |
The Method of Pairwise Comparisons |
| Summary |
Four Methods and Four Fairness Criteria |
| 1.6 |
Rankings |
| 1.7 |
Conclusion: Fairness and Arrow's Impossibility Theorem |
Chapter 2: Weighted Voting
Systems
| Section |
|
| 2.1 |
Weighted Voting Systems |
| 2.2 |
The Banzhaf Power Index |
| 2.3 |
Applications of the Banzhaf Power Index |
| 2.4 |
The Shapley-Shubik Power Index |
| 2.5 |
Applications of the Shapley-Shubik Power Index |
Chapter 5: Euler Circuits
| Section |
|
| 5.1 |
Routing Problems |
| 5.2-5.3 |
Graphs
Graph Concepts and Terminology |
| 5.4 |
Graph Models |
| 5.5 |
Euler's Theorems |
| 5.6 |
Fleury's Algorithm |
| 5.7 |
Eulerizing Graphs |
| 5.8 |
Conclusion |
Chapter 6: The
Traveling-Salesman
Problem
| Section |
|
| 6.1 |
Hamilton Circuits and Hamilton Paths |
| 6.2 |
Complete Graphs |
| 6.3-6.5a |
Traveling-Salesman Problems
The Brute-force Algorithm |
| 6.6 |
Approximate Algorithms |
| 6.5b |
The Nearest-Neighbor Algorithm |
| 6.7 |
The Repetitive Nearest-Neighbor Algorithm |
| 6.8 |
The Cheapest-Link Algorithm |
Chapter 9: Spiral Growth in
Nature
| Section |
|
| 9.1 |
Fibonacci Numbers |
| 9.2 |
The Equation x2 = x + 1 and the
Golden Ratio |
| 9.3 |
Gnomons |
| 9.4 |
Spiral (almost gnomonic) Growth in Nature
|
Chapter 10: The Mathematics of
Population
Growth
| Section |
|
| 10.1 |
The Dynamics of Population Growth |
| 10.2 |
The Linear Growth Model |
| 10.3a |
Growth Rates, Growth Multipliers, and Compound Interest |
| 10.3b |
Non-annual Rates and Annual Yield |
| 10.4 |
The Logistic Growth Model |
Chapter 12:
Fractal Geometry
Chapter
13: Collecting
Statistical
Data
| Section |
|
| 13.1 |
The Population |
| CS1 |
Case Study 1: The 1990 U.S. Census |
| 13.2 |
Surveys |
| CS2 |
Case Study 2: The 1936 Literary Digest Poll |
| CS3 |
Case Study 3: The 1948 Presidential Election |
| 13.3 |
Random Sampling |
| CS4 |
Case Study 4: Modern Public Opinion Polls: Stratified
Samples |
| 13.4 |
Sampling: Terminology and Key Concepts |
13.5
|
The Capture-Recapture Method
|
| 13.6 |
Clinical Studies |
| CS5 |
Case Study 5: The Alar Scare |
| CS6 |
Case Study 6: The 1954 Salk Polio Vaccine Field
Trials |
Chapter 15:
Chances, Probability,
and Odds
| Section |
|
| 15.1 |
Random Experiments and Sample Spaces |
| 15.2 |
Counting: The Multiplication Rule |
| 15.3 |
Permutations and Combinations |
| 15.4a |
Probability and Probability Spaces
|
| 15.4b |
Events |
| 15.5 |
Equiprobable Spaces
|
| 15.6 |
Odds |
| 15.s |
Summary |
Note: these lessons were written for Netscape
Navigator
for Windows. Their appearance may not be acceptable when
viewed using other browsers or platforms other than the
PC. I
am unable to check all my pages for all combinations of browsers and
platforms. If you run across viewing problems, please let me
know
and I will attempt to fix them. E-mail me: